A Bibliography of Publications in American Mathematical Monthly: 1980–1989

Nelson H. F. Beebe University of Utah

Department of Mathematics, 110 LCB

155 S 1400 E RM 233 Salt Lake City, UT 84112-0090

USA

Tel: +1 801 581 5254 FAX: +1 801 581 4148

E-mail: beebe@math.utah.edu, beebe@acm.org,
beebe@computer.org (Internet)
WWW URL: https://www.math.utah.edu/~beebe/

02 November 2023 Version 1.20

Title word cross-reference

#12355 [100]. #5375 [454]. #7672 [640].

(BA^{2}B)^{1/2} ≥ B^{2} [716]. 1 [752]. 21 − 6 = 15 [481]. 2 × 2 [291]. 3x + 1 [625, 388]. 8 [305]. > 1 [606]. [0, 1]^{ω} [47]. a = b [584]. a^{r+s} ≡ a^{r} (mod m) [100, 3]. A_{5} [666, 422, 421, 332]. AB − BA = I [637]. A ≥ B ≥ 0 [716]. a (mod p) ≤ b (mod p) [584]. AX − XB = C [368]. C [301, 606]. C(R) [540, 616]. C^{∗} ≈ S^{1} [266]. C^{∞} [302]. cos f(x) = f(sin x) [490]. e [561]. E^{3} [24]. E^{n} [113]. e^{x} [45]. exp(∑_{k=0}^{∞} a_{k}z^{k}) [347]. f [542]. f(f(z)) = az^{2} + bz + c [31]. γ [627]. i^{2} + 1 = 0 [657]. J [733]. k [502, 476, 93, 61]. L^{p}(μ) [268]. L^{p}(μ) ⊂ L^{q}(μ) [444]. L^{q}(μ)

[268]. n [748, 48, 781, 531, 136, 719, 772, 396, 649, 93, 219, 61, 600]. ∇f(x) = 0 [542]. n × n [553]. p [460, 584, 17]. π [821, 684, 561]. π^{4} [517]. P ≠ NP [262]. R [319]. R^{2} [307]. R^{3} [310, 736]. ρ = 0 [487]. ρ^{2} + ρ + 1 = 0 [657]. S^{1} [305]. S^{3} [305]. S_{6} [229]. sin x/x [13]. ∑ 1/p [52]. ∑_{n=1}^{∞} 1/n^{2} = π^{2}/6 [620]. T^{n+1}x − T^{n}x → 0 [95]. φ [299]. |r| [487]. |x| [250, 726]. x [542]. x′ = Ax [424]. X^{2} + 7 = 2^{n} [574]. x^{2} + y^{m} = z^{2n} [683]. x^{2} + y^{m} = z^{2n} [813]. xyz = x + y + z = 1 [248]. Z_{m} [339]. Z_{m}[i] [657]. Z_{m}[ρ] [657]. Z_{n} [339]. Z_{n}[i] [657]. Z_{n}[ρ], [657].

-adic [460, 17]. -function [299]. -rings [733]. -set [93]. -shuffles [502]. -subsets [93]. -tuplets [649].

01019a [8]. 05016a [512]. 05122a [343]. 05139a [485].

16 [139].

29 [454].

32 [640]. 33005a [770].

57 [100].

61 [139]. 64 [559].

7 [454]. 72 [640].

80e [146, 188]. 80f [8]. 81b [432]. 81m [172]. 83g [818]. 84c [454]. 84h [513]. 84k [361]. 85 [100, 146, 188, 8]. 85a [405]. 85c [463]. 85h [422, 413, 421]. 85i [343]. 86-2 [567]. 86c [532]. 86m [533]. 87 [432, 172]. 87e [512, 816]. 87i [616]. 87j [485]. 88b [639, 615]. 88j [729]. 89 [818]. 89b [750]. 89c [815, 729]. 89d [711]. 89e [745]. 89f [813]. 89g [814]. 89i [712]. 89m [817].

90 [454, 343, 513, 361]. 90c [769, 771]. 90e [770, 812]. 91 [405, 422, 463, 413, 421]. 92 [532, 512, 533, 485]. 93 [816, 616]. 94 [639, 815, 615, 729, 750, 641]. 95 [814, 813, 769, 711, 712, 745, 817, 772]. 96 [771, 770, 812].

a.e [658]. Abel [149]. abelian [621, 323, 670]. Abian [532]. absolute [13, 653]. abstract [232, 231]. academic [107]. accelerations [57]. ACM [454]. Addenda [711]. Addendum [813, 172, 8]. adic [460, 17]. administration [107]. Advanced [700, 819]. Advice [423]. affine [78, 127]. affine-regular [78]. after [20]. Aitken [350]. Algebra [263, 307, 133, 558, 200, 222, 247, 10, 737, 231]. algebraic [659, 67, 263]. algebras [322, 99, 606]. Algorithm [140, 291, 714, 335, 521, 159, 255, 722, 483, 410, 253, 46, 113]. algorithm-inspired [113]. Algorithmic [407, 252]. Algorithms [823, 435, 617]. allocation [283]. Almost [162]. Almost-periodic [162]. alternate [756]. alternating [536, 102]. Alternative [140, 497]. Amer [532, 814, 639, 815, 640, 813, 769, 432, 615, 405, 100, 422, 512, 711, 146, 463, 712, 816, 729, 745, 413, 817, 188, 771, 770, 454, 139, 533, 772, 616, 812, 343, 485, 172, 421, 513, 8, 361, 818, 750, 641]. among [319]. analog [204]. analogue [478]. analysis [767, 505, 753, 435, 16, 344, 670, 256, 760, 157]. analyst [121]. Analytic [330, 150, 379, 285, 676, 84, 660]. analyticity [549]. anatomy [408]. Ancestors [500]. Andrews [812, 812]. Angle [711, 655]. angles [681, 142]. answer [515, 212]. anticommutativity [582]. Antisocial [482]. Any [223]. application [419, 558, 673, 57, 107]. Applications [314, 261, 618, 603, 347, 175]. apportionment [104]. approach [288, 769, 659, 89, 520, 385, 17, 710, 719, 772, 83, 585, 497, 557]. approaches [205]. approximate [681, 269]. approximating [800]. Approximation [365, 730, 541, 342, 413, 591, 762, 278, 610]. approximations [743, 328]. Arakelian [762]. arbitrarily [101]. arc [752]. Archimedean [198, 253, 178]. Archimedes [121, 326]. Arcwise [359]. Area [702]. Area-minimizing [702]. areas [740]. arising [659, 670]. arithmetic [684, 125, 636]. arithmetic-geometric [684, 636]. Aron [616]. Arora [745]. associated [677]. associative [560]. associativity [157]. Asymptotic [183, 784, 700, 819, 480, 163, 591, 366]. Author [311]. Automated [394]. Automorphism [526]. automorphisms [469, 229]. averaging [415]. Award [642, 195, 406, 727].

B [818]. Babylon [42]. balls [767]. Banach [241, 183, 10, 367]. band [329]. Banzhaf [104]. Barycentric [635]. based [502]. Bases [241, 120, 736]. basic [306, 341, 474]. basis [367]. Bateman [771]. Baxter [812]. be [279, 795]. beat [221]. became [701]. behavior [183]. behaviour [707]. being [336]. Bernoulli [769, 667, 710]. Bernstein [381]. Bertrand [419]. Best [610]. beta [43]. between [481, 36, 160]. Bieberbach [693, 534]. biholomorphic [301]. Bijecting [393]. Biler [533]. billion [743]. binary [723, 809]. Binomial [571, 460, 232, 88, 700, 724, 819, 810, 440, 375, 774]. biographers [196]. bipartite [688]. biplanes [117]. bisection [629, 815, 483]. Bishop [320]. Black [170]. Blaschke [746]. blocks [531]. Blowing [237]. body [566]. Bolzano [204]. Bonnesen [604]. Boolean [492]. border [581, 290]. Borsuk [295]. Borsuk-Ulam [295]. both [795]. bottles [33]. bound [494]. boundary [746, 216]. bounded [658, 10]. Bounds [39, 131]. box [615, 575]. branches [539]. Branges [534]. bridges [646, 208]. brief [578, 715, 122]. Brouwer [645, 383, 65]. Brownian [603]. Bruno [98]. bubbles [202]. Buffon [97, 491]. Bulgarian [414]. Burnside [99]. butterflies [27].

C [729, 454]. cake [77, 172]. calculating [215]. calculations [253]. Calculator [30, 278]. Calculus [222, 265, 520, 30, 636, 504]. calibrations [702]. calissons [761]. Can [795, 206, 279]. canonical [588, 252, 497]. Cantor [779, 147, 292]. card [344, 502]. cardinals [500]. cards [514]. Carl [195]. Cartesian [243]. case [385, 311]. Catalonian [503]. category [403, 304, 109]. catenary [122]. Cauchy [185, 552, 265, 599, 398]. Cauchy-Kowalevsky [398]. caustics [177]. Cayley [463, 401, 337, 145, 28]. cells [586]. centered [482]. centers [345]. Central [227, 440]. Centrosymmetric [474]. certain [680, 712]. Ceva [717]. chain [122]. chains [86, 547]. chair [236]. change [92]. change-of-variables [92]. changing [46]. chaotic [405, 318]. characteristic [594]. Characterization [119, 301, 548, 644, 144, 402, 522, 611, 791]. characterizations [549, 327]. Characterizing [409]. Characters [175]. Chebyshev [738, 199, 251, 449]. Chebyshev-type [199]. checking [335]. Choi [513]. Christoffel [317]. circle [555, 405, 318]. circles [572, 86, 321, 310]. circulant [475, 516, 161]. circumscribed [58]. class [148, 560, 791, 670]. classes [119, 319, 37]. classical [237, 144]. Classification [430, 708]. Classroom [140]. climbing [768]. closed [409]. closedness [453]. closure [699, 364]. code [69]. codes [117]. coefficient [487, 700, 724, 819, 810, 440]. coefficients [460, 232, 88, 478, 375, 774]. cohomology [563]. coin [334, 718]. coincidences [143]. coins [577]. College [63]. color [85, 231]. Coloring [816, 511, 530]. Colorings [321]. Combinatorial [570, 451, 767, 475, 357, 471, 247, 689, 437, 415]. combinatorics [459]. come [648]. Comm [454]. Comment [100, 454, 616, 812]. Comments [297]. Commodore [559]. Common [672]. commutative [519, 10]. commutativity [663, 582]. Commutators [523]. compact [373, 453, 442, 630]. Compactness [453, 130]. Companion [721]. Comparing [742]. comparison [486]. complement [305, 412, 485]. complements [550, 297, 448]. Complete [82]. completeness [288]. completions [630]. complex [395, 532, 505, 452, 210, 587, 468, 6, 326, 585, 478, 204]. complexity [714]. complicated [344]. composition [791, 57]. Compound [192]. computation [824, 238]. compute [743]. computer [823, 206, 380]. Computers [193]. computing [722, 410, 609, 173]. concept [4, 8]. concepts [207]. concerning [431, 118, 404, 382]. Concurrences [11]. concurrent [238]. condition [258]. conditions [309]. conformal [572]. congruence [100, 3]. congruences [502, 631, 750]. congruent [580]. conics [151, 626]. conjecture [739, 455, 696, 673, 716, 693, 534, 771, 262, 750]. conjectured [590, 478]. Conjectures [272, 122]. connected [591, 4]. connectedness [359]. connected’ [8]. connection [481, 36]. consecutive [138]. consequence [582]. Consequences [638, 486]. constant [277, 182, 81]. constants [824]. constrained [467]. Constructing [581, 703, 141, 97]. construction [619, 437]. constructions [544]. constructive [225, 778]. contain [606]. contained [268]. Continued [691, 291, 680, 712, 785]. continuity [445, 699, 756, 260, 92, 130, 18, 766]. Continuous [411, 230, 528, 658, 680, 260, 712, 795, 804]. contraction [695]. Convergence [682, 165, 54, 432, 479, 13, 650, 653, 799, 402, 483, 508, 156, 95, 766]. Convergence-preserving [682]. converges [167]. converging [286]. converse [103, 214, 401, 242]. convex [639, 569, 793, 187, 566, 314, 37, 183, 803, 18, 49, 442, 602, 580, 610]. convexity [244, 128]. Convolutions [552]. coordinates [736]. corner [760, 628, 786]. Correction [615, 463, 341, 46, 8]. Corrections [146]. correlation [487]. corresponding [553]. cosets [69, 622]. cost [283]. counterexample [590, 317]. counterexamples [665]. Counting [573, 798, 53, 261, 123]. Courant [599]. Courant-Fischer [599]. cover [704]. cover-up [704]. Covering [793, 631, 750]. coverings [37, 482]. covers [652, 814, 753]. Cowling [70]. criterion [471]. Critical [390, 272]. Cross [316, 474]. cross-symmetric [474]. crossing [491]. cryptograms [256]. Crystallography [563]. cube [373]. Cubelike [496]. cubes [155]. curious [386]. Curvature [572, 202]. curvatures [518, 86]. curve [566, 383, 662, 275]. curves [793, 153, 177, 409, 97, 472, 154, 803, 330, 106, 565]. cut [77, 172]. Cyclic [489, 788, 376]. Cyclotomic [5, 146, 188, 71].

D [769, 405, 816, 745, 513]. d’Alembert [418]. Daniell [287]. Daniell-Stone [287]. databases [259]. Decomposition [688, 747, 38, 775]. Dedekind [465]. defective [334]. definite [551]. definition [328]. deformations [24]. degree [118]. Dehn [714]. dense [411]. density [738]. deranged [725, 811]. derivation [487, 252, 480, 174]. derivative [764, 467, 600]. derivatives [698, 302, 81, 18, 215]. derived [450, 315, 26]. desert [649]. Designing [491]. Detection [334]. determinant [450, 516]. determinants [806]. determination [650]. Determining [290]. detour [457]. development [160, 66]. deviation [634]. diagram [746]. diagrams [732]. diameter [644, 412, 485]. diary [684]. Dice [661, 754]. difference [558, 489, 82, 228, 690]. differences [783]. Differentiability [94, 691]. Differentiable [379, 348]. Differential [228, 210, 799, 515, 203, 293, 209]. Differentiation [163]. difficult [247]. digit [650]. digital [206]. digits [743]. dimension [548, 606]. dimensional [639, 569, 408, 550, 448, 316, 602, 367]. dimensions [536, 717]. Dini [533, 429]. Diophantine [813, 683, 574, 129, 50, 353]. Direct [733, 174]. Dirichlet [508, 75, 70]. discontinuous [795]. discrete [728, 369, 662]. discriminants [609]. discriminator [419]. discs [150]. discussion [7]. Disjoint [631, 750, 310]. disk [70]. Disks [767]. Dispersion [34]. distances [776]. distinguished [642, 481, 195, 406, 727]. distributed [254]. distribution [487, 601, 634, 491]. distributions [552, 97, 69, 25]. divergent [380]. diverges [52]. divided [783]. dividing [774]. Divisibility [71]. division [307, 180, 744, 606, 671]. divisor [509]. divisors [519]. Do [284, 496]. does [528, 95]. domain [709, 468]. domains [180, 301]. Double [366, 250, 726]. down [191]. down-to-earth [191]. Dr. [195]. Drawing [305]. dual [502, 554]. Duality [729, 592, 641, 441]. dynamics [668].

E2982 [250, 726]. E3061 [586]. E3106 [386]. E3166 [692]. E3267 [674, 820]. E3303 [723, 809]. E3309 [724, 810]. E3335 [725, 811]. each [274]. ears [35]. earth [191]. easy [562, 137]. economics [355, 270]. editor [532, 769, 432, 405, 439, 422, 512, 729, 745, 413, 771, 770, 533, 679, 772, 760, 485, 421, 513, 628, 786, 361, 787]. effectiveness [14]. Egorov [76]. Eigenvalues [181, 553, 721, 454, 267, 470, 474]. eigenvectors [553, 721, 474]. Eisenstein [136]. Elem [632]. element [751, 607]. Elementary [674, 144, 250, 725, 723, 724, 726, 811, 809, 810, 203, 820, 288, 658, 764, 289, 620, 493, 266, 89, 520, 96, 385, 402, 135, 741, 38, 636, 373, 623, 492, 367, 557, 398, 678, 537]. elements [808]. elimination [675]. ellipses [684, 40]. elliptic [174, 565]. Empty [586]. encryption [335]. ensures [716]. entire [280]. entries [239, 721, 454, 267]. Enumeration [392, 7]. epsilon [265]. equal [707, 457]. equality [62]. equation [683, 813, 181, 368, 574, 129, 418, 690, 248, 353, 417]. Equations [744, 395, 532, 44, 743, 210, 521, 799, 50, 17, 203, 293, 82, 228, 106, 209]. equilateral [187]. Equivalence [157, 340]. Erdos [543]. Errata [814, 639, 815, 640, 712, 816, 817, 818, 641, 729]. error [21, 585, 404]. errors [359, 30]. Estimating [21]. estimators [634]. etc [246]. Euclid [755, 140]. Euclidean [438, 709, 735, 316, 695, 73, 155, 340]. Euler [361, 559, 784, 393, 299, 32, 617, 345, 294, 182, 613, 386, 127, 465, 205, 370]. Euler-Dedekind [465]. Eulerian [484]. Évariste [196]. ever [344]. Everett [406]. Every [114, 695, 751]. Evolution [4, 8]. exact [652, 814, 750]. examinations [63]. example [597, 680, 712, 805, 19, 664]. Examples [652, 814, 415]. excenters [635]. exchangeable [447]. exclusion [96, 427]. excursion [353]. exotic [805]. expansion [700, 819, 695, 347]. expansions [784, 366, 205]. experience [166]. exponential [39, 677, 148]. Exponentials [132, 564, 286]. exposed [35]. extended [79]. Extending [233, 385]. extension [76, 498]. extensions [43, 344, 67]. extrema [467]. Extreme [602].

F [485]. Faà [98]. fabrics [643].

Fabrykowski [712]. faces [702]. fact [152]. Factoring [234]. Factorization [349, 439, 527, 5, 146, 59, 188, 664]. factors [293]. fails [718]. Fair [754, 104, 581, 290, 661]. fairly [77, 172]. families [580]. family [19]. Fan [139]. fantastic [344]. fascination [623]. Fat [147]. Fermat [308, 759, 258, 689, 530]. fiber [305]. Fibonacci [350]. fiction [152]. fictionalization [196]. field [395, 532]. fields [595, 67, 17, 729, 507, 686, 592, 641]. fifths [555]. figure [305]. figure- [305]. filling [154, 275]. Finding [713, 553]. Finite [559, 589, 356, 550, 573, 558, 233, 37, 751, 595, 621, 627, 17, 448, 323, 547, 607, 376, 19, 671, 565, 175, 70]. finite-dimensional [550, 448]. first [134, 63, 209, 61]. first-order [209]. Fischer [599]. Fixed [788, 283, 243, 120, 34, 27, 227, 383, 65, 509]. fixed-point [65]. Fixed-route [283]. flexible [105]. flow [667]. Folding [668, 659]. followed [695]. form [588, 252, 689, 557]. Forms [538, 497, 662]. Formula [821, 218, 740, 493, 384, 92, 182, 770, 734, 451, 90, 98, 173]. Formulae [86]. formulas [96, 427, 163]. four [426, 194, 85]. four-color [85]. four-or-more [426]. four-squares [194]. Fourier [432, 54, 554]. Fourteen [612]. fraction [291]. fractions [680, 712, 785, 691]. frameworks [105]. Fredholm [576]. free [605, 115]. fresh [806]. Fresnel [211, 669]. Fricke [616]. Frobenius [62]. fronts [221]. Fry [195]. Fubini [789, 331]. full [753]. function [39, 230, 528, 399, 280, 658, 348, 677, 299, 315, 302, 794, 522, 386, 611, 434, 805, 286, 346, 278, 628, 70]. functional [520, 570, 763, 418]. Functions [101, 81, 313, 274, 43, 505, 390, 119, 235, 379, 773, 162, 285, 479, 411, 680, 233, 676, 179, 712, 543, 227, 693, 6, 75, 691, 796, 792, 10, 189, 174, 204, 804, 245, 682, 112, 610]. fundamental [133, 323, 547]. furthest [356, 782].

G [139, 616, 812]. Gale [159]. Gallian [421]. Galois [741, 196]. game [767, 704, 221, 674, 820, 142]. games [713, 109, 608]. gamma [43, 399, 611]. Gauss [684, 578, 103]. Gaussian [299, 675, 596, 778]. gave [265]. Gelbaum [410]. general [226, 201, 665]. generalisation [530]. generalisations [492]. Generalization [617, 562, 717, 624, 173, 127]. generalizations [388]. Generalized [470, 245, 164, 601, 555, 648, 515, 333, 68, 757, 529]. Generalizing [164, 740, 15]. Generating [93]. Generation [822, 454]. generator [462]. Generic [300]. Genius [196]. Geometric [495, 322, 777, 684, 487, 125, 16, 434, 636, 484]. geometrically [747]. geometries [481]. Geometry [473, 785, 375, 371, 153, 300, 289, 506, 257, 186, 263, 735, 12, 281, 6, 73, 325, 23, 116]. Gini [545]. given [491]. global [542]. go [249]. Goel [745]. Goldbach [624]. Goldbach-Shnirelman [624]. Goldberg [51]. golden [591]. Golomb’s [188]. graph [781, 412, 613, 441, 485, 795]. graph-theoretic [441]. Graphical [544]. graphs [644, 688, 238, 420, 116]. Grassmann [200]. Grassmannians [702]. great [111, 208]. greeting [568]. group [120, 110, 676, 126, 277, 741, 433, 607, 91, 376, 358]. groups [2, 559, 640, 573, 141, 751, 563, 621, 627, 323, 670, 462, 28, 175, 466, 526]. Growth [675, 277, 209]. guide [271, 343].

H [769, 512, 816, 616, 361]. Hadamard [244]. half [12]. Halley [165, 400]. halves [336]. Hamilton [463, 401, 337]. hanging [423]. Hanoi [435]. Harary [485]. Harmonic [505, 102, 75]. harmonicity [29]. Haruki [361, 361]. Harvard [63]. Hausdorff [453]. heads [499]. heart [64]. heat [181, 25]. Helly [352, 223]. heptagon [711, 655]. Hermann [200]. Hermitian [455, 590]. Herstein [582]. hexagon [27]. higher [698, 717, 316]. higher-dimensional [316]. higher-order [698]. Hilbert [513, 276, 186, 373]. historical [118]. history [578, 546, 122, 311]. Holmes [42]. holomorphic [240, 70]. Homeomorphisms [155]. homology [295, 537]. Homomorphisms [540, 657, 616, 339]. Hurwitz [399]. hyperanalytic [6]. Hyperbolic [626, 186, 12, 245]. hypergame [608]. hypergeometric [571]. hyperplane [672]. hyperpower [479]. hypersurfaces [645]. hypothesis [477, 568].

ideal [709]. identities

[758, 663, 570, 812, 571]. identity

[137, 692, 357, 174, 157, 618, 678]. II [74]. Ilieff [696]. implications [85]. implies [584]. imply [663, 95]. impossibility [187]. impossible [80]. improper [653]. inadequacy [217]. incenter [635]. inclusion [96, 427, 444]. inclusion-exclusion [96, 427]. incomplete [322, 271]. incongruent [652, 814]. increments [707]. independence [154]. index [104]. Inequalities [58, 442, 777, 455, 450, 220, 716, 420, 199, 796]. inequality [303, 738, 125, 1, 590, 730, 78, 431, 184, 724, 810, 551, 244, 636, 139, 338, 51, 604, 775]. Infinite [539, 367, 395, 532, 652, 814, 653, 731, 250, 726, 109, 602, 108]. Infinite-dimensional [367, 602]. Infinitesimal [24]. Infinitesimals [537, 233, 360]. infinitude [755]. informal [7]. information [334, 225]. ingrained [404]. initial [476, 25]. Injective [240]. inner [346]. inscribed [58, 803]. inspired [747, 113]. Integer [510, 291, 721, 454, 736, 267, 628]. integers [748, 354, 619, 299, 451, 61]. integrability [36, 372]. integrable [658]. integral [562, 13, 1, 126, 515, 139, 757, 23]. Integrals [660, 654, 211, 653, 294, 698, 213, 745, 669, 83, 60, 361, 818]. Integration [47, 654, 314, 745, 593]. interconnections [263]. Interesting [440, 292]. interlace [599]. Interlaced [403]. interpolation [365]. interpretation [484]. intersects [329]. interval [374, 479, 274, 189]. introduction [633, 151, 660]. invariant [676, 151, 621, 516]. invariants [656, 377]. invented [344]. inverse [173]. inverses [446, 161]. inversion [224]. invertible [808]. involution [531]. involving [440]. irrational [147, 561]. irrationality [517]. irrationals [230]. Ising [633]. isomorphism [266]. Isonemal [643]. isoperimetric [730, 457]. isospectral [703]. Iterated [88, 564]. Iterating [150, 315]. iteration [452, 800, 400, 443]. Iterative [289]. itself [695]. Ivan [727].

J [405, 712, 771, 770, 454, 772, 812, 421, 750]. J.-C [454]. Jacobi [461]. Jacobian [174]. Jacobson [818]. Jech [343]. Jensen [338]. Jensen-Steffensen [338]. Jerusalem [687]. Jordan [578, 588, 252, 89, 645, 508, 383, 662, 557]. Jordan-Brouwer [645]. Jr [771].

Kantorovich [220]. Kantorovich-type [220]. Kaprekar [650]. Kathy [778]. Kepler [281]. key [335]. Klamkim [642]. Klein [33]. knockout [207, 567]. knot [305]. knots [656]. Königsberg [646]. Kovalevsky [168]. Kowalevsky [398]. Kronecker [541].

L [100, 771]. ladder [768]. Ladies [684]. Lagrange [218, 355]. Landau [524, 369]. Landen [684]. Laplace [32]. Laplacian [181, 202]. Large [312, 44, 109, 596]. last [759, 689]. later [646]. law [134, 694, 109, 718]. laws [91, 596]. least [333, 470]. leaving [516]. Lebesgue [372]. Lebesgue-Stieltjes [372]. Legendre [90]. Lehmer [769, 816, 706]. lemniscate [149]. length [781]. lengths [736]. Leo [776]. less [65]. lesson [168]. Letter [532, 769, 432, 405, 439, 422, 512, 729, 413, 771, 770, 533, 679, 772, 485, 421, 513, 361, 787]. Letters [745]. level [311]. levels [507]. Lévy [598]. Lewin [772, 772]. Lie [341, 306]. life [378]. lim [36]. limit [600]. Limiting [601, 479]. limits [285, 366]. Line [698, 329, 206, 127]. Linear [210, 483, 434, 559, 428, 799, 129, 763, 82, 247, 69, 737, 554]. lines [566, 345, 794]. Liouville [501]. lists [589]. little [530, 231]. Livingston [100, 100]. Local [472, 411, 274, 467]. locally [453, 19, 630]. logarithm [800]. logarithmic [396, 68]. logic [363, 441, 262]. logics [160]. Long [197, 282]. look [251]. loop [650]. looped [409]. loops [141]. Lorentz [139, 382]. Lorentzian [371]. Louis [534]. low [408]. low-dimensional [408]. Lucas [706]. Lucas-Lehmer [706]. Ludwig [534]. Lusin [124].

M [100, 745, 770, 772, 616, 513]. Machiavelli [159, 416]. Magic [686, 579, 53, 780]. man [806]. manifolds [703]. many [528]. map [695]. mapping [498]. mappings [183, 240]. maps [572, 150, 405, 749, 301, 318]. marked [238]. Markov [547]. matched [366]. matching [601, 416]. Math [532, 814, 639, 815, 640, 813, 769, 432, 615, 405, 100, 422, 512, 711, 146, 463, 712, 816, 729, 745, 413, 817, 188, 771, 770, 454, 139, 533, 772, 616, 812, 343, 485, 172, 421, 513, 8, 361, 818, 750, 641]. Mathematical [270, 158, 238, 407, 264, 262, 168, 74, 175]. mathematician [271, 343]. mathematicians [311]. mathematics [191, 143, 64, 14, 170, 823, 158, 546, 152, 225, 378]. Matrices [637, 454, 267, 291, 742, 527, 475, 619, 190, 239, 721, 99, 731, 520, 570, 551, 822, 497, 41, 474, 516, 161]. Matrix [377, 527, 553, 455, 276, 368, 590, 255, 722, 431, 410, 420, 603, 807, 173, 701, 557, 775, 513]. maxima [411]. maximally [409]. maximum [607, 274]. McCarty [171]. Mean [202, 164, 684, 103, 125, 213, 636, 396, 279, 818]. mean-geometric [125]. mean-value [164, 103]. Meaning [225, 262]. means [707, 545, 313, 544, 68, 465, 529]. measurability [324]. measurable [254]. Measure [304]. measures [605, 402]. mechanical [237]. medians [672]. meet [566]. meets [566]. memoryless [638]. ménage [535]. Merlin [579, 780]. Mersenne [771, 739]. method [165, 629, 815, 553, 405, 16, 400, 50, 318, 554]. methods [800, 270, 434, 585]. metric [450, 130, 73]. metrics [648]. microsimplexes [537]. middle [700, 819, 311]. Mikusiński [72]. Milnor [65]. minima [144]. Minimal [728, 255, 410, 46]. minimal-path [46]. minimization [269]. minimizing [702]. minimum [542]. minors [431]. missing [746]. mixed [87]. Möbius [676, 340]. mod [460, 748]. model [633, 186, 735, 12, 73]. models [238, 158]. Modern [55, 823]. Modified [156, 443]. modular [743, 120]. modules [115]. modulo [510]. modulus [260]. Moebius [329]. moments [740]. money [46]. monkey [518]. monoid [781]. Monostatic [456]. Monotone [773, 235, 543, 647, 189, 112]. monotonicity [148, 599]. Montel [111]. Monthly [532, 814, 639, 815, 640, 813, 769, 432, 615, 405, 100, 422, 512, 711, 146, 463, 712, 816, 729, 745, 413, 817, 188, 771, 770, 454, 139, 533, 772, 616, 812, 343, 485, 172, 421, 513, 8, 361, 818, 750, 641]. Moore [161]. Morley [242]. Moser [776]. Most [235, 112, 344]. motion [405, 603, 318]. motions [151, 626]. motivated [758, 812]. Mountain [768]. moving [768]. MR [532, 814, 639, 815, 640, 813, 769, 432, 615, 405, 100, 422, 512, 711, 146, 463, 712, 816, 729, 745, 413, 817, 188, 771, 770, 454, 139, 533, 616, 812, 343, 485, 172, 421, 513, 8, 361, 818, 750]. Ms. [416]. multigraphs [87]. multiple [13]. multiplication [576]. Multiplicative [476, 773, 543, 296, 494]. multiplicity [553, 193]. multiplier [355, 55]. Murray [642]. music [392]. Musical [555]. must [367].

Napoleon [78]. natural [738, 800, 7]. naturally [230]. nearest [628]. nearly [560]. Necessary [309, 258]. needle [491]. negative [39, 636]. neglected [760]. Neighborly [580]. neighbors [20]. neighbour [356, 782]. net [286]. nets [238]. Newton [405, 796, 318]. Nikodým [764, 765]. Niven [80, 727]. no [532, 814, 639, 815, 813, 769, 432, 615, 405, 801, 100, 422, 512, 711, 146, 463, 712, 135, 816, 729, 745, 413, 817, 188, 771, 770, 454, 533, 772, 616, 812, 189, 343, 485, 172, 421, 513, 8, 361, 818, 750, 641]. no-retraction [135]. nodes [365]. non [178]. non-Archimedean [178]. nonconvergence [779]. nonexpansive [183]. nonmeasurable [286, 437]. nonnegative [742, 7]. nonnormal [729, 592, 641]. Nonsexist [535]. nonsolvability [226]. Nonstandard [766]. nonstationary [385]. Nonunique [59, 664]. Nonuniqueness [209]. norm [763]. normal [120, 634]. normality [471]. Normalized [796]. Normed [180, 322]. Note [337, 463, 80, 139, 594, 452, 536, 699, 100, 625, 541, 501, 705, 188, 732, 128, 60, 444]. Notes [420, 140]. notion [15]. nowhere [379, 348]. NP [288]. NP-completeness [288]. null [789]. Number [344, 356, 639, 569, 782, 781, 659, 339, 296, 667, 494, 84, 591, 90, 376, 507, 353, 660]. Number-theoretic [344, 659, 353]. numbers [395, 532, 784, 223, 506, 650, 694, 258, 109, 636, 561, 350, 484, 138, 7, 312, 596]. numeration [397]. Numerical [506, 121].

obstructions [589]. Occurrences [138]. occurring [230]. odd [138]. Offbeat [23]. O’Hara [778]. Old [205, 588, 142]. one [743, 553, 570, 462, 417]. one-parameter [570]. one-relation [462]. ones [690]. only [230]. open [749, 498]. operator [381, 788, 716]. operators [48, 428, 72, 791, 219, 576]. Oppenheim [551]. opponent [221]. Optimal [803, 365]. optimization [790, 66]. orbits [728, 667]. orchard [488]. order [564, 233, 751, 698, 607, 209, 565]. ordinary [203]. origins [265]. Orthogonal [736]. oscillations [309]. other [561]. Outer [229]. overlooked [664].

P [771, 533]. pairs [356, 782]. paper [659, 362]. paper-folding [659]. paradox [198, 608]. parallelogram [78]. parameter [570]. parametrize [313]. partial [564, 334]. partition [374]. partitions [438, 393, 531, 296, 494, 618]. partitions-recurrence [393]. Pascal [27, 451]. past [253]. path [46]. paths [688]. Patin [770]. Patterns [737]. pedal [685]. Penrose [161]. perfect [192]. periodic [162, 176, 667, 15]. periodicity [325]. periods [728, 101]. permanent [184]. permit [37]. permutations [94]. Perpendicular [389]. persistence [359]. person [713]. Petri [238]. phase [16]. phi [539]. phi-tree [539]. philosophical [85]. philosophy [158, 546]. Pi [784, 743]. Picard [111, 208]. Pick [464]. pictures [423]. pigeonhole [79]. Pitcher [406]. Planar [450, 752, 356, 613]. Plancherel [26]. plane [210, 177, 16, 472, 12, 73, 326, 442, 364, 325]. Planes [117, 360]. Platonic [816, 511]. Playing [608]. Ploeg [729]. Plücker [106]. Poincaré [107]. point [243, 782, 542, 383, 65, 457]. Points [565, 390, 120, 34, 788, 176, 473, 27, 227, 272, 35, 602]. Pointwise [54, 432, 285]. Poisson [328, 385]. polar [38, 775]. Pólya [488, 123]. polygon [768]. Polygons [161, 740, 389, 659, 78, 58, 803]. polyhedra [639, 569]. polylogarithmic [824]. Polynomial [91, 395, 532, 663, 226, 521, 756, 110, 255, 741, 692, 410, 272, 215, 509, 193]. polynomials [538, 510, 769, 381, 696, 677, 131, 384, 5, 146, 145, 365, 67, 458, 327, 710, 188, 251, 594, 478, 668, 778]. polytopes [580]. Pompeiu [9]. popular [271, 343]. population [167]. portions [24]. Positive [25, 390, 429, 48, 551, 533, 219]. postulate [419]. power [512, 799, 136, 114, 45, 556, 68, 425]. power-sums [512, 425]. powerful [138]. Powers [774, 354, 525, 451, 476, 61]. prehistory [200]. prescribed [25]. present [253]. preserving [108, 682]. primality [349, 439, 258]. Prime [649, 59, 667, 84, 90, 774]. primes [510, 755, 584, 387, 199]. Principal [35, 709, 518]. principle [269, 79, 215]. prismatic [33]. Prob [632]. probabilistic [342, 413, 391]. probabilities [705]. probability [495, 499, 427, 20, 443]. Problem [386, 567, 488, 790, 535, 601, 495, 761, 776, 524, 416, 674, 269, 166, 250, 362, 503, 586, 700, 692, 725, 723, 724, 726, 819, 811, 809, 810, 625, 388, 333, 281, 369, 75, 46, 820, 346, 325, 85, 9, 687, 786]. problems [355, 714, 659, 247, 284]. process [328]. processes [289, 385]. product [137, 126, 357, 618]. products [243, 523, 316]. Professor [642, 406]. programming [554]. projective [27]. Proof [335, 133, 758, 666, 747, 658, 111, 134, 588, 620, 436, 755, 756, 125, 493, 266, 137, 308, 124, 332, 422, 517, 269, 461, 543, 96, 135, 287, 534, 342, 413, 357, 715, 508, 323, 208, 547, 244, 670, 38, 373, 770, 84, 391, 471, 734, 338, 449, 62, 812, 65, 706, 194, 530, 421, 367, 604, 398, 765, 113, 778]. proofreading [705]. Proofs [52, 264, 197, 451, 282, 612]. proper [249, 411, 274]. properties [201, 232, 619, 71, 364, 474]. property [447, 243, 40, 638]. protocol [651]. provability [363]. prove [759]. proving [596]. public [335]. puzzles [496]. Pythagorean [681].

Quadrangles [27]. Quadratic [673, 134, 201, 507]. Quadrature [529, 585]. quadratures [203]. quadruples [351]. quantifiers [94]. quarterly [298]. quartic [741, 729, 592, 641]. quaternion [157]. quaternions [110]. queen [171]. question [651]. quick [525]. quintisection [246].

R [616, 812, 485]. R. [750]. radicals [458]. radii [742]. radius [799]. Radon [764, 224, 765]. Ramanujan [812, 684, 758, 43, 298, 743]. ramifications [157]. random [447, 672, 567, 603, 638, 20]. rank [722, 62]. ranking [271]. rapid [824]. rate [277]. Rational [627, 390, 110, 730, 7]. rationals [798]. Real [606, 753, 458, 478]. rearrangements [20, 108]. Rearranging [102]. reasoning [394]. reciprocity [134, 673, 136]. Reconstructing [794]. rectangle [612]. recurrence [393, 725, 811, 107]. recursion [179, 351]. reducible [510]. reduction [578]. referee [311]. Reflection [797, 215]. reflective [40]. region [187]. Regions [29]. regular [605, 659, 78, 808]. reiterated [132]. relation [462]. Relational [259]. Relations [319, 179, 476]. relative [489]. relatives [613]. remain [20]. remainder [218]. remark [755, 595, 783, 376]. remarkable [598]. Remarks [546, 118]. remembered [378]. Renaud [454]. reordering [583]. repeated [776]. reply [812]. reports [298]. representation [802, 273, 287, 635]. representations [627]. representatives [500]. repunits [234]. required [619]. residues [136]. result [314, 80, 612]. resultant [538, 384, 145]. resultants [404]. results [79]. retraction [135]. revenge [433]. Review [504]. revisited [697, 134, 273, 636, 780, 464]. Riemann [562, 658, 372, 515, 83, 60, 757, 568]. Riemann-Stieltjes [372, 83, 60]. Riesz [273]. right [81, 446]. Rigid [151, 105]. rigorous [265]. ring [126, 768, 582, 603]. ring-width [768]. Ringing [622]. Rings [808, 663, 120, 519, 560, 744, 733, 671, 492]. Robbins [87]. Robinson [485]. Rodriguez [745]. Rogers [812, 758]. Rolle [468, 478]. rolling [153]. Romberg [593]. root [629, 815, 116]. Roots [67, 48, 756, 731, 219, 193]. rose [614]. Rouché [214, 804]. roundoff [30]. route [525, 283]. RSA [335]. Rubik [433, 466]. rule [182, 21]. ruled [329]. rules [55]. Runge [597].

S [745, 771, 361, 457]. S. [298, 188, 168]. Saari [405]. saddle [518]. saddlepoints [713]. safe [801]. Sard [477]. satisfying [179, 637, 542]. scales [555]. Schur [391]. Schwarz [317]. science [823]. sciences [74]. screen [786]. search [468]. second [403, 467]. seeding [207]. Seifert [305]. Selecting [634]. self [150, 502, 301, 482, 329]. self-centered [482]. self-dual [502]. self-intersects [329]. self-maps [150, 301]. Selfridge [771]. semidefinite [431]. semigroups [59]. Semitopological [2, 640]. separable [387]. separation [645]. sequence [479, 680, 712, 302, 685, 15, 718]. sequences [797, 148, 71, 350, 465, 217]. series [802, 429, 536, 54, 432, 495, 102, 322, 799, 22, 440, 719, 114, 480, 533, 772, 571, 593, 45, 108, 380, 156, 26]. service [642, 195, 406, 727]. set [779, 356, 793, 292, 176, 411, 782, 315, 794, 93, 49, 796, 279, 437]. sets [147, 403, 789, 314, 37, 304, 489, 18, 442, 602, 254]. several [536, 587]. shadow [279]. Shanks [678]. Shannon [26]. shapes [506]. Shapley [159]. Sherlock [42]. shift [788]. shifting [381]. Shnirelman [624]. Short [282, 436, 269, 770, 734, 449, 604]. shortest [752, 566]. shuffles [502]. Shuffling [514]. sided [446]. sigmoidicity [390]. signed [116]. Similarity [41, 190, 822, 454]. Simple [821, 84, 419, 666, 704, 447, 696, 308, 332, 422, 517, 261, 461, 287, 611, 719, 508, 323, 57, 547, 462, 480, 338, 772, 194, 421]. simplexes [456]. simplicity [666]. Simpson [750]. Simultaneous [550, 448]. simultaneously [26]. sine [522]. Singular [256, 747, 235, 112]. singularities [408, 237]. size [748]. sketch [158]. slow [291]. small [694, 101, 279]. smooth [728, 239, 301, 645, 695]. smoothness [477]. soap [202]. solids [816, 511]. solitaire [414, 674, 820]. Solution [458, 503, 586, 692, 726, 819, 811, 809, 810, 820, 247, 535, 716, 567, 433]. solutions [799, 269, 17, 82, 284]. Solvability [395, 532]. solve [496, 424, 353]. solves [417]. solving [521, 166, 50]. Some [777, 663, 79, 486, 364, 118, 415, 573, 232, 319, 617, 659, 263, 71, 327, 347, 175]. sorts [469]. space [438, 249, 37, 154, 695, 216, 275]. space-filling [154]. Spaces [445, 630, 697, 550, 676, 130, 241, 183, 448, 720, 817, 316, 178, 453, 602, 155, 367]. Special [654, 693, 745]. spectral [742, 113]. sphere [24, 776]. spheres [438]. spherical [314]. sports [271, 343]. square [527, 308, 461, 731, 387, 579, 780]. square-separable [387]. squares [192, 171, 333, 470, 194, 507, 686, 53, 618]. stability [167]. stable [408, 416]. standard [24, 634]. States [170]. Steffensen [338]. Steinhaus [436]. Steinitz [598]. Stieltjes [372, 83, 60]. Stirling [770, 493, 182, 480, 734]. Stochastic [154, 522]. Stone [320, 512, 287]. Stone-Weierstrass [320]. stopping [514]. story [627]. straight [329, 206]. Strange [178, 65]. Straus [51]. strict [128]. strings [44, 690, 628]. strong [103, 694, 718, 596, 242]. stronger [796]. structure [462]. Structuring [264]. Sturm [486]. Sub [596]. Sub-Gaussian [596]. subcovers [482]. subgroups [573, 376]. Submodules [115]. subnets [217]. subsemigroups [59]. subsequences [647]. Subseries [45]. subsets [748, 319, 93]. subspaces [249]. substrings [628]. sufficient [309, 258]. Sum [748, 108, 250, 386, 503, 726, 733, 713, 61]. Sum-preserving [108]. summability [436, 760]. Summation [22, 380, 723, 809]. Sums [354, 179, 507, 525, 512, 304, 451, 476, 661, 556, 425, 618]. sup [36]. supplement [343]. surface [257]. surfaces [708, 430, 305, 702]. surprising [51]. survey [744, 122, 792]. Sylow [583]. Sylvester [559, 239, 715]. symmetric [147, 527, 607, 442, 796, 284, 474]. Symmetry [293, 472, 340]. system [424].

Systems [397, 395, 532, 201, 237, 631, 116, 750].

T [771, 343]. tale [577]. Tangent [360, 794]. taxicab [358]. Taylor [218, 677, 427, 114, 347, 593, 156, 757]. technique [261]. techniques [654, 745, 596]. tell [206]. temperatures [25]. tensors [123]. term [719, 772]. terrain [178]. tessellations [80]. test [741, 719, 508, 822, 454, 772, 706, 467]. tests [349, 439, 801]. textbooks [504]. th [48, 136, 719, 476, 772, 219, 61, 600]. th-power [136]. their [707, 97, 345, 301, 523, 117, 474, 668]. them [496, 417]. theme [224]. theorem [164, 169, 352, 76, 185, 87, 133, 111, 103, 320, 214, 401, 475, 436, 789, 308, 124, 239, 78, 72, 498, 337, 463, 477, 459, 99, 273, 461, 543, 599, 213, 331, 135, 287, 541, 486, 667, 717, 427, 501, 342, 413, 645, 715, 323, 582, 208, 383, 57, 547, 468, 38, 759, 123, 107, 462, 624, 84, 28, 391, 426, 449, 689, 65, 762, 149, 598, 576, 478, 671, 204, 194, 530, 382, 26, 662, 757, 804, 464, 295, 398, 765, 113, 242, 818, 70]. theorems [429, 5, 146, 188, 533, 583, 312, 282]. theoretic [344, 659, 441, 353]. theoretical [433]. theory [314, 89, 151, 306, 341, 656, 434, 603, 66, 392, 760, 118, 701, 660, 537]. There [801, 143]. thinking [407]. Thornton [195]. three [639, 569, 696, 650, 221, 507, 504]. three-digit [650]. three-dimensional [639, 569]. ticket [687]. Tietze [498]. tiling [187, 612]. times [514]. Titchmarsh [72]. toilet [362]. tool [760]. Topological [438, 720, 817, 28, 4, 8]. topologies [648]. topology [665, 216]. torchbearer [701]. torsion [56]. toss [718]. Total [56]. totient [386]. tournament [567]. tournaments [207, 271]. tours [613]. Towers [435]. transcendental [428, 792]. transcendentally [792]. transfinite [217]. transform [32, 317]. Transformations [516, 822, 454, 382]. translates [793, 49]. trapezoid [182]. trapezoidal [21]. treatment [806, 764]. treats [276, 513]. tree [539]. Trees [512, 613, 425, 556]. triangle [11, 635, 457]. triangles [681, 187, 345, 685]. trick [344, 502]. Tricks [276, 513]. trigonometric [654, 802, 745, 205]. Trigonometry [371]. triple [137, 357]. triple-product [137]. trisection [246, 711, 655]. trisector [242]. triskaidecagon [711, 655]. tritangent [345]. tumbling [615, 575]. tuplets [649]. Twisted [33, 788]. Two [665, 492, 662, 742, 538, 481, 644, 527, 308, 384, 160, 145, 461, 577, 713, 462, 247, 446, 336]. two-generator [462]. two-person [713]. two-sided [446]. two-square [308, 461]. type [429, 533, 9, 220, 199]. types [364].

UC [697]. Ulam [295]. Unbounded [465]. uncountable [324, 367]. unequal [187]. Uniform [18, 445, 36, 653, 130, 766]. uniformization [169]. uniformly [183]. unimodality [778]. union [605, 310]. unions [324, 49]. Unique [446, 59]. Uniqueness [802]. unit [374]. United [170]. Universal [720, 817, 280, 200]. unprovable [312]. unreasonable [14]. unsymmetric [331]. upper [12]. Urenko [405]. use [753, 800]. uses [175]. Using [681, 757].

value [164, 747, 103, 213, 256, 818].

Vandermonde [450, 807]. vanishing [126]. variable [204]. variables [707, 447, 92, 587, 638, 396, 718, 585]. variation [524, 10]. variational [269]. variations [303, 224]. various [824]. vector [550, 448, 157]. vectors [672, 316]. Venn [732]. verification [696]. version [32, 145, 65, 804, 295]. vertex [426]. vertices [35]. Very [306, 341, 560, 770, 734]. via [291, 381, 383, 123]. vibrations [44]. view [191, 568]. viewpoint [505]. virus [801]. volume [49]. volumes [352]. vs [311].

W [188, 485]. Waerden [348]. Wagstaff [771]. walk [603]. walls [767]. want [249]. War [74]. Wars [160]. way [604]. weak [402]. Wedderburn [671]. Weierstrass [413, 320, 342]. weight [334, 69]. Well [254]. Well-distributed [254]. where [249, 445, 657]. whether [206]. which [249, 629, 815, 751, 560, 329, 313, 718]. white [786]. Who [265]. wholes [336]. whose [110]. width [752, 768, 236]. will [249]. Wilson [459]. Wirtinger [604]. without [473, 72, 92]. Women [152, 170]. word [714]. words [781]. World [160, 74]. written [63]. Wronski [384]. Wythoff [221].

years [646].

Zero [519, 748, 81, 719, 733, 713, 772]. zeros [528, 696, 677, 131]. zeta [399]. zetafunction [399].

References

Fan:1954:II

[1] K. Fan and G. G. Lorentz. An integral inequality. American Mathematical Monthly, 61(??):626–631, ???? 1954. See note [139].

Anonymous:1965:SG

[2] Anonymous. Semitopological groups. American Mathematical Monthly, 72 (??):996–998, ???? 1965. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [640].

Livingston:1978:C

[3] A. E. Livingston and M. L. Livingston. The congruence a^{r+s} ≡ a^{r} (mod m).

American Mathematical Monthly, 85(2): 97–100, ???? 1978. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See comment [100].

Wilder:1978:ETC

[4] R. L. Wilder. Evolution of the topological concept of “connected”. American Mathematical Monthly, 85(9):720– 726, ???? 1978. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [8].

Golomb:1978:CPF

[5] Solomon W. Golomb. Cyclotomic polynomials and factorization theorems. American Mathematical Monthly, 85(9): 734–737, ???? 1978. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See corrections [146] and note [188].

Murrill:1980:HGC

[6] Malcolm Murrill. On a hyperanalytic geometry for complex functions. American Mathematical Monthly, 87(1):8–25, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Shen:1980:NEN

[7] Yu Ting Shen. A “natural” enumeration of nonnegative rational numbers—an informal discussion. American Mathematical Monthly, 87(1):25–29, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilder:1980:CAE

[8] R. L. Wilder. Correction and addendum to: “Evolution of the topological concept of ‘connected’ ” [Amer. Math. Monthly 85 (1978), no. 9, 720–726, MR 80f:01019a]. American Mathematical Monthly, 87(1):31–32, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [4].

Thompson:1980:PPT

[9] K. W. Thompson and T. Schonbek. A problem of the Pompeiu type. American Mathematical Monthly, 87(1):32– 36, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Russell:1980:CBA

[10] A. M. Russell. A commutative Banach algebra of functions of bounded variation. American Mathematical Monthly, 87(1):39–40, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kirby:1980:CT

[11] D. Kirby. Concurrences for a triangle. American Mathematical Monthly, 87(1): 45–47, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Millman:1980:UHP

[12] Richard S. Millman. The upper half plane model for hyperbolic geometry. American Mathematical Monthly, 87(1): 48–53, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dym:1980:ACM

[13] Harry Dym. On the absolute convergence of a multiple integral of sin x/x. American Mathematical Monthly, 87(1): 53–54, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hamming:1980:UEM

[14] R. W. Hamming. The unreasonable effectiveness of mathematics. American Mathematical Monthly, 87(2):81– 90, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

MacGregor:1980:GNP

[15] Robert M. MacGregor. Generalizing the notion of a periodic sequence. American Mathematical Monthly, 87(2):90– 102, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

DeTemple:1980:GMP

[16] Duane W. DeTemple. A geometric method of phase plane analysis. American Mathematical Monthly, 87(2):102– 112, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Koblitz:1980:AAS

[17] Neal Koblitz. The p-adic approach to solutions of equations over finite fields. American Mathematical Monthly, 87(2): 115–118, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nienhuys:1980:UCD

[18] J. W. Nienhuys. Uniform continuity of derivatives in convex sets. American Mathematical Monthly, 87(2):118– 120, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Sarma:1980:ELF

[19] V. L. N. Sarma, Nand Lal, and V. K. Singh. An example of a locally finite family. American Mathematical Monthly, 87(2):121–122, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Robbins:1980:PNR

[20] David P. Robbins. The probability that neighbors remain neighbors after random rearrangements. American Mathematical Monthly, 87(2):122–124, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rozema:1980:EET

[21] Edward Rozema. Estimating the error in the trapezoidal rule. American Mathematical Monthly, 87(2):124–128, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Klambauer:1980:SS

[22] Gabriel Klambauer. Summation of series. American Mathematical Monthly, 87(2):128–130, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zalcman:1980:OIG

[23] Lawrence Zalcman. Offbeat integral geometry. American Mathematical Monthly, 87(3):161–175, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bleecker:1980:IDP

[24] David D. Bleecker. Infinitesimal deformations of portions of the standard sphere in E^{3}. American Mathematical Monthly, 87(3):175–182, ???? 1980.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilcox:1980:PTP

[25] Calvin H. Wilcox. Positive temperatures with prescribed initial heat distributions. American Mathematical Monthly, 87(3):183–186, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Steiner:1980:PTS

[26] Antonio Steiner. Plancherel’s theorem and the Shannon series derived simultaneously. American Mathematical Monthly, 87(3):193–197, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Jones:1980:QBP

[27] Dixon Jones. Quadrangles, butterflies, Pascal’s hexagon, and projective fixed points. American Mathematical Monthly, 87(3):197–200, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nummela:1980:CTT

[28] Eric C. Nummela. Cayley’s theorem for topological groups. American Mathematical Monthly, 87(3):202–203, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Netuka:1980:RH

[29] I. Netuka and J. Veselý. Regions of harmonicity. American Mathematical Monthly, 87(3):203–205, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Miel:1980:CCR

[30] George Miel. Calculator calculus and roundoff errors. American Mathematical Monthly, 87(4):243–252, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rice:1980:W

[31] R. E. Rice, B. Schweizer, and A. Sklar. When is f(f(z)) = az^{2} + bz + c. American Mathematical Monthly, 87(4):252– 263, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Deakin:1980:EVL

[32] Michael A. B. Deakin. Euler’s version of the Laplace transform. American Mathematical Monthly, 87(4):264–269, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Sequin:1980:TPK

[33] Carlo H. Sequin. Twisted prismatic Klein bottles. American Mathematical Monthly, 87(4):269–277, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cobb:1980:DPF

[34] J. Cobb and W. Voxman. Dispersion points and fixed points. American Mathematical Monthly, 87(4):278–281, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Meisters:1980:PVE

[35] G. H. Meisters. Principal vertices, exposed points, and ears. American Mathematical Monthly, 87(4):284–285, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Darst:1980:CBL

[36] Richard B. Darst. The connection between lim sup and uniform integrability. American Mathematical Monthly, 87 (4):285–286, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Groemer:1980:FCC

[37] H. Groemer. On finite classes of convex sets that permit space coverings. American Mathematical Monthly, 87(4):286– 288, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Martins:1980:EPP

[38] L. C. Martins and P. Podio-Guidugli. An elementary proof of the polar decomposition theorem. American Mathematical Monthly, 87(4):288–290, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Alam:1980:BNE

[39] Khursheed Alam. Bounds on the negative exponential function. American Mathematical Monthly, 87(4):290– 292, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Foster:1980:RPE

[40] James H. Foster and Jean J. Pedersen. On the reflective property of ellipses. American Mathematical Monthly, 87(4): 294–297, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Watkins:1980:SM

[41] William Watkins. Similarity of matrices. American Mathematical Monthly, 87(4): 300, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Buck:1980:SHB

[42] R. Creighton Buck. Sherlock Holmes in Babylon. American Mathematical Monthly, 87(5):335–345, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Askey:1980:REG

[43] Richard Askey. Ramanujan’s extensions of the gamma and beta functions. American Mathematical Monthly, 87(5):346– 359, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Antman:1980:ELV

[44] Stuart S. Antman. The equations for large vibrations of strings. American Mathematical Monthly, 87(5):359– 370, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rubel:1980:SPS

[45] Lee Rubel and Kenneth Stolarsky. Subseries of the power series for e^{x}. American Mathematical Monthly, 87(5):371– 376, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nijenhuis:1980:CMP

[46] Albert Nijenhuis. Correction to: “A minimal-path algorithm for the ‘money changing problem’ ”. American Mathematical Monthly, 87(5):377, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dow:1980:I

[47] Alan Dow and John Ginsburg. Integration on [0, 1]^{ω}. American Mathematical Monthly, 87(5):378–380, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brown:1980:RPO

[48] D. R. Brown and M. J. O’Malley. On nth roots of positive operators. American Mathematical Monthly, 87(5):380– 382, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rehder:1980:VUT

[49] Wulf Rehder. On the volume of unions of translates of a convex set. American Mathematical Monthly, 87(5):382– 384, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kiss:1980:MSD

[50] Péter Kiss. A method for solving Diophantine equations. American Mathematical Monthly, 87(5):384–387, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Redheffer:1980:SIG

[51] Ray Redheffer and Carey Smith. On a surprising inequality of Goldberg and Straus. American Mathematical Monthly, 87(5):387–390, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

VandenEynden:1980:PD

[52] Charles Vanden Eynden. Proofs that ∑ 1/p diverges. American Mathematical Monthly, 87(5):394–397, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Spencer:1980:CMS

[53] Joel Spencer. Counting magic squares. American Mathematical Monthly, 87(5): 397–399, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chernoff:1980:PCF

[54] Paul R. Chernoff. Pointwise convergence of Fourier series. American Mathematical Monthly, 87(5):399–400, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [432].

Pourciau:1980:MMR

[55] B. H. Pourciau. Modern multiplier rules. American Mathematical Monthly, 87(6): 433–452, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Penna:1980:TT

[56] Michael A. Penna. Total torsion. American Mathematical Monthly, 87(6):452– 461, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Maitra:1980:SAT

[57] S. N. Maitra. A simple application of the theorem of composition of accelerations. American Mathematical Monthly, 87(6):466–468, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Klamkin:1980:IIC

[58] M. S. Klamkin. Inequalities for inscribed and circumscribed polygons. American Mathematical Monthly, 87(6):469– 473, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Greiter:1980:NFS

[59] Gebhard Greiter. Nonunique factorization in subsemigroups of semigroups with unique prime factorization. American Mathematical Monthly, 87(6):473– 474, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Satyanarayana:1980:NRS

[60] U. V. Satyanarayana. A note on Riemann-Stieltjes integrals. American Mathematical Monthly, 87(6):477– 478, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schultz:1980:SPF

[61] Henry J. Schultz. The sum of the kth powers of the first n integers. American Mathematical Monthly, 87(6):478– 481, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Robinson:1980:PFR

[62] Donald W. Robinson. A proof of the Frobenius rank equality. American Mathematical Monthly, 87(6):481– 482, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kennedy:1980:FWE

[63] Hubert Kennedy. The first written examinations at Harvard College. American Mathematical Monthly, 87(6):483– 486, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Halmos:1980:HM

[64] P. R. Halmos. The heart of mathematics. American Mathematical Monthly, 87 (7):519–524, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rogers:1980:LSV

[65] C. A. Rogers. A less strange version of Milnor’s proof of Brouwer’s fixedpoint theorem. American Mathematical Monthly, 87(7):525–527, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Prekopa:1980:DOT

[66] András Prékopa. On the development of optimization theory. American Mathematical Monthly, 87(7):527–542, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Isaacs:1980:RPA

[67] I. M. Isaacs. Roots of polynomials in algebraic extensions of fields. American Mathematical Monthly, 87(7):543– 544, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stolarsky:1980:PGL

[68] Kenneth B. Stolarsky. The power and generalized logarithmic means. American Mathematical Monthly, 87(7):545– 548, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schatz:1980:WDC

[69] James R. Schatz. On the weight distributions of cosets of a linear code. American Mathematical Monthly, 87(7):548– 551, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Yamashita:1980:CTD

[70] Shinji Yamashita. Cowling’s theorem on a Dirichlet finite holomorphic function in the disk. American Mathematical Monthly, 87(7):551–552, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lagarias:1980:DPS

[71] J. C. Lagarias and A. M. Odlyzko. Divisibility properties of some cyclotomic sequences. American Mathematical Monthly, 87(7):561–564, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Golberg:1980:MOT

[72] M. A. Golberg and H. Bowman. Mikusiński operators without the Titchmarsh theorem. American Mathematical Monthly, 87(7):564–567, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Parker:1980:MMP

[73] George D. Parker. A metric model of plane Euclidean geometry. American Mathematical Monthly, 87(7):567– 572, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rees:1980:MSW

[74] Mina Rees. The mathematical sciences and World War II. American Mathematical Monthly, 87(8):607–621, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Netuka:1980:DPH

[75] Ivan Netuka. The Dirichlet problem for harmonic functions. American Mathematical Monthly, 87(8):621–628, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bartle:1980:EET

[76] Robert G. Bartle. An extension of Egorov’s theorem. American Mathematical Monthly, 87(8):628–633, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stromquist:1980:HCC

[77] Walter Stromquist. How to cut a cake fairly. American Mathematical Monthly, 87(8):640–644, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See addendum [172].

Gerber:1980:NTP

[78] Leon Gerber. Napoleon’s theorem and the parallelogram inequality for affineregular polygons. American Mathematical Monthly, 87(8):644–648, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hutchinson:1980:SPP

[79] Joan P. Hutchinson and Paul B. Trow. Some pigeonhole principle results extended. American Mathematical Monthly, 87(8):648–651, ???? 1980.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Klamkin:1980:NRN

[80] M. S. Klamkin and A. Liu. Note on a result of Niven on impossible tessellations. American Mathematical Monthly, 87(8):651–653, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knight:1980:FZR

[81] William J. Knight. Functions with zero right derivatives are constant. American Mathematical Monthly, 87(8):657– 658, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nijenhuis:1980:CSL

[82] Albert Nijenhuis. Complete solutions of linear difference equations. American Mathematical Monthly, 87(8):658– 660, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ross:1980:AAR

[83] Kenneth A. Ross. Another approach to Riemann-Stieltjes integrals. American Mathematical Monthly, 87(8):660– 662, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Newman:1980:SAP

[84] D. J. Newman. Simple analytic proof of the prime number theorem. American Mathematical Monthly, 87(9):693– 696, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Swart:1980:PIF

[85] E. R. Swart. The philosophical implications of the four-color problem. American Mathematical Monthly, 87(9):697– 707, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fox:1980:FCC

[86] M. D. Fox. Formulae for the curvatures of circles in chains. American Mathematical Monthly, 87(9):708–715, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Boesch:1980:RTM

[87] Frank Boesch and Ralph Tindell. Robbins’s theorem for mixed multigraphs. American Mathematical Monthly, 87(9): 716–719, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Golomb:1980:IBC

[88] Solomon W. Golomb. Iterated binomial coefficients. American Mathematical Monthly, 87(9):719–727, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Galperin:1980:EAJ

[89] A. Galperin and Z. Waksman. An elementary approach to Jordan theory. American Mathematical Monthly, 87(9): 728–732, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pintz:1980:LPN

[90] János Pintz. On Legendre’s prime number formula. American Mathematical Monthly, 87(9):733–735, ???? 1980.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nakao:1980:PGL

[91] Zensho Nakao. Polynomial group laws. American Mathematical Monthly, 87(9): 735–736, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Guzman:1980:CVF

[92] Miguel de Guzmán. A change-of-variables formula without continuity. American Mathematical Monthly, 87(9): 736–739, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Prather:1980:GSS

[93] Ronald E. Prather. Generating the ksubsets of an n-set. American Mathematical Monthly, 87(9):740–743, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Whaley:1980:DPQ

[94] Thomas Whaley and Judson Williford. Differentiability and permutations of quantifiers. American Mathematical Monthly, 87(9):745–748, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Smart:1980:WDI

[95] D. R. Smart. When does T^{n+1}x−T^{n}x → 0 imply convergence. American Mathematical Monthly, 87(9):748–749, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnson:1980:EPI

[96] B. R. Johnson. An elementary proof of inclusion-exclusion formulas. American Mathematical Monthly, 87(9):750– 751, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

DeTemple:1980:CBC

[97] Duane W. DeTemple and Jack M. Robertson. Constructing Buffon curves from their distributions. American Mathematical Monthly, 87(10):779–784, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Roman:1980:FFB

[98] Steven Roman. The formula of Faà di Bruno. American Mathematical Monthly, 87(10):805–809, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Halperin:1980:BTA

[99] Israel Halperin and Peter Rosenthal. Burnside’s theorem on algebras of matrices. American Mathematical Monthly, 87(10):810, ???? 1980. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ecker:1980:CNC

[100] A. Ecker. Comment on the note:

“The congruence a^{r+s} ≡ a^{r} (mod m)” [Amer. Math. Monthly 85 (1978), no. 2, 97–100, MR 57 #12355] by A. E. Livingston and M. L. Livingston. American Mathematical Monthly, 87(10):811– 814, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [3].

Henle:1980:FAS

[101] J. M. Henle. Functions with arbitrarily small periods. American Mathematical Monthly, 87(10):816, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cowen:1980:RAH

[102] C. C. Cowen, K. R. Davidson, and R. P. Kaufman. Rearranging the alternating harmonic series. American Mathematical Monthly, 87(10):817–819, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Burckel:1980:SCG

[103] R. B. Burckel. A strong converse to Gauss’s mean-value theorem. American Mathematical Monthly, 87(10):819– 820, ???? 1980. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Grofman:1981:FAB

[104] Bernard Grofman. Fair apportionment and the Banzhaf index. American Mathematical Monthly, 88(1):1–5, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Roth:1981:RFF

[105] B. Roth. Rigid and flexible frameworks. American Mathematical Monthly, 88(1): 6–21, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Quine:1981:PEC

[106] J. R. Quine. Plücker equations for curves. American Mathematical Monthly, 88(1):21–29, ???? 1981. CO-DEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Meyer:1981:APR

[107] Kenneth R. Meyer. An application of Poincaré’s recurrence theorem to academic administration. American Mathematical Monthly, 88(1):32–33, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schaefer:1981:SPR

[108] Paul Schaefer. Sum-preserving rearrangements of infinite series. American Mathematical Monthly, 88(1):33– 40, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Mendez:1981:LLN

[109] C. G. Méndez. On the law of large numbers, infinite games, and category. American Mathematical Monthly, 88(1): 40–42, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dean:1981:RPW

[110] Richard A. Dean. A rational polynomial whose group is the quaternions. American Mathematical Monthly, 88(1): 42–45, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bridges:1981:MPG

[111] Douglas S. Bridges. On Montel’s proof of the great Picard theorem. American Mathematical Monthly, 88(1):45– 47, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zamfirescu:1981:MMF

[112] Tudor Zamfirescu. Most monotone functions are singular. American Mathematical Monthly, 88(1):47–49, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilf:1981:AIP

[113] Herbert S. Wilf. An algorithm-inspired proof of the spectral theorem in E^{n}. American Mathematical Monthly, 88(1): 49–50, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Meyerson:1981:EPS

[114] Mark D. Meyerson. Every power series is a Taylor series. American Mathematical Monthly, 88(1):51–52, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Isbell:1981:SFM

[115] John Isbell. Submodules of free modules. American Mathematical Monthly, 88(1): 53, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zaslavsky:1981:GRS

[116] Thomas Zaslavsky. The geometry of root systems and signed graphs. American Mathematical Monthly, 88(2):88– 105, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Salwach:1981:PBT

[117] Chester J. Salwach. Planes, biplanes, and their codes. American Mathematical Monthly, 88(2):106–125, ???? 1981.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Siegberg:1981:SHR

[118] Hans Willi Siegberg. Some historical remarks concerning degree theory. American Mathematical Monthly, 88(2):125– 139, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Buck:1981:CCF

[119] R. Creighton Buck. Characterization of classes of functions. American Mathematical Monthly, 88(2):139–142, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Childs:1981:MGR

[120] Lindsay N. Childs and Morris Orzech.

On modular group rings, normal bases, and fixed points. American Mathematical Monthly, 88(2):142–145, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Phillips:1981:ANA

[121] G. M. Phillips. Archimedes the numerical analyst. American Mathematical Monthly, 88(3):165–169, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ratliff:1981:BHS

[122] L. J. Ratliff, Jr. A brief history and survey of the catenary chain conjectures. American Mathematical Monthly, 88(3): 169–178, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Merris:1981:PCT

[123] Russell Merris. Pólya’s counting theorem via tensors. American Mathematical Monthly, 88(3):179–185, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Feldman:1981:PLT

[124] Marcus B. Feldman. A proof of Lusin’s theorem. American Mathematical Monthly, 88(3):191–192, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cusmariu:1981:PAM

[125] Adolf Cusmariu. A proof of the arithmetic mean-geometric mean inequality. American Mathematical Monthly, 88(3): 192–194, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gagola:1981:VPI

[126] S. M. Gagola, Jr., S. C. Garrison, and M. R. Pettet. On a vanishing product in the integral group ring. American Mathematical Monthly, 88(3):195–196, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Snapper:1981:AGE

[127] Ernst Snapper. An affine generalization of the Euler line. American Mathematical Monthly, 88(3):196–198, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Riley:1981:NSC

[128] Charles Riley. A note on strict convexity. American Mathematical Monthly, 88 (3):198–199, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kertzner:1981:LDE

[129] Stanley Kertzner. The linear Diophantine equation. American Mathematical Monthly, 88(3):200–203, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hueber:1981:UCC

[130] Hermann Hueber. On uniform continuity and compactness in metric spaces. American Mathematical Monthly, 88(3): 204–205, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Deutsch:1981:BZP

[131] Emeric Deutsch. Bounds for the zeros of polynomials. American Mathematical Monthly, 88(3):205–206, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knoebel:1981:ER

[132] R. Arthur Knoebel. Exponentials reiterated. American Mathematical Monthly, 88(4):235–252, April 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brenner:1981:PFT

[133] J. L. Brenner and R. C. Lyndon. Proof of the fundamental theorem of algebra. American Mathematical Monthly, 88(4): 253–256, April 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brown:1981:FPQ

[134] Ezra Brown. The first proof of the quadratic reciprocity law, revisited.

American Mathematical Monthly, 88(4): 257–264, April 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kannai:1981:EPN

[135] Yakar Kannai. An elementary proof of the no-retraction theorem. American Mathematical Monthly, 88(4):264– 268, April 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kraft:1981:ERP

[136] James Kraft and Michael Rosen. Eisenstein reciprocity and nth-power residues. American Mathematical Monthly, 88(4): 269–270, April 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ewell:1981:EPT

[137] John A. Ewell. An easy proof of the triple-product identity. American Mathematical Monthly, 88(4):270–272, April 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Sentance:1981:OCO

[138] W. A. Sentance. Occurrences of consecutive odd powerful numbers. American Mathematical Monthly, 88(4):272– 274, April 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pecaric:1981:NII

[139] Josip E. Pečarić. Note on: “An integral inequality” [Amer. Math. Monthly 61 (1954), 626–631, MR 16, 342] by K. Fan and G. G. Lorentz. American Mathematical Monthly, 88(4):275–276, April 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [1].

Marcus:1981:CNA

[140] Daniel A. Marcus. Classroom notes: An alternative to Euclid’s algorithm. American Mathematical Monthly, 88(4):280– 283, April 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (elec-

tronic). URL http://www.jstor.org/
stable/2320557.

Copeland:1981:CLG

[141] Arthur H. Copeland, Jr. and Albert O.

Shar. Constructing loops from groups. American Mathematical Monthly, 88(4): 283–285, April 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Porter:1981:NAO

[142] G. J. Porter. New angles on an old game.

American Mathematical Monthly, 88(4): 285–286, April 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Davis:1981:TCM

[143] Philip J. Davis. Are there coincidences in mathematics. American Mathematical Monthly, 88(5):311–320, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hrusa:1981:ECC

[144] W. Hrusa and J. L. Troutman. Elementary characterization of classical minima. American Mathematical Monthly, 88(5):321–327, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Griffiths:1981:CVR

[145] H. B. Griffiths. Cayley’s version of the resultant of two polynomials. American Mathematical Monthly, 88(5):328– 338, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Golomb:1981:CCP

[146] Solomon W. Golomb. Corrections to: “Cyclotomic polynomials and factorization theorems” [Amer. Math. Monthly 85 (1978), no. 9, 734–737, MR 80e:10011]. American Mathematical Monthly, 88(5):338–339, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [5].

Boes:1981:FSI

[147] Duane Boes, Richard Darst, and Paul Erdős. Fat, symmetric, irrational Cantor sets. American Mathematical Monthly, 88(5):340–341, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dence:1981:MCE

[148] Thomas P. Dence. On the monotonicity of a class of exponential sequences. American Mathematical Monthly, 88(5): 341–344, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rosen:1981:ATL

[149] Michael Rosen. Abel’s theorem on the lemniscate. American Mathematical Monthly, 88(6):387–395, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Burckel:1981:IAS

[150] R. B. Burckel. Iterating analytic selfmaps of discs. American Mathematical Monthly, 88(6):396–407, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Grosshans:1981:RMC

[151] Frank D. Grosshans. Rigid motions of conics: an introduction to invariant theory. American Mathematical Monthly, 88(6):407–413, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Luchins:1981:WMF

[152] Edith H. Luchins. Women and mathematics: fact and fiction. American Mathematical Monthly, 88(6):413– 419, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bloom:1981:GRC

[153] John Bloom and Lee Whitt. The geometry of rolling curves. American Mathematical Monthly, 88(6):420–426, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Holbrook:1981:SIS

[154] John A. R. Holbrook. Stochastic independence and space-filling curves. American Mathematical Monthly, 88(6): 426–432, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Sternfeld:1981:HCE

[155] Y. Sternfeld. Homeomorphisms of cubes into Euclidean spaces. American Mathematical Monthly, 88(6):436–439, ????

1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Small:1981:MCT

[156] Robert D. Small. Modified convergence of Taylor series. American Mathematical Monthly, 88(6):439–441, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Sobczyk:1981:EIV

[157] Andrew Sobczyk. Equivalence of an identity in vector analysis to quaternion associativity, and ramifications. American Mathematical Monthly, 88(6):441– 443, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lane:1981:MMS

[158] Saunders Mac Lane. Mathematical models: a sketch for the philosophy of mathematics. American Mathematical Monthly, 88(7):462–472, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dubins:1981:MGS

[159] L. E. Dubins and D. A. Freedman. Machiavelli and the Gale–Shapley algorithm. American Mathematical Monthly, 88(7):485–494, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Grattan-Guinness:1981:DLB

[160] I. Grattan-Guinness. On the development of logics between the two World Wars. American Mathematical Monthly, 88(7):495–509, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wong:1981:PCM

[161] Edward T. Wong. Polygons, circulant matrices, and Moore–Penrose inverses. American Mathematical Monthly, 88(7): 509–515, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cooke:1981:APF

[162] Roger L. Cooke. Almost-periodic functions. American Mathematical Monthly, 88(7):515–526, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Newman:1981:DAF

[163] D. J. Newman. Differentiation of asymptotic formulas. American Mathematical Monthly, 88(7):526–527, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Abian:1981:GGM

[164] Alexander Abian. Generalizing the generalized mean-value theorem. American Mathematical Monthly, 88(7):528– 530, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Alefeld:1981:CHM

[165] G. Alefeld. On the convergence of Halley’s method. American Mathematical Monthly, 88(7):530–536, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Katchalski:1981:EPS

[166] M. Katchalski, M. S. Klamkin, and A. Liu. An experience in problem solving. American Mathematical Monthly, 88(8):551–556, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Arthur:1981:WPC

[167] W. B. Arthur. Why a population converges to stability. American Mathematical Monthly, 88(8):557–563, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rappaport:1981:KML

[168] Karen D. Rappaport. S. Kovalevsky: a mathematical lesson. American Mathematical Monthly, 88(8):564–574, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Abikoff:1981:UT

[169] William Abikoff. The uniformization theorem. American Mathematical Monthly, 88(8):574–592, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kenschaft:1981:BWM

[170] Patricia C. Kenschaft. Black women in mathematics in the United States. American Mathematical Monthly, 88(8): 592–604, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Garner:1981:MQS

[171] Cyril W. L. Garner and Agnes M. Herzberg. On McCarty’s queen squares. American Mathematical Monthly, 88(8): 612–613, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stromquist:1981:AHC

[172] Walter Stromquist. Addendum to:

“How to cut a cake fairly” [Amer. Math. Monthly 87 (1980), no. 8, 640–644, MR 81m:05016]. American Mathematical Monthly, 88(8):613–614, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [77].

Shafroth:1981:GFC

[173] Chantal Shafroth. A generalization of the formula for computing the inverse of a matrix. American Mathematical Monthly, 88(8):614–616, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schoenberg:1981:DDJ

[174] I. J. Schoenberg. A direct derivation of a Jacobian identity from elliptic functions. American Mathematical Monthly, 88(8):616–618, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Srinivasan:1981:CFG

[175] Bhama Srinivasan. Characters of finite groups: some uses and mathematical applications. American Mathematical Monthly, 88(9):639–646, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Delahaye:1981:SPP

[176] J.-P. Delahaye. The set of periodic points. American Mathematical Monthly, 88(9):646–651, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bruce:1981:CPC

[177] J. W. Bruce, P. J. Giblin, and C. G. Gibson. On caustics of plane curves. American Mathematical Monthly, 88(9):651– 667, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Narici:1981:STN

[178] Lawrence Narici and Edward Beckenstein. Strange terrain — non-Archimedean spaces. American Mathematical Monthly, 88(9):667–676, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hansen:1981:SFS

[179] Eldon Hansen. Sums of functions satisfying recursion relations. American Mathematical Monthly, 88(9):676–679, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Golomb:1981:NDD

[180] Solomon W. Golomb. Normed division domains. American Mathematical Monthly, 88(9):680–686, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dodziuk:1981:ELH

[181] Jozef Dodziuk. Eigenvalues of the Laplacian and the heat equation. American Mathematical Monthly, 88(9):686– 695, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnsonbaugh:1981:TRS

[182] Richard Johnsonbaugh. The trapezoid rule, Stirling’s formula, and Euler’s constant. American Mathematical Monthly, 88(9):696–698, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kohlberg:1981:ABN

[183] Elon Kohlberg and Abraham Neyman. Asymptotic behavior of nonexpansive mappings in uniformly convex Banach spaces. American Mathematical Monthly, 88(9):698–700, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1981:PI

[184] Donald E. Knuth. A permanent inequality. American Mathematical Monthly, 88 (10):731–740, 798, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Berresford:1981:CT

[185] Geoffrey C. Berresford. Cauchy’s theorem. American Mathematical Monthly, 88(10):741–744, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Guggenheimer:1981:HMH

[186] Heinrich Guggenheimer. The Hilbert model of hyperbolic geometry. American Mathematical Monthly, 88(10):744– 748, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Buchman:1981:ITC

[187] Edwin Buchman. The impossibility of tiling a convex region with unequal equilateral triangles. American Mathematical Monthly, 88(10):748–753, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

McLain:1981:NWG

[188] Katherine E. McLain and Hugh M. Edgar. A note on S. W. Golomb’s: “Cyclotomic polynomials and factorization theorems” [Amer. Math. Monthly 85 (1978), no. 9, 734–737, MR 80e:10011]. American Mathematical Monthly, 88 (10):753, ???? 1981. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [5].

Salat:1981:FMN

[189] Tibor Šalát. On functions that are monotone on no interval. American Mathematical Monthly, 88(10):754–755, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Davis:1981:MSM

[190] Richard A. Davis. More on similarity of matrices. American Mathematical Monthly, 88(10):761–762, ???? 1981. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bonsall:1982:EVM

[191] F. F. Bonsall. A down-to-earth view of mathematics. American Mathematical Monthly, 89(1):8–15, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Duijvestijn:1982:CPS

[192] A. J. W. Duijvestijn, P. J. Federico, and P. Leeuw. Compound perfect squares. American Mathematical Monthly, 89(1): 15–32, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wavrik:1982:CMP

[193] John Wavrik. Computers and the multiplicity of polynomial roots. American Mathematical Monthly, 89(1):34–36, 45– 56, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Small:1982:SPF

[194] Charles Small. A simple proof of the four-squares theorem. American Mathematical Monthly, 89(1):59–61, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Price:1982:ADS

[195] G. Baley Price. Award for distinguished service to Dr. Thornton Carl Fry. American Mathematical Monthly, 89(2):81–83 (1 plate), ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rothman:1982:GBF

[196] Tony Rothman. Genius and biographers:

the fictionalization of Évariste Galois. American Mathematical Monthly, 89(2): 84–106, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Norwood:1982:LP

[197] F. H. Norwood. Long proofs. American Mathematical Monthly, 89(2):110– 112, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Simoson:1982:AP

[198] Andrew Simoson. An “Archimedean”

paradox. American Mathematical Monthly, 89(2):114–116, 125, ???? 1982.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nair:1982:CTI

[199] M. Nair. On Chebyshev-type inequalities for primes. American Mathematical Monthly, 89(2):126–129, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fearnley-Sander:1982:HGP

[200] Desmond Fearnley-Sander. Hermann Grassmann and the prehistory of universal algebra. American Mathematical Monthly, 89(3):161–166, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chicone:1982:GPQ

[201] Carmen Chicone and Jing Huang Tian. On general properties of quadratic systems. American Mathematical Monthly, 89(3):167–178, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Reilly:1982:MCL

[202] Robert C. Reilly. Mean curvature, the Laplacian, and soap bubbles. American Mathematical Monthly, 89(3):180– 188, 197–198, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Li:1982:EQO

[203] Hong Xiang Li. Elementary quadratures of ordinary differential equations. American Mathematical Monthly, 89(3):198– 208, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Shih:1982:ABT

[204] Mau Hsiang Shih. An analog of Bolzano’s theorem for functions of a complex variable. American Mathematical Monthly, 89(3):210–211, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Walter:1982:ONA

[205] Wolfgang Walter. Old and new approaches to Euler’s trigonometric expansions. American Mathematical Monthly, 89(4):225–230, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rosenfeld:1982:HDC

[206] Azriel Rosenfeld. How a digital computer can tell whether a line is straight. American Mathematical Monthly, 89(4): 231–235, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hwang:1982:NCS

[207] F. K. Hwang. New concepts in seeding knockout tournaments. American Mathematical Monthly, 89(4):235–239, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Madguerova:1982:BPG

[208] Andreana S. Madguerova. On Bridges’ proof of the great Picard theorem. American Mathematical Monthly, 89(4): 239, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rudin:1982:NGF

[209] Walter Rudin. Nonuniqueness and growth in first-order differential equations. American Mathematical Monthly, 89(4):241–244, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bose:1982:LDE

[210] A. K. Bose. Linear differential equations on the complex plane. American Mathematical Monthly, 89(4):244–249, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Flanders:1982:FI

[211] Harley Flanders. On the Fresnel integrals. American Mathematical Monthly, 89(4):264–266, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilf:1982:WA

[212] Herbert S. Wilf. What is an answer. American Mathematical Monthly, 89(5): 289–292, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Jacobson:1982:MVT

[213] Bernard Jacobson. On the mean value theorem for integrals. American Mathematical Monthly, 89(5):300–301, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [818].

Challener:1982:CRT

[214] David Challener and Lee Rubel. A converse to Rouché’s theorem. American Mathematical Monthly, 89(5):302– 305, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Salzberg:1982:RPC

[215] Pablo M. Salzberg. A reflection principle for calculating the derivatives of a polynomial. American Mathematical Monthly, 89(5):305–307, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Scott:1982:BTS

[216] Brian M. Scott and Zachary Robinson. The boundary topology of a space. American Mathematical Monthly, 89(5): 307–309, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wolk:1982:IST

[217] E. S. Wolk. On the inadequacy of subnets and transfinite sequences. American Mathematical Monthly, 89(5):310– 311, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Azpeitia:1982:LRT

[218] Alfonso G. Azpeitia. On the Lagrange remainder of the Taylor formula. American Mathematical Monthly, 89(5):311– 312, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rice:1982:RPO

[219] Norman M. Rice. On nth roots of positive operators. American Mathematical Monthly, 89(5):313–314, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Clausing:1982:KTI

[220] Achim Clausing. Kantorovich-type inequalities. American Mathematical Monthly, 89(5):314, 327–330, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fraenkel:1982:HBY

[221] Aviezri S. Fraenkel. How to beat your Wythoff games’ opponent on three fronts. American Mathematical Monthly, 89(6):353–361, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hatcher:1982:CA

[222] William S. Hatcher. Calculus is algebra. American Mathematical Monthly, 89(6):362–370, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Buchman:1982:NHN

[223] Edwin O. Buchman and Frederick A. Valentine. Any new Helly numbers. American Mathematical Monthly, 89(6): 370–375, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Strichartz:1982:RIV

[224] Robert S. Strichartz. Radon inversion — variations on a theme. American Mathematical Monthly, 89(6):377–384, 420– 423, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Richman:1982:MIC

[225] Fred Richman. Meaning and information in constructive mathematics. American Mathematical Monthly, 89(6):385– 388, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ayoub:1982:NGP

[226] Raymond G. Ayoub. On the nonsolvability of the general polynomial. American Mathematical Monthly, 89(6):397– 401, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kalman:1982:CFF

[227] Dan Kalman. Central functions and fixed points. American Mathematical Monthly, 89(6):401–402, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Potts:1982:DDE

[228] Renfrey B. Potts. Differential and difference equations. American Mathematical Monthly, 89(6):402–407, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Janusz:1982:OA

[229] Gerald Janusz and Joseph Rotman.

Outer automorphisms of S_{6}. American Mathematical Monthly, 89(6):407– 410, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bagchi:1982:NOF

[230] Amitava Bagchi and Edward M. Reingold. A naturally occurring function continuous only at irrationals. American Mathematical Monthly, 89(6):411– 417, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wene:1982:LCA

[231] G. P. Wene. A little color in abstract algebra. American Mathematical Monthly, 89(6):417–419, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Clark:1982:SAP

[232] Dean S. Clark. On some abstract properties of binomial coefficients. American Mathematical Monthly, 89(7):433– 443, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fisher:1982:EFI

[233] Dawn Fisher. Extending functions to infinitesimals of finite order. American Mathematical Monthly, 89(7):443– 449, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Snyder:1982:FR

[234] W. M. Snyder. Factoring repunits. American Mathematical Monthly, 89(7): 462–466, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cater:1982:MMF

[235] F. S. Cater. Most monotone functions are not singular. American Mathematical Monthly, 89(7):466–469, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Strang:1982:WC

[236] Gilbert Strang. The width of a chair. American Mathematical Monthly, 89(8): 529–534, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Devaney:1982:BSC

[237] Robert L. Devaney. Blowing up singularities in classical mechanical systems. American Mathematical Monthly, 89(8): 535–552, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnsonbaugh:1982:PNM

[238] Richard Johnsonbaugh and Tadao Murata. Petri nets and marked graphs — mathematical models of concurrent computation. American Mathematical Monthly, 89(8):552–566, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fredricks:1982:STM

[239] Gregory A. Fredricks. Sylvester’s theorem for matrices with smooth entries. American Mathematical Monthly, 89(8): 586–587, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rosay:1982:IHM

[240] Jean-Pierre Rosay. Injective holomorphic mappings. American Mathematical Monthly, 89(8):587–588, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

James:1982:BBS

[241] Robert C. James. Bases in Banach spaces. American Mathematical Monthly, 89(9):625–640, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wong:1982:SCM

[242] Yung Chow Wong and Kai Man Tsang.

A strong converse of Morley’s trisector theorem. American Mathematical Monthly, 89(9):642–653, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brown:1982:FPP

[243] Robert F. Brown. The fixed point property and Cartesian products. American Mathematical Monthly, 89(9):654– 678, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Marshall:1982:CPH

[244] A. W. Marshall and I. Olkin. A convexity proof of Hadamard’s inequality. American Mathematical Monthly, 89(9): 687–688, ???? 1982. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ungar:1982:GHF

[245] Abraham Ungar. Generalized hyperbolic functions. American Mathematical Monthly, 89(9):688–691, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Duncan:1982:TQL

[246] Donald Duncan and William Barnier. On trisection, quintisection, …, etc. American Mathematical Monthly, 89(9): 693, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Proctor:1982:STD

[247] Robert A. Proctor. Solution of two difficult combinatorial problems with linear algebra. American Mathematical Monthly, 89(10):721–734, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Small:1982:E

[248] Charles Small. On the equation xyz = x + y + z = 1. American Mathematical Monthly, 89(10):736–749, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bell:1982:SWW

[249] Murray Bell and John Ginsburg. A space which will not go where its proper subspaces want it to go. American Mathematical Monthly, 89(10):749–751, ???? 1982. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1983:EPE

[250] Donald E. Knuth. Elementary problem E2982, a double infinite sum for |x|. American Mathematical Monthly, 90 (??):54, 1983. ISSN 0002-9890 (print), 1930-0972 (electronic). Solution in [726].

Ortiz:1983:ALC

[251] E. L. Ortiz and T. J. Rivlin. Another look at the Chebyshev polynomials. American Mathematical Monthly, 90(1):3–10, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fletcher:1983:ADJ

[252] R. Fletcher and D. C. Sorensen. An algorithmic derivation of the Jordan canonical form. American Mathematical Monthly, 90(1):12–16, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Miel:1983:CPP

[253] George Miel. Of calculations past and present: the Archimedean algorithm. American Mathematical Monthly, 90(1):

17–35, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rudin:1983:WDM

[254] Walter Rudin. Well-distributed measurable sets. American Mathematical Monthly, 90(1):41–42, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gelbaum:1983:AMP

[255] Bernard R. Gelbaum. An algorithm for the minimal polynomial of a matrix. American Mathematical Monthly, 90(1): 43–44, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Moler:1983:SVA

[256] Cleve Moler and Donald Morrison. Singular value analysis of cryptograms. American Mathematical Monthly, 90(2): 78–87, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fenn:1983:WGS

[257] Roger Fenn. What is the geometry of a surface. American Mathematical Monthly, 90(2):87–98, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

McIntosh:1983:NSC

[258] Richard McIntosh. A necessary and sufficient condition for the primality of Fermat numbers. American Mathematical Monthly, 90(2):98–99, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stout:1983:RD

[259] Quentin F. Stout and Patricia A. Woodworth. Relational databases. American Mathematical Monthly, 90(2):101– 118, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Guthrie:1983:CMC

[260] J. A. Guthrie. A continuous modulus of continuity. American Mathematical Monthly, 90(2):126–127, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hausner:1983:ASC

[261] Melvin Hausner. Applications of a simple counting technique. American Mathematical Monthly, 90(2):127–129, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Mycielski:1983:MCM

[262] Jan Mycielski. The meaning of the conjecture P ≠ NP for mathematical logic. American Mathematical Monthly, 90(2): 129–130, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kendig:1983:AGA

[263] Keith M. Kendig. Algebra, geometry, and algebraic geometry: some interconnections. American Mathematical Monthly, 90(3):161–174, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Leron:1983:SMP

[264] Uri Leron. Structuring mathematical proofs. American Mathematical Monthly, 90(3):174–185, ???? 1983.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Grabiner:1983:WGY

[265] Judith V. Grabiner. Who gave you the epsilon? Cauchy and the origins of rigorous calculus. American Mathematical Monthly, 90(3):185–194, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Duffy:1983:EPI

[266] L. Richard Duffy. An elementary proof of the isomorphism C^{∗} ≈ S^{1}. American Mathematical Monthly, 90(3):201– 202, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Renaud:1983:MIE

[267] J.-C. Renaud. Matrices with integer entries and integer eigenvalues. American Mathematical Monthly, 90(3):202– 203, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See comment [454].

Romero:1983:WC

[268] Juan L. Romero. When is L^{p}(μ) contained in L^{q}(μ)? American Mathematical Monthly, 90(3):203–206, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hiriart-Urruty:1983:SPV

[269] J.-B. Hiriart-Urruty. A short proof of the variational principle for approximate solutions of a minimization problem. American Mathematical Monthly, 90(3):206–207, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Franklin:1983:MME

[270] Joel Franklin. Mathematical methods of economics. American Mathematical Monthly, 90(4):229–244, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Jech:1983:RIT

[271] Thomas Jech. The ranking of incomplete tournaments: a mathematician’s guide to popular sports. American Mathematical Monthly, 90(4):246–266, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See supplement [343].

Marden:1983:CCP

[272] Morris Marden. Conjectures on the critical points of a polynomial. American Mathematical Monthly, 90(4):267– 276, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hartig:1983:RRT

[273] Donald G. Hartig. The Riesz representation theorem revisited. American Mathematical Monthly, 90(4):277–280, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Posey:1983:FPL

[274] E. E. Posey and J. E. Vaughan. Functions with a proper local maximum in each interval. American Mathematical Monthly, 90(4):281–282, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wen:1983:SFC

[275] Liu Wen. A space filling curve. American Mathematical Monthly, 90(4):283, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Choi:1983:TTH

[276] Man Duen Choi. Tricks or treats with the Hilbert matrix. American Mathematical Monthly, 90(5):301–312, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [513].

Hirshon:1983:GCG

[277] R. Hirshon. A group with constant growth rate. American Mathematical Monthly, 90(5):312–317, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schelin:1983:CFA

[278] Charles W. Schelin. Calculator function approximation. American Mathematical Monthly, 90(5):317–325, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schwenk:1983:HSC

[279] Allen J. Schwenk and J. Ian Munro. How small can the mean shadow of a set be. American Mathematical Monthly, 90 (5):325–329, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Blair:1983:UEF

[280] Charles Blair and Lee A. Rubel. A universal entire function. American Mathematical Monthly, 90(5):331–332, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Milnor:1983:GKP

[281] John Milnor. On the geometry of the Kepler problem. American Mathematical Monthly, 90(6):353–365, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Spencer:1983:STL

[282] Joel Spencer. Short theorems with long proofs. American Mathematical Monthly, 90(6):365–366, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fishburn:1983:FRC

[283] P. C. Fishburn and H. O. Pollak. Fixedroute cost allocation. American Mathematical Monthly, 90(6):366–378, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Waterhouse:1983:DSP

[284] William C. Waterhouse. Do symmetric problems have symmetric solutions. American Mathematical Monthly, 90(6): 378–387, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Davidson:1983:PLA

[285] Kenneth R. Davidson. Pointwise limits of analytic functions. American Mathematical Monthly, 90(6):391–394, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rubel:1983:NEC

[286] Lee A. Rubel and Aristomenis Siskakis.

A net of exponentials converging to a nonmeasurable function. American Mathematical Monthly, 90(6):394– 396, ???? 1983. CODEN AMMYAE.

ISSN 0002-9890 (print), 1930-0972 (electronic).

Kindler:1983:SPD

[287] Jürgen Kindler. A simple proof of the Daniell-Stone representation theorem. American Mathematical Monthly, 90(6):396–397, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Austin:1983:EAN

[288] A. Keith Austin. An elementary approach to NP-completeness. American Mathematical Monthly, 90(6):398– 399, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chang:1983:IPE

[289] Geng Zhe Chang and Philip J. Davis. Iterative processes in elementary geometry. American Mathematical Monthly, 90(7):421–431, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hill:1983:DFB

[290] Theodore P. Hill. Determining a fair border. American Mathematical Monthly, 90(7):438–442, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Appelgate:1983:SCF

[291] Harry Appelgate and Hironori Onishi. The slow continued fraction algorithm via 2 × 2 integer matrices. American Mathematical Monthly, 90(7):443– 455, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Coppel:1983:ICS

[292] W. A. Coppel. An interesting Cantor set. American Mathematical Monthly, 90 (7):456–460, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Littlejohn:1983:SFD

[293] Lance L. Littlejohn. Symmetry factors for differential equations. American Mathematical Monthly, 90(7):462– 464, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Haruki:1983:EI

[294] H. Haruki and S. Haruki. Euler’s integrals. American Mathematical Monthly, 90(7):464–466, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [361].

Walker:1983:HVB

[295] James W. Walker. A homology version of the Borsuk-Ulam theorem. American Mathematical Monthly, 90(7):466– 468, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hughes:1983:NMP

[296] John F. Hughes and J. O. Shallit. On the number of multiplicative partitions. American Mathematical Monthly, 90(7): 468–471, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Haimo:1983:CC

[297] Deborah Tepper Haimo and Franklin Tepper Haimo. Comments and complements. American Mathematical Monthly, 90(7):472–478, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Berndt:1983:QRR

[298] Bruce C. Berndt. The quarterly reports of S. Ramanujan. American Mathematical Monthly, 90(8):505–516, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cross:1983:EFG

[299] James T. Cross. The Euler φ-function in the Gaussian integers. American Mathematical Monthly, 90(8):518–528, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bruce:1983:GG

[300] J. W. Bruce and P. J. Giblin. Generic geometry. American Mathematical Monthly, 90(8):529–545, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Krantz:1983:CSD

[301] Steven G. Krantz. Characterization of smooth domains in C by their biholomorphic self-maps. American Mathematical Monthly, 90(8):555–557, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hoffman:1983:SDF

[302] Michael J. Hoffman and Richard Katz. The sequence of derivatives of a C^{∞} function. American Mathematical Monthly, 90(8):557–560, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bullen:1983:IV

[303] P. S. Bullen. An inequality for variations. American Mathematical Monthly, 90(8):560, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kominek:1983:MCS

[304] Z. Kominek. Measure, category, and the sums of sets. American Mathematical Monthly, 90(8):561–562, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Francis:1983:DSS

[305] George K. Francis. Drawing Seifert surfaces that fiber the figure-8 knot complement in S^{3} over S^{1}. American Mathematical Monthly, 90(9):589–599, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Howe:1983:VBL

[306] Roger Howe. Very basic Lie theory.

American Mathematical Monthly, 90(9): 600–623, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Althoen:1983:WDA

[307] Steven C. Althoen and Lawrence D. Kugler. When is R^{2} a division algebra. American Mathematical Monthly, 90(9): 625–635, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ewell:1983:SPF

[308] John A. Ewell. A simple proof of Fermat’s two-square theorem. American Mathematical Monthly, 90(9):635– 637, ???? 1983. CODEN AMMYAE.

ISSN 0002-9890 (print), 1930-0972 (electronic).

Ladas:1983:NSC

[309] G. Ladas, Y. G. Sficas, and I. P. Stavroulakis. Necessary and sufficient conditions for oscillations. American Mathematical Monthly, 90(9):637–640, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Szulkin:1983:UDC

[310] Andrzej Szulkin. R^{3} is the union of disjoint circles. American Mathematical Monthly, 90(9):640–641, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Thompson:1983:AVR

[311] Robert C. Thompson. Author vs. referee: a case history for middle level mathematicians. American Mathematical Monthly, 90(10):661–668, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Spencer:1983:LNU

[312] Joel Spencer. Large numbers and unprovable theorems. American Mathematical Monthly, 90(10):669–675, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Mays:1983:FWP

[313] Michael E. Mays. Functions which parametrize means. American Mathematical Monthly, 90(10):677–683, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Falconer:1983:ARS

[314] K. J. Falconer. Applications of a result on spherical integration to the theory of convex sets. American Mathematical Monthly, 90(10):690–693, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Higgs:1983:IDS

[315] Denis Higgs. Iterating the derived set function. American Mathematical Monthly, 90(10):693–697, ???? 1983. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Massey:1983:CPV

[316] W. S. Massey. Cross products of vectors in higher-dimensional Euclidean spaces. American Mathematical Monthly, 90 (10):697–701, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnston:1983:CSC

[317] Elgin Johnston. A “counterexample”

for the Schwarz–Christoffel transform. American Mathematical Monthly, 90 (10):701–703, ???? 1983. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Saari:1984:NMC

[318] Donald G. Saari and John B. Urenko.

Newton’s method, circle maps, and chaotic motion. American Mathematical Monthly, 91(1):3–17, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [405].

Diamond:1984:RAS

[319] Harvey Diamond and Gregory Gellès. Relations among some classes of subsets of R. American Mathematical Monthly, 91(1):19–22, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Burckel:1984:BSW

[320] R. B. Burckel. Bishop’s Stone-Weierstrass theorem. American Mathematical Monthly, 91(1):22–32, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Jackson:1984:CC

[321] Brad Jackson and Gerhard Ringel. Colorings of circles. American Mathematical Monthly, 91(1):42–49, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fuster:1984:GSI

[322] R. Fuster and A. Marquina. Geometric series in incomplete normed algebras. American Mathematical Monthly, 91(1): 49–51, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

MacCluer:1984:SPF

[323] C. R. MacCluer. A simple proof of the fundamental theorem on finite abelian groups. American Mathematical Monthly, 91(1):52, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kupka:1984:MUU

[324] Joseph Kupka and Karel Prikry. The measurability of uncountable unions. American Mathematical Monthly, 91(2):

85–97, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Shapiro:1984:PPP

[325] Daniel B. Shapiro. A periodicity problem in plane geometry. American Mathematical Monthly, 91(2):97–108, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Phillips:1984:ACP

[326] George M. Phillips. Archimedes and the complex plane. American Mathematical Monthly, 91(2):108–114, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Laird:1984:SCP

[327] P. G. Laird and R. McCann. On some characterizations of polynomials. American Mathematical Monthly, 91(2):114– 116, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brown:1984:PAD

[328] Timothy C. Brown. Poisson approximations and the definition of the Poisson process. American Mathematical Monthly, 91(2):116–123, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

MacDonnell:1984:RMB

[329] Joseph MacDonnell. A ruled Moebius band which self-intersects in a straight line. American Mathematical Monthly, 91(2):125–127, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Miller:1984:AC

[330] Thomas L. Miller and Robert F. Olin. Analytic curves. American Mathematical Monthly, 91(2):127–130, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnson:1984:UFT

[331] G. W. Johnson. An unsymmetric Fubini theorem. American Mathematical Monthly, 91(2):131–133, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gallian:1984:APS

[332] Joseph A. Gallian. Another proof that A_{5} is simple. American Mathematical Monthly, 91(2):134–135, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [421, 422].

Li:1984:GPL

[333] Hung C. Li. A generalized problem of least squares. American Mathematical Monthly, 91(2):135–137, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Christen:1984:DDC

[334] Claude Christen and Frank K. Hwang. Detection of a defective coin with partial weight information. American Mathematical Monthly, 91(3):173–179, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Boyer:1984:PCR

[335] Robert S. Boyer and J. Strother Moore. Proof checking the RSA public key encryption algorithm. American Mathematical Monthly, 91(3):181–189, ????

1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Simoson:1984:THB

[336] Andrew Simoson. On two halves being two wholes. American Mathematical Monthly, 91(3):190–193, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Greenberg:1984:NCH

[337] Marvin Jay Greenberg. Note on the Cayley–Hamilton theorem. American Mathematical Monthly, 91(3):193–195, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See correction [463].

Pecaric:1984:SPJ

[338] Josip E. Pečarić. A simple proof of the Jensen-Steffensen inequality. American Mathematical Monthly, 91(3):195– 196, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gallian:1984:NH

[339] Joseph A. Gallian and James Van Buskirk. The number of homomorphisms from Z_{m} into Z_{n}. American Mathematical Monthly, 91(3):196– 197, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilker:1984:MEE

[340] J. B. Wilker. Möbius equivalence and Euclidean symmetry. American Mathematical Monthly, 91(4):225–247, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Howe:1984:CVB

[341] Roger Howe. Correction to: “Very basic Lie theory”. American Mathematical Monthly, 91(4):247, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Levasseur:1984:PPW

[342] Kenneth M. Levasseur. A probabilistic proof of the Weierstrass approximation theorem. American Mathematical Monthly, 91(4):249–250, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [413].

Stob:1984:SMG

[343] Michael Stob. A supplement to: “A mathematician’s guide to popular sports” [Amer. Math. Monthly 90 (1983), no. 4, 246–266, MR 85i:05122a] by T. Jech. American Mathematical Monthly, 91(5):277–282, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [271].

Eisemann:1984:NTA

[344] Kurt Eisemann. Number-theoretic analysis and extensions of “the most complicated and fantastic card trick ever invented”. American Mathematical Monthly, 91(5):284–289, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Guinand:1984:ELT

[345] Andrew P. Guinand. Euler lines, tritangent centers, and their triangles. American Mathematical Monthly, 91(5):290– 300, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rudin:1984:IFP

[346] Walter Rudin. The inner function problem. American Mathematical Monthly, 91(5):301–302, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pourahmadi:1984:TES

[347] Mohsen Pourahmadi. Taylor expansion of exp(∑_{k=0}^{∞} a_{k}z^{k}) and some applications. American Mathematical Monthly, 91(5):303–307, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cater:1984:VWN

[348] F. S. Cater. On van der Waerden’s nowhere differentiable function. American Mathematical Monthly, 91(5):307– 308, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dixon:1984:FPT

[349] John D. Dixon. Factorization and primality tests. American Mathematical Monthly, 91(6):333–352, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Phillips:1984:ASF

[350] G. M. Phillips. Aitken sequences and Fibonacci numbers. American Mathematical Monthly, 91(6):354–357, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Magyar:1984:RQ

[351] Zoltán Magyar. A recursion on quadruples. American Mathematical Monthly, 91(6):360–362, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Barany:1984:HTV

[352] I. Bárány, M. Katchalski, and János Pach. Helly’s theorem with volumes. American Mathematical Monthly, 91(6): 362–365, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stroeker:1984:HSD

[353] R. J. Stroeker. How to solve a Diophantine equation — a numbertheoretic excursion. American Mathematical Monthly, 91(7):385–392, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Burrows:1984:SPI

[354] B. L. Burrows and R. F. Talbot. Sums of powers of integers. American Mathematical Monthly, 91(7):394–403, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Baxley:1984:LMP

[355] John V. Baxley and John C. Moorhouse. Lagrange multiplier problems in economics. American Mathematical Monthly, 91(7):404–412, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Avis:1984:NFN

[356] David Avis. The number of furthest neighbour pairs of a finite planar set. American Mathematical Monthly, 91(7): 417–420, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lewis:1984:CPT

[357] R. P. Lewis. A combinatorial proof of the triple product identity. American Mathematical Monthly, 91(7):420–423, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schattschneider:1984:TG

[358] Doris J. Schattschneider. The taxicab group. American Mathematical Monthly, 91(7):423–428, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ball:1984:ACP

[359] B. J. Ball. Arcwise connectedness and the persistence of errors. American Mathematical Monthly, 91(7):431– 433, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Henle:1984:TPI

[360] J. M. Henle. Tangent planes with infinitesimals. American Mathematical Monthly, 91(7):433–435, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Williams:1984:LEE

[361] Kenneth S. Williams. Letter to the editor: “Euler’s integrals” [Amer. Math. Monthly 90 (1983), no. 7, 464–466, MR 84k:26012], by H. Haruki and S. Haruki. American Mathematical Monthly, 91(7): 455, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [294].

Knuth:1984:TPP

[362] Donald E. Knuth. The toilet paper problem. American Mathematical Monthly, 91(8):465–470, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Boolos:1984:LP

[363] George Boolos. The logic of provability. American Mathematical Monthly, 91 (8):470–480, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Scherer:1984:SNT

[364] Karl Scherer. Some new types of closure properties in the plane. American Mathematical Monthly, 91(8):480–487, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Henry:1984:API

[365] Myron S. Henry. Approximation by polynomials: interpolation and optimal nodes. American Mathematical Monthly, 91(8):497–499, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Spigler:1984:DLM

[366] R. Spigler. Double limits and matched asymptotic expansions. American Mathematical Monthly, 91(8):501–505, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Tsing:1984:IDB

[367] Nam Kiu Tsing. Infinite-dimensional Banach spaces must have uncountable basis—an elementary proof. American Mathematical Monthly, 91(8):505– 506, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Feintuch:1984:ME

[368] Avraham Feintuch and Matatyahu Rubin. The matrix equation AX − XB = C. American Mathematical Monthly, 91 (8):506–507, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Morsche:1984:DLP

[369] H. G. ter Morsche and G. W. Veltkamp.

A discrete Landau problem. American Mathematical Monthly, 91(8):508– 509, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Weil:1984:E

[370] André Weil. Euler. American Mathematical Monthly, 91(9):537–542, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Birman:1984:TLG

[371] Graciela S. Birman and Katsumi Nomizu. Trigonometry in Lorentzian geometry. American Mathematical Monthly, 91(9):543–549, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Horst:1984:RSL

[372] H. J. ter Horst. Riemann-Stieltjes and Lebesgue-Stieltjes integrability. American Mathematical Monthly, 91(9):551– 559, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Morris:1984:EPH

[373] Sidney A. Morris. An elementary proof that the Hilbert cube is compact. American Mathematical Monthly, 91(9):563– 564, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cater:1984:PUI

[374] F. S. Cater. A partition of the unit interval. American Mathematical Monthly, 91(9):564–566, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wolfram:1984:GBC

[375] Stephen Wolfram. Geometry of binomial coefficients. American Mathematical Monthly, 91(9):566–571, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Richards:1984:RNC

[376] I. M. Richards. A remark on the number of cyclic subgroups of a finite group. American Mathematical Monthly, 91(9): 571–572, ???? 1984. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Koch:1984:MI

[377] Richard Koch. Matrix invariants. American Mathematical Monthly, 91(9):573– 575, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Taylor:1984:LMR

[378] Angus E. Taylor. A life in mathematics remembered. American Mathematical Monthly, 91(10):605–618, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cater:1984:DNA

[379] F. S. Cater. Differentiable, nowhere analytic functions. American Mathematical Monthly, 91(10):618–624, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schechter:1984:SDS

[380] Murray Schechter. Summation of divergent series by computer. American Mathematical Monthly, 91(10):629– 632, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chang:1984:BPS

[381] Geng Zhe Chang. Bernstein polynomials via the shifting operator. American Mathematical Monthly, 91(10):634– 638, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Solomon:1984:TCL

[382] Frederick Solomon. A theorem concerning Lorentz transformations. American Mathematical Monthly, 91(10):638– 641, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Maehara:1984:JCT

[383] Ryuji Maehara. The Jordan curve theorem via the Brouwer fixed point theorem. American Mathematical Monthly, 91(10):641–643, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gerber:1984:WFR

[384] Hans U. Gerber. Wronski’s formula and the resultant of two polynomials. American Mathematical Monthly, 91(10):644– 646, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnson:1984:EAE

[385] Bruce R. Johnson. An elementary approach for extending Poisson processes to the nonstationary case. American Mathematical Monthly, 91(10):646– 648, ???? 1984. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1985:PCS

[386] Donald E. Knuth. Problem E3106, A curious sum for Euler’s totient function. American Mathematical Monthly, 92 (??):590, 1985. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lehmer:1985:SSP

[387] Emma Lehmer. On square-separable primes. American Mathematical Monthly, 92(??):719–720, ???? 1985. CODEN CACMA2. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lagarias:1985:PG

[388] Jeffrey C. Lagarias. The 3x + 1 problem and its generalizations. American Mathematical Monthly, 92(1):3–23, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fisher:1985:PP

[389] J. Chris Fisher, D. Ruoff, and J. Shilleto. Perpendicular polygons. American Mathematical Monthly, 92(1):23– 37, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bardsley:1985:CPS

[390] W. G. Bardsley and R. M. W. Wood. Critical points and sigmoidicity of positive rational functions. American Mathematical Monthly, 92(1):37–48, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Olkin:1985:PPT

[391] Ingram Olkin. A probabilistic proof of a theorem of Schur. American Mathematical Monthly, 92(1):50–51, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Reiner:1985:EMT

[392] David L. Reiner. Enumeration in music theory. American Mathematical Monthly, 92(1):51–54, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bressoud:1985:BEP

[393] David M. Bressoud and Doron Zeilberger. Bijecting Euler’s partitionsrecurrence. American Mathematical Monthly, 92(1):54–55, ???? 1985. CO-DEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wos:1985:AR

[394] L. Wos. Automated reasoning. American Mathematical Monthly, 92(2):85– 92, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Abian:1985:SIS

[395] Alexander Abian. Solvability of infinite systems of polynomial equations over the field of complex numbers. American Mathematical Monthly, 92(2):94– 98, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [429] and letter to the editor

Pittenger:1985:LMV

[396] A. O. Pittenger. The logarithmic mean in n variables. American Mathematical Monthly, 92(2):99–104, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fraenkel:1985:SN

[397] Aviezri S. Fraenkel. Systems of numeration. American Mathematical Monthly, 92(2):105–114, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Walter:1985:EPC

[398] Wolfgang Walter. An elementary proof of the Cauchy-Kowalevsky theorem. American Mathematical Monthly, 92(2): 115–126, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Berndt:1985:GFH

[399] Bruce C. Berndt. The gamma function and the Hurwitz zeta-function. American Mathematical Monthly, 92(2):126– 130, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gander:1985:HIM

[400] Walter Gander. On Halley’s iteration method. American Mathematical Monthly, 92(2):131–134, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chicone:1985:CCH

[401] Carmen Chicone, N. J. Kalton, and Ira J. Papick. A converse for the Cayley– Hamilton theorem. American Mathematical Monthly, 92(2):134–136, ????

1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnson:1985:ECW

[402] Jerry Johnson. An elementary characterization of weak convergence of measures. American Mathematical Monthly, 92(2):136–137, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Diamond:1985:ISC

[403] Harvey Diamond and Gregory Gelles.

Interlaced second category sets. American Mathematical Monthly, 92(2):138– 140, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Snapper:1985:IEC

[404] Ernst Snapper. An ingrained error concerning resultants. American Mathematical Monthly, 92(2):141, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cosnard:1985:LEN

[405] M. Cosnard and C. Masse. Letter to the editor: “Newton’s method, circle maps, and chaotic motion” [Amer. Math. Monthly 91 (1984), no. 1, 3– 17, MR 85a:58060] by D. Saari and J. Urenko. American Mathematical Monthly, 92(2):157–158, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [318].

Roselle:1985:ADS

[406] David Roselle. Award for distinguished service to Professor Everett Pitcher. American Mathematical Monthly, 92(3):

169–170, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1985:ATM

[407] Donald E. Knuth. Algorithmic thinking and mathematical thinking. American Mathematical Monthly, 92(3):170– 181, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). This is a revised version of [823].

Britt:1985:ALD

[408] Jonathan Britt. The anatomy of lowdimensional stable singularities. American Mathematical Monthly, 92(3):183– 201, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Carvalho:1985:CML

[409] F. J. Craveiro de Carvalho. Characterizing maximally looped closed curves. American Mathematical Monthly, 92(3): 202–207, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Leach:1985:GAC

[410] Ronald J. Leach. On Gelbaum’s algorithm for computing the minimal polynomial of a matrix. American Mathematical Monthly, 92(3):208–209, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Drobot:1985:CFD

[411] Vladimir Drobot and MichałMorayne. Continuous functions with a dense set of proper local maxima. American Mathematical Monthly, 92(3):209–211, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Harary:1985:DGC

[412] Frank Harary and Robert W. Robinson.

The diameter of a graph and its complement. American Mathematical Monthly, 92(3):211–212, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [485].

Levasseur:1985:LEP

[413] Kenneth M. Levasseur. Letter to the editor: “A probabilistic proof of the Weierstrass approximation theorem” [Amer. Math. Monthly 91 (1984), no. 4, 249– 250, MR 85h:41016]. American Mathematical Monthly, 92(3):227, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [342].

Akin:1985:BS

[414] Ethan Akin and Morton Davis. Bulgarian solitaire. American Mathematical Monthly, 92(4):237–250, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilf:1985:SEC

[415] Herbert S. Wilf. Some examples of combinatorial averaging. American Mathematical Monthly, 92(4):250–261, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gale:1985:MMS

[416] David Gale and Marilda Sotomayor.

Ms. Machiavelli and the stable matching problem. American Mathematical Monthly, 92(4):261–268, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Waterhouse:1985:WOE

[417] William C. Waterhouse. When one equation solves them all. American Mathematical Monthly, 92(4):270–273, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Papp:1985:AFE

[418] F. J. Papp. The d’Alembert functional equation. American Mathematical Monthly, 92(4):273–275, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Arnold:1985:DSA

[419] L. K. Arnold, S. J. Benkoski, and B. J. McCabe. The discriminator (a simple application of Bertrand’s postulate). American Mathematical Monthly, 92(4): 275–277, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lipschutz:1985:NGM

[420] Seymour Lipschutz. Notes on graphs and matrix inequalities. American Mathematical Monthly, 92(4):277–280, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Teo:1985:LEA

[421] K. L. Teo and M. D. Hendy. Letter to the editor: “Another proof that A_{5} is simple” [Amer. Math. Monthly 91 (1984), no. 2, 134–135, MR 85h:20020] by J. A. Gallian. American Mathematical Monthly, 92(4):303, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [332, 422].

Gallian:1985:LEA

[422] Joseph A. Gallian. Letter to the editor: “Another proof that A_{5} is simple” [Amer. Math. Monthly 91 (1984), no. 2, 134–135, MR 85h:20020]. American Mathematical Monthly, 92(4):303– 304, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [332, 421].

Bloore:1985:AHP

[423] F. J. Bloore and H. R. Morton. Advice on hanging pictures. American Mathematical Monthly, 92(5):309–321, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rootselaar:1985:HSS

[424] B. van Rootselaar. How to solve the system x′ = Ax. American Mathematical Monthly, 92(5):321–327, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stone:1985:TPS

[425] A. H. Stone. Trees and power-sums.

American Mathematical Monthly, 92(5): 328–331, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [512].

Osserman:1985:FMV

[426] Robert Osserman. The four-or-more vertex theorem. American Mathematical Monthly, 92(5):332–337, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Leader:1985:IEP

[427] Solomon Leader. The inclusionexclusion probability formulas by Taylor’s theorem. American Mathematical Monthly, 92(5):343–345, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Charnow:1985:TLO

[428] A. Charnow and E. Charnow. On transcendental linear operators. American Mathematical Monthly, 92(5):345– 347, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Biler:1985:DTT

[429] Piotr Biler. Dini type theorems on positive series. American Mathematical Monthly, 92(5):347–349, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letters to the editor [395, 533].

Burgess:1985:CS

[430] C. E. Burgess. Classification of surfaces. American Mathematical Monthly, 92(5):349–354, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kimelfeld:1985:ICM

[431] Boris Kimelfeld. An inequality concerning minors of a semidefinite matrix. American Mathematical Monthly, 92(5): 354–355, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chernoff:1985:LEP

[432] Paul R. Chernoff. Letter to the editor: “Pointwise convergence of Fourier series” [Amer. Math. Monthly 87 (1980), no. 5, 399–400, MR 81b:42028]. American Mathematical Monthly, 92(5):373– 374, ???? 1985. CODEN AMMYAE.

ISSN 0002-9890 (print), 1930-0972 (electronic). See [54].

Larsen:1985:RRG

[433] Mogens Esrom Larsen. Rubik’s revenge:

the group theoretical solution. American Mathematical Monthly, 92(6):381– 390, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

MacGregor:1985:LMG

[434] T. H. MacGregor. Linear methods in geometric function theory. American Mathematical Monthly, 92(6):392– 406, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cull:1985:THA

[435] Paul Cull and E. F. Ecklund, Jr. Towers of Hanoi and analysis of algorithms. American Mathematical Monthly, 92(6): 407–420, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Connor:1985:SPS

[436] Jeff Connor. A short proof of Steinhaus’ theorem on summability. American Mathematical Monthly, 92(6):420– 421, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Thomas:1985:CCN

[437] Robin Thomas. A combinatorial construction of a nonmeasurable set. American Mathematical Monthly, 92(6):421– 422, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bankston:1985:TPE

[438] Paul Bankston and Ralph Fox. Topological partitions of Euclidean space by spheres. American Mathematical Monthly, 92(6):423–424, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dixon:1985:LEF

[439] John D. Dixon. Letter to the editor: “Factorization and primality tests”. American Mathematical Monthly, 92(6): 444, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lehmer:1985:ISI

[440] D. H. Lehmer. Interesting series involving the central binomial coefficient. American Mathematical Monthly, 92(7): 449–457, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

McKee:1985:LGT

[441] T. A. McKee. The logic of graphtheoretic duality. American Mathematical Monthly, 92(7):457–464, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rogalski:1985:IAS

[442] Marc Rogalski and Jean Saint-Raymond. Inequalities about symmetric compact convex sets in the plane. American Mathematical Monthly, 92(7):466– 480, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wallen:1985:MIP

[443] Lawrence J. Wallen. Modified iteration and probability. American Mathematical Monthly, 92(7):481–485, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Villani:1985:ANI

[444] Alfonso Villani. Another note on the inclusion L^{p}(μ) ⊂ L^{q}(μ). American Mathematical Monthly, 92(7):485–487, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chaves:1985:SWA

[445] M. Arala Chaves. Spaces where all continuity is uniform. American Mathematical Monthly, 92(7):487–489, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rudin:1985:URI

[446] Walter Rudin. Unique right inverses are two-sided. American Mathematical Monthly, 92(7):489–490, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Blom:1985:SPE

[447] Gunnar Blom. A simple property of exchangeable random variables. American Mathematical Monthly, 92(7):491– 492, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lord:1985:SCF

[448] N. J. Lord. Simultaneous complements in finite-dimensional vector spaces. American Mathematical Monthly, 92(7): 492–493, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pereira:1985:SPC

[449] N. Costa Pereira. A short proof of Chebyshev’s theorem. American Mathematical Monthly, 92(7):494–495, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chang:1985:PMI

[450] Geng Zhe Chang. Planar metric inequalities derived from the Vandermonde determinant. American Mathematical Monthly, 92(7):495–499, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Paul:1985:CPP

[451] Jerome L. Paul. Combinatorial proofs of Pascal’s formula for sums of powers of the integers. American Mathematical Monthly, 92(7):499–501, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Baker:1985:NCI

[452] I. N. Baker and P. J. Rippon. A note on complex iteration. American Mathematical Monthly, 92(7):501–504, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Page:1985:CCL

[453] Warren Page. Compactness and closedness in locally compact Hausdorff spaces. American Mathematical Monthly, 92(7):504–506, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ortega:1985:CMI

[454] James M. Ortega. Comment on: “Matrices with integer entries and integer eigenvalues” by J.-C. Renaud [Amer. Math. Monthly 90 (1983), no. 3, 202– 203, MR 84c:15024 ] and “Generation of test matrices by similarity transformations” by Ortega [Comm. ACM 7 (1964), 377–378, MR 29 #5375]. American Mathematical Monthly, 92(7):526, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [822, 267].

Chan:1985:HMI

[455] N. N. Chan and Man Kam Kwong. Hermitian matrix inequalities and a conjecture. American Mathematical Monthly, 92(8):533–541, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dawson:1985:MS

[456] R. J. MacG. Dawson. Monostatic simplexes. American Mathematical Monthly, 92(8):541–546, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Veldkamp:1985:IPP

[457] G. R. Veldkamp. The isoperimetric point and the point(s) of equal detour in a triangle. American Mathematical Monthly, 92(8):546–558, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Isaacs:1985:SPR

[458] I. M. Isaacs. Solution of polynomials by real radicals. American Mathematical Monthly, 92(8):571–575, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gupta:1985:TCW

[459] Haragauri N. Gupta. A theorem in combinatorics and Wilson’s theorem. American Mathematical Monthly, 92(8):575– 576, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Alperin:1985:ABC

[460] Roger C. Alperin. p-adic binomial coefficients mod p. American Mathematical Monthly, 92(8):576–578, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hirschhorn:1985:SPJ

[461] Michael D. Hirschhorn. A simple proof of Jacobi’s two-square theorem. American Mathematical Monthly, 92(8):579– 580, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Minassian:1985:SST

[462] Donald P. Minassian. A simple structure theorem for two-generator, onerelation groups. American Mathematical Monthly, 92(8):580–583, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Greenberg:1985:CNC

[463] Marvin Jay Greenberg. Correction to: “Note on the Cayley–Hamilton theorem” [Amer. Math. Monthly 91 (1984), no. 3, 193–195, MR 85c:15023]. American Mathematical Monthly, 92(8):583, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [337].

Varberg:1985:PTR

[464] Dale E. Varberg. Pick’s theorem revisited. American Mathematical Monthly, 92(8):584–587, ???? 1985. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wall:1985:USE

[465] Charles R. Wall. Unbounded sequences of Euler-Dedekind means. American Mathematical Monthly, 92(8):587, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Turner:1985:RG

[466] Edward C. Turner and Karen F. Gold.

Rubik’s groups. American Mathematical Monthly, 92(9):617–629, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Spring:1985:SDT

[467] D. Spring. On the second derivative test for constrained local extrema. American Mathematical Monthly, 92(9):631– 643, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Marden:1985:SRT

[468] Morris Marden. The search for a Rolle’s theorem in the complex domain. American Mathematical Monthly, 92(9):643– 650, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hilton:1985:ASA

[469] Peter Hilton. On all sorts of automorphisms. American Mathematical Monthly, 92(9):650–656, ???? 1985.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Shuchat:1985:GLS

[470] Alan Shuchat. Generalized least squares and eigenvalues. American Mathematical Monthly, 92(9):656–659, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Owings:1985:CPC

[471] James C. Owings, Jr. A combinatorial proof of a criterion for normality. American Mathematical Monthly, 92(9):662– 663, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Giblin:1985:LSP

[472] P. J. Giblin and S. A. Brassett. Local symmetry of plane curves. American Mathematical Monthly, 92(10):689– 707, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gerla:1985:GP

[473] G. Gerla and R. Volpe. Geometry without points. American Mathematical Monthly, 92(10):707–711, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Weaver:1985:CCS

[474] James R. Weaver. Centrosymmetric (cross-symmetric) matrices, their basic properties, eigenvalues, and eigenvectors. American Mathematical Monthly, 92(10):711–717, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Clark:1985:CTC

[475] Dean S. Clark. A combinatorial theorem on circulant matrices. American Mathematical Monthly, 92(10):725–729, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Penney:1985:MRS

[476] David E. Penney and Carl Pomerance.

Multiplicative relations for sums of initial kth powers. American Mathematical Monthly, 92(10):729–731, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Grinberg:1985:SHS

[477] Eric L. Grinberg. On the smoothness hypothesis in Sard’s theorem. American Mathematical Monthly, 92(10):733– 734, ???? 1985. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schoenberg:1986:CAR

[478] I. J. Schoenberg. A conjectured analogue of Rolle’s theorem for polynomials with real or complex coefficients. American Mathematical Monthly, 93(1):8–13, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

DeVilliers:1986:ICL

[479] J. M. De Villiers and P. N. Robinson.

The interval of convergence and limiting functions of a hyperpower sequence. American Mathematical Monthly, 93(1): 13–23, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Namias:1986:SDS

[480] Victor Namias. A simple derivation of Stirling’s asymptotic series. American Mathematical Monthly, 93(1):25– 29, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Beutelspacher:1986:CBT

[481] Albrecht Beutelspacher. 21 − 6 = 15: a connection between two distinguished geometries. American Mathematical Monthly, 93(1):29–41, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Krantz:1986:ASS

[482] Steven G. Krantz and T. D. Parsons. Antisocial subcovers of selfcentered coverings. American Mathematical Monthly, 93(1):45–48, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kaufman:1986:LCB

[483] Edwin H. Kaufman, Jr. and Terry D. Lenker. Linear convergence and the bisection algorithm. American Mathematical Monthly, 93(1):48–51, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Salama:1986:GIE

[484] Ibrahim A. Salama and Lawrence L. Kupper. A geometric interpretation for the Eulerian numbers. American Mathematical Monthly, 93(1):51– 52, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Straffin:1986:LED

[485] Philip D. Straffin, Jr. Letter to the editor: “The diameter of a graph and its complement” [Amer. Math. Monthly 92 (1985), no. 3, 211–212, MR 87j:05139a] by F. Harary and R. W. Robinson. American Mathematical Monthly, 93(1): 76, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [412].

Laforgia:1986:SCS

[486] Andrea Laforgia and Martin E. Muldoon. Some consequences of the Sturm comparison theorem. American Mathematical Monthly, 93(2):89–94, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chance:1986:GDD

[487] William A. Chance. A geometric derivation of the distribution of the correlation coefficient |r| when ρ = 0. American Mathematical Monthly, 93(2):94– 98, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Allen:1986:POP

[488] Thomas Tracy Allen. Pólya’s orchard problem. American Mathematical Monthly, 93(2):98–104, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Leonard:1986:CRD

[489] Philip A. Leonard. Cyclic relative difference sets. American Mathematical Monthly, 93(2):106–111, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

McCoy:1986:CFX

[490] T. L. McCoy. On “cos f(x) = f(sin x)”. American Mathematical Monthly, 93(2): 111–115, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Robertson:1986:DBN

[491] Jack M. Robertson and Andrew F. Siegel. Designing Buffon’s needle for a given crossing distribution. American Mathematical Monthly, 93(2):116– 119, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Searcoid:1986:TEG

[492] Mícheál Ó Searcóid and Desmond MacHale. Two elementary generalisations of Boolean rings. American Mathematical Monthly, 93(2):121–122, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Diaconis:1986:EPS

[493] P. Diaconis and D. Freedman. An elementary proof of Stirling’s formula. American Mathematical Monthly, 93(2): 123–125, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Mattics:1986:BNM

[494] L. E. Mattics and F. W. Dodd. A bound for the number of multiplicative partitions. American Mathematical Monthly, 93(2):125–126, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cooper:1986:GSP

[495] Curtis Cooper. Geometric series and a probability problem. American Mathematical Monthly, 93(2):126–127, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Eidswick:1986:CPW

[496] J. A. Eidswick. Cubelike puzzles — what are they and how do you solve them. American Mathematical Monthly, 93(3):157–176, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schmidt:1986:AAC

[497] E. J. P. Georg Schmidt. An alternative approach to canonical forms of matrices. American Mathematical Monthly, 93(3):176–184, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Grabiner:1986:TET

[498] Sandy Grabiner. The Tietze extension theorem and the open mapping theorem. American Mathematical Monthly, 93(3):190–191, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Keller:1986:PH

[499] Joseph B. Keller. The probability of heads. American Mathematical Monthly, 93(3):191–197, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Parsons:1986:ACR

[500] T. D. Parsons. Ancestors, cardinals, and representatives. American Mathematical Monthly, 93(3):197–200, ???? 1986.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lenard:1986:NLT

[501] A. Lenard. A note on Liouville’s theorem. American Mathematical Monthly, 93(3):200–201, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Eisemann:1986:SDC

[502] Kurt Eisemann. A self-dual card trick based on congruences and k-shuffles. American Mathematical Monthly, 93(3): 201–205, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1986:SPC

[503] Donald E. Knuth. Solution to problem 6480, A Catalonian sum. American Mathematical Monthly, 93(3):220, March 1986. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ungar:1986:RTC

[504] Peter Ungar. Review of three calculus textbooks. American Mathematical Monthly, 93(3):221–230, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Axler:1986:HFC

[505] Sheldon Axler. Harmonic functions from a complex analysis viewpoint. American Mathematical Monthly, 93(4):246– 258, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cleary:1986:NGN

[506] Joan Cleary, Sidney A. Morris, and David Yost. Numerical geometry — numbers for shapes. American Mathematical Monthly, 93(4):260–275, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Small:1986:STS

[507] Charles Small. Sums of three squares and levels of quadratic number fields. American Mathematical Monthly, 93(4): 276–279, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lion:1986:SPD

[508] Georges A. Lion. A simple proof of the Dirichlet–Jordan convergence test. American Mathematical Monthly, 93(4): 281–282, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Turk:1986:FDP

[509] Jan Turk. The fixed divisor of a polynomial. American Mathematical Monthly, 93(4):282–286, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brandl:1986:IPR

[510] Rolf Brandl. Integer polynomials that are reducible modulo all primes. American Mathematical Monthly, 93(4):286– 288, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lehmer:1986:CPS

[511] D. H. Lehmer. Coloring the Platonic solids. American Mathematical Monthly, 93(4):288–292, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [816].

Gessel:1986:LET

[512] Ira Gessel. Letter to the editor: “Trees and power-sums” [Amer. Math. Monthly 92 (1985), no. 5, 328–331, MR 87e:05016a] by A. H. Stone. American Mathematical Monthly, 93(4):323– 324, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [425].

Weintraub:1986:LET

[513] Steven H. Weintraub. Letter to the editor: “Tricks or treats with the Hilbert matrix” [Amer. Math. Monthly 90 (1983), no. 5, 301–312, MR 84h:47031] by M. D. Choi. American Mathematical Monthly, 93(4):324, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [276].

Aldous:1986:SCS

[514] David Aldous and Persi Diaconis. Shuffling cards and stopping times. American Mathematical Monthly, 93(5):333– 348, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Leader:1986:WDN

[515] Solomon Leader. What is a differential? A new answer from the generalized Riemann integral. American Mathematical Monthly, 93(5):348–356, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilde:1986:TLD

[516] Alan C. Wilde. Transformations leaving the determinant of circulant matrices invariant. American Mathematical Monthly, 93(5):356–361, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hancl:1986:SPI

[517] Jaroslav Hančl. A simple proof of the irrationality of π^{4}. American Mathematical Monthly, 93(5):374–375, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cecil:1986:PCM

[518] Thomas E. Cecil and Patrick J. Ryan.

The principal curvatures of the monkey saddle. American Mathematical Monthly, 93(5):380–382, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gilmer:1986:ZDC

[519] Robert Gilmer. Zero divisors in commutative rings. American Mathematical Monthly, 93(5):382–387, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ikebe:1986:EAF

[520] Yasuhiko Ikebe and Toshiyuki Inagaki.

An elementary approach to the functional calculus for matrices. American Mathematical Monthly, 93(5):390– 392, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Burgstahler:1986:ASP

[521] Sylvan Burgstahler. An algorithm for solving polynomial equations. American Mathematical Monthly, 93(6):421– 430, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kedem:1986:SCS

[522] Benjamin Kedem. A stochastic characterization of the sine function. American Mathematical Monthly, 93(6):430– 440, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Macdonald:1986:CTP

[523] I. D. Macdonald. Commutators and their products. American Mathematical Monthly, 93(6):440–444, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Farwig:1986:VLP

[524] R. Farwig and D. Zwick. A variation on the Landau problem. American Mathematical Monthly, 93(6):444–451, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Edwards:1986:QRS

[525] A. W. F. Edwards. A quick route to sums of powers. American Mathematical Monthly, 93(6):451–455, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Walls:1986:AG

[526] Gary L. Walls. Automorphism groups. American Mathematical Monthly, 93(6): 459–462, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bosch:1986:FSM

[527] A. J. Bosch. The factorization of a square matrix into two symmetric matrices. American Mathematical Monthly, 93(6):462–464, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Benavides:1986:HMZ

[528] Tomás Domínguez Benavides. How many zeros does a continuous function have. American Mathematical Monthly, 93(6):464–466, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wimp:1986:QGM

[529] Jet Wimp. Quadrature with generalized means. American Mathematical Monthly, 93(6):466–468, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Smyth:1986:CPG

[530] C. J. Smyth. A coloring proof of a generalisation of Fermat’s little theorem. American Mathematical Monthly, 93(6): 469–471, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hoare:1986:IBP

[531] A. H. M. Hoare. An involution of blocks in the partitions of n. American Mathematical Monthly, 93(6):475–476, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Anderson:1986:LES

[532] David F. Anderson. Letter to the editor:

“Solvability of infinite systems of polynomial equations over the field of complex numbers” [Amer. Math. Monthly 92 (1985), no. 2, 94–98, MR 86c:12004] by A. Abian. American Mathematical Monthly, 93(6):496–497, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See

Pelling:1986:LED

[533] M. J. Pelling. Letter to the editor: “Dini type theorems on positive series” [Amer. Math. Monthly 92 (1985), no. 5, 347– 349, MR 86m:40001] by P. Biler. American Mathematical Monthly, 93(6):497– 498, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [429].

Korevaar:1986:LBC

[534] J. Korevaar. Ludwig Bieberbach’s conjecture and its proof by Louis de Branges. American Mathematical Monthly, 93(7):505–514, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bogart:1986:NSM

[535] Kenneth P. Bogart and Peter G. Doyle. Nonsexist solution of the ménage problem. American Mathematical Monthly, 93(7):514–519, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Borwein:1986:NAS

[536] David Borwein and Jonathan M. Borwein. A note on alternating series in several dimensions. American Mathematical Monthly, 93(7):531–539, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zivaljevic:1986:IME

[537] Rade T. Živaljević. Infinitesimals, microsimplexes and elementary homology theory. American Mathematical Monthly, 93(7):540–544, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Barnett:1986:FRT

[538] S. Barnett. Forms of the resultant of two polynomials. American Mathematical Monthly, 93(7):551–552, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Jacobson:1986:IBP

[539] Eliot T. Jacobson and Alan E. Parks.

Infinite branches of the phi-tree. American Mathematical Monthly, 93(7):552– 554, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Aron:1986:H

[540] Richard M. Aron and Gerd H. Fricke.

Homomorphisms on C(R). American Mathematical Monthly, 93(7):555, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See comments [575, 616].

Kueh:1986:NKA

[541] Ka-Lam Kueh. A note on Kronecker’s approximation theorem. American Mathematical Monthly, 93(7):555– 556, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hiriart-Urruty:1986:WPS

[542] J.-B. Hiriart-Urruty. When is a point x satisfying ∇f(x) = 0 a global minimum of f. American Mathematical Monthly, 93(7):556–558, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Howe:1986:NPE

[543] Everett Howe. A new proof of Erdős’ theorem on monotone multiplicative functions. American Mathematical Monthly, 93(8):593–595, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Savage:1986:GCM

[544] Richard P. Savage, Jr. Graphical constructions of means. American Mathematical Monthly, 93(8):595–603, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Farnsworth:1986:GM

[545] David Farnsworth and Richard Orr. Gini means. American Mathematical Monthly, 93(8):603–607, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Long:1986:RHP

[546] Robert L. Long. Remarks on the history and philosophy of mathematics. American Mathematical Monthly, 93(8):609– 619, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Maltese:1986:SPF

[547] George Maltese. A simple proof of the fundamental theorem of finite Markov chains. American Mathematical Monthly, 93(8):629–630, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Allen:1986:CD

[548] Charles S. Allen. A characterization of dimension. American Mathematical Monthly, 93(8):635–636, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Folland:1986:CA

[549] G. B. Folland. On characterizations of analyticity. American Mathematical Monthly, 93(8):640–641, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Byrd:1986:SCF

[550] Richard D. Byrd. Simultaneous complements in finite-dimensional vector spaces. American Mathematical Monthly, 93(8):641–642, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Markham:1986:OIP

[551] Thomas L. Markham. Oppenheim’s inequality for positive definite matrices. American Mathematical Monthly, 93(8): 642–644, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Blyth:1986:CCD

[552] Colin R. Blyth. Convolutions of Cauchy distributions. American Mathematical Monthly, 93(8):645–647, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Carchidi:1986:MFE

[553] M. Carchidi. A method for finding the eigenvectors of an n × n matrix corresponding to eigenvalues of multiplicity one. American Mathematical Monthly, 93(8):647–649, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Williams:1986:FML

[554] H. P. Williams. Fourier’s method of linear programming and its dual. American Mathematical Monthly, 93(9):681– 695, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Clough:1986:MSG

[555] John Clough and Gerald Myerson. Musical scales and the generalized circle of fifths. American Mathematical Monthly, 93(9):695–701, ???? 1986. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Simpson:1986:MTP

[556] James E. Simpson. More trees and power sums. American Mathematical Monthly, 93(9):701–708, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Valiaho:1986:EAJ

[557] H. Väliaho. An elementary approach to the Jordan form of a matrix. American Mathematical Monthly, 93(9):711– 714, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chan:1986:AFD

[558] Beda Chan. An application of finite difference algebra. American Mathematical Monthly, 93(9):716–717, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Benson:1986:FLG

[559] David Benson, Walter Feit, and Roger Howe. Finite linear groups, the Commodore 64, Euler and Sylvester. American Mathematical Monthly, 93(9):717– 719, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kleinfeld:1986:CRW

[560] Erwin Kleinfeld. A class of rings which are very nearly associative. American Mathematical Monthly, 93(9):720– 722, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Parks:1986:OIN

[561] Alan E. Parks. π, and e, and other irrational numbers. American Mathematical Monthly, 93(9):722–723, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Botsko:1986:EGR

[562] Michael W. Botsko. An easy generalization of the Riemann integral. American Mathematical Monthly, 93(9):728– 732, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hiller:1986:CCG

[563] Howard Hiller. Crystallography and cohomology of groups. American Mathematical Monthly, 93(10):765–779, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brunson:1986:POI

[564] Barry W. Brunson. The partial order of iterated exponentials. American Mathematical Monthly, 93(10):779–786, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Silverman:1986:PFO

[565] Joseph H. Silverman. Points of finite order on elliptic curves. American Mathematical Monthly, 93(10):793–795, ????

1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Faber:1986:SCM

[566] V. Faber and J. Mycielski. The shortest curve that meets all the lines that meet a convex body. American Mathematical Monthly, 93(10):796–801, ???? 1986. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1987:PRK

[567] Donald E. Knuth. Problem 86-2, a random knockout tournament (with solution). American Mathematical Monthly, 93(??):127–129, 1987. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilf:1987:GVR

[568] Herbert S. Wilf. A greeting: and a view of Riemann’s hypothesis. American Mathematical Monthly, 94(1):3–6, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bender:1987:NTD

[569] Edward A. Bender. The number of three-dimensional convex polyhedra. American Mathematical Monthly, 94(1): 7–21, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [639].

Kalman:1987:CFI

[570] Dan Kalman and Abraham Ungar. Combinatorial and functional identities in one-parameter matrices. American Mathematical Monthly, 94(1):21– 35, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Roy:1987:BIH

[571] Ranjan Roy. Binomial identities and hypergeometric series. American Mathematical Monthly, 94(1):36–46, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Beardon:1987:CCC

[572] Alan F. Beardon. Curvature, circles, and conformal maps. American Mathematical Monthly, 94(1):48–53, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Calhoun:1987:CSS

[573] William C. Calhoun. Counting the subgroups of some finite groups. American Mathematical Monthly, 94(1):54– 59, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Johnson:1987:DE

[574] Wells Johnson. The Diophantine equation X^{2} + 7 = 2^{n}. American Mathematical Monthly, 94(1):59–62, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Colley:1987:TB

[575] Susan Jane Colley. The tumbling box.

American Mathematical Monthly, 94(1): 62–68, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [540] and correction [615].

Sarason:1987:MTF

[576] Donald Sarason. The multiplication theorem for Fredholm operators. American Mathematical Monthly, 94(1):68– 70, ???? 1987. CODEN AMMYAE.

ISSN 0002-9890 (print), 1930-0972 (electronic).

Hwang:1987:TTC

[577] F. K. Hwang. A tale of two coins. American Mathematical Monthly, 94(2):121– 129, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Althoen:1987:GJR

[578] Steven C. Althoen and Renate McLaughlin. Gauss–Jordan reduction: a brief history. American Mathematical Monthly, 94(2):130–142, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pelletier:1987:MMS

[579] Don Pelletier. Merlin’s magic square. American Mathematical Monthly, 94(2): 143–150, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zaks:1987:NFC

[580] Joseph Zaks. Neighborly families of congruent convex polytopes. American Mathematical Monthly, 94(2):151– 155, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Beck:1987:CFB

[581] Anatole Beck. Constructing a fair border. American Mathematical Monthly, 94(2):157–162, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

MacHale:1987:ACR

[582] Desmond MacHale. An anticommutativity consequence of a ring commutativity theorem of Herstein. American Mathematical Monthly, 94(2):162–165, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Searcoid:1987:RST

[583] Mícheál Ó Searcóid. A reordering of the Sylow theorems. American Mathematical Monthly, 94(2):165–168, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Erdos:1987:API

[584] P. Erdős, P. P. Pálfy, and M. Szegedy.

a (mod p) ≤ b (mod p) for all primes p implies a = b. American Mathematical Monthly, 94(2):169–170, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Saff:1987:EQM

[585] E. B. Saff and Jon C. Snader. The error for quadrature methods: a complex variables approach. American Mathematical Monthly, 94(2):175–180, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1987:SPEa

[586] Donald E. Knuth. Solution to problem E3061, empty cells. American Mathematical Monthly, 94(2):189, February 1987. ISSN 0002-9890 (print), 1930-0972 (electronic).

Krantz:1987:WSC

[587] Steven G. Krantz. What is several complex variables. American Mathematical Monthly, 94(3):236–256, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brualdi:1987:JCF

[588] Richard A. Brualdi. The Jordan canonical form: an old proof. American Mathematical Monthly, 94(3):257–267, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilf:1987:FLO

[589] Herbert S. Wilf. Finite lists of obstructions. American Mathematical Monthly, 94(3):267–271, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Furuta:1987:CCH

[590] Takayuki Furuta. A counterexample to a conjectured Hermitian matrix inequality. American Mathematical Monthly, 94 (3):271–272, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Paris:1987:AAC

[591] R. B. Paris. An asymptotic approximation connected with the golden number. American Mathematical Monthly, 94(3):272–278, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

vanderPloeg:1987:DNQ

[592] C. E. van der Ploeg. Duality in nonnormal quartic fields. American Mathematical Monthly, 94(3):279–284, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [729] and errata [641].

Rozema:1987:RIT

[593] Edward R. Rozema. Romberg integration by Taylor series. American Mathematical Monthly, 94(3):284–288, ????

1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rovnyak:1987:NCP

[594] James Rovnyak. Note on characteristic polynomials. American Mathematical Monthly, 94(3):289–290, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Herstein:1987:RFF

[595] I. N. Herstein. A remark on finite fields.

American Mathematical Monthly, 94(3): 290–291, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Taylor:1987:SGT

[596] Robert Lee Taylor and Tien Chung Hu. Sub-Gaussian techniques in proving strong laws of large numbers. American Mathematical Monthly, 94(3):295– 299, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Epperson:1987:RE

[597] James F. Epperson. On the Runge example. American Mathematical Monthly, 94(4):329–341, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rosenthal:1987:RTL

[598] Peter Rosenthal. The remarkable theorem of Lévy and Steinitz. American Mathematical Monthly, 94(4):342– 351, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ikebe:1987:MTC

[599] Yasuhiko Ikebe, Toshiyuki Inagaki, and Sadaaki Miyamoto. The monotonicity theorem, Cauchy’s interlace theorem, and the Courant-Fischer theorem. American Mathematical Monthly, 94(4): 352–354, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilker:1987:DL

[600] J. B. Wilker. The nth derivative as a limit. American Mathematical Monthly, 94(4):354–356, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Choi:1987:LDG

[601] Bong Dae Choi. Limiting distribution for the generalized matching problem. American Mathematical Monthly, 94(4): 356–360, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Roy:1987:EPC

[602] Nina M. Roy. Extreme points of convex sets in infinite-dimensional spaces. American Mathematical Monthly, 94(5): 409–422, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Mauldon:1987:MAR

[603] J. G. Mauldon. A matrix with applications to random walk, Brownian motion, and ring theory. American Mathematical Monthly, 94(5):423–436, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wallen:1987:AWW

[604] Lawrence J. Wallen. All the way with Wirtinger: a short proof of Bonnesen’s inequality. American Mathematical Monthly, 94(5):440–442, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Beer:1987:WFU

[605] Gerald Beer and Luzviminda Villar.

When is a free union of regular measures regular. American Mathematical Monthly, 94(5):443–445, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Petro:1987:RDA

[606] John Petro. Real division algebras of dimension > 1 contain C. American Mathematical Monthly, 94(5):445–449, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Miller:1987:MOE

[607] William Miller. The maximum order of an element of a finite symmetric group. American Mathematical Monthly, 94(6): 497–506, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zwicker:1987:PGG

[608] William S. Zwicker. Playing games with games: the hypergame paradox. American Mathematical Monthly, 94(6):507– 514, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

McKay:1987:CD

[609] John McKay. On computing discriminants. American Mathematical Monthly, 94(6):523–527, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zwick:1987:BAC

[610] D. Zwick. Best approximation by convex functions. American Mathematical Monthly, 94(6):528–534, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Laugwitz:1987:SCG

[611] Detlef Laugwitz and Bernd Rodewald. A simple characterization of the gamma function. American Mathematical Monthly, 94(6):534–536, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wagon:1987:FPR

[612] Stan Wagon. Fourteen proofs of a result about tiling a rectangle. American Mathematical Monthly, 94(7):601– 617, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kidwell:1987:TET

[613] Mark E. Kidwell and R. Bruce Richter. Trees and Euler tours in a planar graph and its relatives. American Mathematical Monthly, 94(7):618–630, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Maurer:1987:RR

[614] Peter M. Maurer. A rose is a rose. . .. American Mathematical Monthly, 94(7): 631–645, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Colley:1987:CTB

[615] Susan Jane Colley. Correction: “The tumbling box” [Amer. Math. Monthly 94 (1987), no. 1, 62–68, MR 88b:53010]. American Mathematical Monthly, 94(7): 646, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [575].

Pursell:1987:CHA

[616] Lyle E. Pursell. Comment: “Homomorphisms on C(R)” [Amer. Math. Monthly 93 (1986), no. 7, 555, MR 87i:46109] by R. M. Aron and G. H. Fricke. American Mathematical Monthly, 94(7):646, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [540].

Ferguson:1987:GSA

[617] Helaman Ferguson. Generalization of some algorithms of Euler. American Mathematical Monthly, 94(7):647– 652, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

VandenEynden:1987:API

[618] Charles Vanden Eynden. Applications of a product identity to sums of squares and partitions. American Mathematical Monthly, 94(7):652–656, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cronin:1987:CMR

[619] T. M. Cronin. The construction of matrices with required properties over the integers. American Mathematical Monthly, 94(7):656–662, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Choe:1987:EP

[620] Boo Rim Choe. An elementary proof of ∑_{n=1}^{∞} 1/n^{2} = π^{2}/6. American Mathematical Monthly, 94(7):662–663, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hoffman:1987:IFA

[621] Michael Hoffman. An invariant of finite abelian groups. American Mathematical Monthly, 94(7):664–666, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

White:1987:RC

[622] Arthur T. White. Ringing the cosets. American Mathematical Monthly, 94(8): 721–746, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Scott:1987:FE

[623] Paul R. Scott. The fascination of the elementary. American Mathematical Monthly, 94(8):759–768, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nathanson:1987:GGS

[624] Melvyn B. Nathanson. A generalization of the Goldbach-Shnirel′man theorem. American Mathematical Monthly, 94(8):768–771, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Korec:1987:NP

[625] I. Korec and Š. Znám. A note on the 3x + 1 problem. American Mathematical Monthly, 94(8):771–772, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Mendes:1987:HMC

[626] Claudio Martins Mendes and Maria Aparecida Soares Ruas. Hyperbolic motions of conics. American Mathematical Monthly, 94(9):825–845, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kletzing:1987:RRF

[627] Dennis Kletzing. Rational representations of finite groups: the story of γ. American Mathematical Monthly, 94(9): 846–854, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilf:1987:ECS

[628] Herbert S. Wilf. The editor’s corner:

strings, substrings, and the “nearest integer” function. American Mathematical Monthly, 94(9):855–860, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Benjamin:1987:BMW

[629] Arthur Benjamin. The bisection method: which root. American Mathematical Monthly, 94(9):861–863, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [815].

Villani:1987:SLC

[630] Alfonso Villani. Spaces with locally compact completions are compact. American Mathematical Monthly, 94(9):863– 865, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Simpson:1987:DCS

[631] R. J. Simpson. Disjoint covering systems of congruences. American Mathematical Monthly, 94(9):865–868, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See comment [750].

Johnson:1987:EP

[632] C. Johnson, G. Wolkowicz, and H. Wolkowicz. Elem. prob. E. 3234. American Mathematical Monthly, 94(9): 877, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cipra:1987:IIM

[633] Barry A. Cipra. An introduction to the Ising model. American Mathematical Monthly, 94(10):937–959, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Freund:1987:SES

[634] David E. Freund. Selecting estimators for the standard deviation of a normal distribution. American Mathematical Monthly, 94(10):971–975, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Tondeur:1987:BRI

[635] Philippe Tondeur. Barycentric representation for the incenter and excenters of a triangle. American Mathematical Monthly, 94(10):975–976, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Minassian:1987:AGM

[636] Donald P. Minassian. The arithmeticgeometric mean inequality revisited: elementary calculus and negative numbers. American Mathematical Monthly, 94(10):977–978, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Heatherly:1987:MS

[637] Henry Heatherly. Matrices satisfying AB − BA = I. American Mathematical Monthly, 94(10):979–980, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Nelsen:1987:CMP

[638] Roger B. Nelsen. Consequences of the memoryless property for random variables. American Mathematical Monthly, 94(10):981–984, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bender:1987:ENT

[639] Edward A. Bender. Errata: “The number of three-dimensional convex polyhedra” [Amer. Math. Monthly 94 (1987), no. 1, 7–21, MR 88b:52010]. American Mathematical Monthly, 94(10):994, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [569].

Bohn:1987:ESG

[640] S. Elwood Bohn and Jong Lee. Errata: “Semitopological groups” [Amer. Math. Monthly 72 (1965), 996–998, MR 32 #7672]. American Mathematical Monthly, 94(10):994, ???? 1987. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [2].

vanderPloeg:1987:EDN

[641] C. E. van der Ploeg. Errata: “Duality in nonnormal quartic fields” [Amer.

Math. Monthly 94 (1987), no. 3, 279– 284]. American Mathematical Monthly, 94(10):994, ???? 1987. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [592] and letter to the editor [729].

Alexanderson:1988:ADS

[642] Gerald L. Alexanderson. Award for distinguished service to Professor Murray Klamkim. American Mathematical Monthly, 95(1):1–4, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Grunbaum:1988:IF

[643] Branko Grünbaum and G. C. Shephard. Isonemal fabrics. American Mathematical Monthly, 95(1):5–30, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bloom:1988:CGD

[644] Gary S. Bloom, John W. Kennedy, and Louis V. Quintas. A characterization of graphs of diameter two. American Mathematical Monthly, 95(1):37– 38, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lima:1988:JBS

[645] Elon L. Lima. The Jordan-Brouwer separation theorem for smooth hypersurfaces. American Mathematical Monthly, 95(1):39–42, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fowler:1988:KBY

[646] Peter A. Fowler. The Königsberg bridges—250 years later. American Mathematical Monthly, 95(1):42– 43, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Newman:1988:MS

[647] Donald J. Newman and T. D. Parsons.

On monotone subsequences. American Mathematical Monthly, 95(1):44– 45, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kopperman:1988:ATC

[648] Ralph Kopperman. All topologies come from generalized metrics. American Mathematical Monthly, 95(2):89– 97, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Polites:1988:PDT

[649] George W. Polites. Prime desert n-tuplets. American Mathematical Monthly, 95(2):98–104, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Eldridge:1988:DKC

[650] Klaus E. Eldridge and Seok Sagong.

The determination of Kaprekar convergence and loop convergence of all threedigit numbers. American Mathematical Monthly, 95(2):105–112, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bouwer:1988:QP

[651] I. Bouwer and Z. Star. A question of protocol. American Mathematical Monthly, 95(2):118–121, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Beebee:1988:EII

[652] John Beebee. Examples of infinite, incongruent exact covers. American Mathematical Monthly, 95(2):121–123, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [814].

Hallenbeck:1988:AUC

[653] David J. Hallenbeck and Katarzyna Tkaczyńska. The absolute and uniform convergence of infinite improper integrals. American Mathematical Monthly, 95(2):124–126, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Arora:1988:SIT

[654] Ashok K. Arora, Sudhir K. Goel, and Dennis M. Rodriguez. Special integration techniques for trigonometric integrals. American Mathematical Monthly, 95(2):126–130, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [745].

Gleason:1988:ATH

[655] Andrew M. Gleason. Angle trisection, the heptagon, and the triskaidecagon. American Mathematical Monthly, 95(3): 185–194, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See addenda [711].

Kauffman:1988:NIT

[656] Louis H. Kauffman. New invariants in the theory of knots. American Mathematical Monthly, 95(3):195–242, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gallian:1988:HW

[657] Joseph A. Gallian and Douglas S. Jungreis. Homomorphisms from Z_{m}[i] into Z_{n}[i] and Z_{m}[ρ] into Z_{n}[ρ], where i^{2} + 1 = 0 and ρ^{2} + ρ + 1 = 0. American Mathematical Monthly, 95(3):247– 249, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Botsko:1988:EPB

[658] Michael W. Botsko. An elementary proof that a bounded a.e. continuous function is Riemann integrable. American Mathematical Monthly, 95(3):249– 252, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Froemke:1988:AAS

[659] Jon Froemke and Jerrold W. Grossman. An algebraic approach to some number-theoretic problems arising from paper-folding regular polygons. American Mathematical Monthly, 95(4):289– 307, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Vardi:1988:IIA

[660] Ilan Vardi. Integrals, an introduction to analytic number theory. American Mathematical Monthly, 95(4):308– 315, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Robertson:1988:DFS

[661] Lewis C. Robertson, Rae Michael Shortt, and Stephen G. Landry. Dice with fair sums. American Mathematical Monthly, 95(4):316–328, ???? 1988.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stout:1988:TDF

[662] Lawrence Neff Stout. Two discrete forms of the Jordan curve theorem. American Mathematical Monthly, 95(4):332– 336, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ashraf:1988:SPI

[663] Mohd. Ashraf, Murtaza A. Quadri, and Daniel Zelinsky. Some polynomial identities that imply commutativity for rings. American Mathematical Monthly, 95(4):336–339, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Trotter:1988:OEN

[664] Hale F. Trotter. An overlooked example of nonunique factorization. American Mathematical Monthly, 95(4):339– 342, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Krishnaiah:1988:TCG

[665] P. V. Krishnaiah. Two counterexamples in general topology. American Mathematical Monthly, 95(4):342–343, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Artmann:1988:SPS

[666] Benno Artmann. A simple proof for the simplicity of A_{5}. American Mathematical Monthly, 95(4):344–349, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lalley:1988:PNT

[667] S. P. Lalley. The “prime number theorem” for the periodic orbits of a Bernoulli flow. American Mathematical Monthly, 95(5):385–398, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Withers:1988:FPT

[668] Wm. Douglas Withers. Folding polynomials and their dynamics. American Mathematical Monthly, 95(5):399– 413, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Leonard:1988:MFI

[669] I. E. Leonard. More on Fresnel integrals. American Mathematical Monthly, 95(5):431–433, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Martin:1988:CAG

[670] Gary A. Martin. A class of abelian groups arising from an analysis of a proof. American Mathematical Monthly, 95(5):433–436, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Schue:1988:WTF

[671] John Schue. The Wedderburn theorem of finite division rings. American Mathematical Monthly, 95(5):436–437, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hill:1988:CHM

[672] Theodore P. Hill. Common hyperplane medians for random vectors. American Mathematical Monthly, 95(5):437– 441, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cox:1988:QRC

[673] David A. Cox. Quadratic reciprocity: its conjecture and application. American Mathematical Monthly, 95(5):442– 448, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hayes:1988:EPE

[674] Barry Hayes, Donald E. Knuth, and Carlos Subi. Elementary problem E3267, a solitaire game. American Mathematical Monthly, 95(5):456–457, May 1988. ISSN 0002-9890 (print), 1930-0972 (electronic). Solutions in [820].

Day:1988:GGE

[675] Jane Day and Brian Peterson. Growth in Gaussian elimination. American Mathematical Monthly, 95(6):489–513, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fisher:1988:MGI

[676] Stephen D. Fisher. The Möbius group and invariant spaces of analytic functions. American Mathematical Monthly, 95(6):514–527, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Conrey:1988:ZTP

[677] Brian Conrey and Amit Ghosh. On the zeros of the Taylor polynomials associated with the exponential function. American Mathematical Monthly, 95(6): 528–533, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wendel:1988:SIE

[678] J. G. Wendel. Shanks’ identity is elementary. American Mathematical Monthly, 95(6):534, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pelling:1988:LE

[679] M. J. Pelling. Letter to the editor.

American Mathematical Monthly, 95(6): 535–536, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fabrykowski:1988:CFC

[680] J. Fabrykowski. On continued fractions and a certain example of a sequence of continuous functions. American Mathematical Monthly, 95(6):537–539, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [712].

Anglin:1988:UPT

[681] W. S. Anglin. Using Pythagorean triangles to approximate angles. American Mathematical Monthly, 95(6):540– 541, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wildenberg:1988:CPF

[682] Gerald Wildenberg. Convergencepreserving functions. American Mathematical Monthly, 95(6):542–544, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Boyd:1988:DE

[683] David W. Boyd. The Diophantine equation x^{2} + y^{m} = z^{2n}. American Mathematical Monthly, 95(6):544–547, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See addendum [813].

Almkvist:1988:GLR

[684] Gert Almkvist and Bruce Berndt. Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, π, and the ladies diary. American Mathematical Monthly, 95(7):585–608, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kingston:1988:SPT

[685] John G. Kingston and John L. Synge. The sequence of pedal triangles. American Mathematical Monthly, 95(7):609– 620, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Small:1988:MSF

[686] Charles Small. Magic squares over fields. American Mathematical Monthly, 95(7): 621–625, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Tremain:1988:JTP

[687] Janet Crandell Tremain. The Jerusalem ticket problem. American Mathematical Monthly, 95(7):626–630, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chilakamarri:1988:DBG

[688] Kiran B. Chilakamarri. Decomposition of bipartite graphs into paths. American Mathematical Monthly, 95(7):634– 636, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Quine:1988:FLT

[689] W. V. Quine. Fermat’s last theorem in combinatorial form. American Mathematical Monthly, 95(7):636, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Simoson:1988:DES

[690] Andrew Simoson. A difference equation for strings of ones. American Mathematical Monthly, 95(7):636–638, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Norton:1988:CFD

[691] Alec Norton. Continued fractions and differentiability of functions. American Mathematical Monthly, 95(7):639– 643, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1988:SPE

[692] Donald E. Knuth. Solution to problem E3166, A polynomial identity. American Mathematical Monthly, 95(7):662–663, August–September 1988. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kazarinoff:1988:SFB

[693] Nicholas D. Kazarinoff. Special functions and the Bieberbach conjecture. American Mathematical Monthly, 95(8): 689–696, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Guy:1988:SLS

[694] Richard K. Guy. The strong law of small numbers. American Mathematical Monthly, 95(8):697–712, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Mitchell:1988:ESM

[695] John Mitchell and Lee A. Rubel. Every smooth map of Euclidean space into itself is an expansion followed by a contraction. American Mathematical Monthly, 95(8):713–716, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cohen:1988:SVI

[696] G. L. Cohen and G. H. Smith. A simple verification of Ilieff’s conjecture for polynomials with three zeros. American Mathematical Monthly, 95(8):734– 737, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Beer:1988:USR

[697] Gerald Beer. UC spaces revisited. American Mathematical Monthly, 95(8):737– 739, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hile:1988:LIH

[698] G. N. Hile and R. Z. Yeh. Line integrals of higher-order derivatives. American Mathematical Monthly, 95(8):739– 744, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Chew:1988:NCC

[699] James Chew. A note on closure continuity. American Mathematical Monthly, 95 (8):744–745, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1988:APA

[700] Donald E. Knuth and Ilan Vardi. Advanced problem 6581, the asymptotic expansion of the middle binomial coefficient. American Mathematical Monthly, 95(8):774, October 1988. ISSN 0002-9890 (print), 1930-0972 (electronic). Solutions in [819].

Taussky:1988:HBT

[701] Olga Taussky. How I became a torchbearer for matrix theory. American Mathematical Monthly, 95(9):801–812, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Morgan:1988:AMS

[702] Frank Morgan. Area-minimizing surfaces, faces of Grassmannians, and calibrations. American Mathematical Monthly, 95(9):813–822, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Brooks:1988:CIM

[703] Robert Brooks. Constructing isospectral manifolds. American Mathematical Monthly, 95(9):823–839, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Baston:1988:SCG

[704] V. J. Baston and F. A. Bostock. A simple cover-up game. American Mathematical Monthly, 95(9):850–854, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Liu:1988:NPP

[705] Fa Sheng Liu. A note on probabilities in proofreading. American Mathematical Monthly, 95(9):854, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rosen:1988:PLL

[706] Michael I. Rosen. A proof of the Lucas-Lehmer test. American Mathematical Monthly, 95(9):855–856, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Aczel:1988:BMU

[707] J. Aczél and Zs. Páles. The behaviour of means under equal increments of their variables. American Mathematical Monthly, 95(9):856–860, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Andrews:1988:CS

[708] Peter Andrews. The classification of surfaces. American Mathematical Monthly, 95(9):861–867, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Campoli:1988:PID

[709] Oscar A. Cámpoli. A principal ideal domain that is not a Euclidean domain. American Mathematical Monthly, 95(9): 868–871, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lehmer:1988:NAB

[710] D. H. Lehmer. A new approach to Bernoulli polynomials. American Mathematical Monthly, 95(10):905–911, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [769].

Gleason:1988:AAT

[711] Andrew M. Gleason. Addenda: “Angle trisection, the heptagon, and the triskaidecagon” [Amer. Math. Monthly 95 (1988), no. 3, 185–194, MR 89d:51028]. American Mathematical Monthly, 95(10):911, ???? 1988. CO-DEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [655].

Hensley:1988:ECF

[712] Doug Hensley. Errata: “On continued fractions and a certain example of a sequence of continuous functions” [Amer. Math. Monthly 95 (1988), no. 6, 537– 539, MR 89i:40001] by J. Fabrykowski. American Mathematical Monthly, 95 (10):911, ???? 1988. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [680].

Llewellyn:1988:FST

[713] Donna Crystal Llewellyn, Craig Tovey, and Michael Trick. Finding saddlepoints of two-person, zero sum games. American Mathematical Monthly, 95(10):912– 918, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Book:1988:DAC

[714] Ronald V. Book. Dehn’s algorithm and the complexity of word problems. American Mathematical Monthly, 95(10):919– 925, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lin:1988:ABP

[715] X.-B. Lin. Another brief proof of the Sylvester theorem. American Mathematical Monthly, 95(10):932–933, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Furuta:1988:ESC

[716] Takayuki Furuta. A ≥ B ≥ 0 ensures (BA^{2}B)^{1/2} ≥ B^{2}—solution to a conjecture on operator inequalities. American Mathematical Monthly, 95(10):933– 934, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Landy:1988:GCT

[717] Steven Landy. A generalization of Ceva’s theorem to higher dimensions. American Mathematical Monthly, 95(10):936– 939, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ramakrishnan:1988:SCT

[718] S. Ramakrishnan and W. D. Sudderth. A sequence of coin toss variables for which the strong law fails. American Mathematical Monthly, 95(10):939– 941, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lewin:1988:STT

[719] Jonathan Lewin and Myrtle Lewin. A simple test for the nth term of a series to approach zero. American Mathematical Monthly, 95(10):942, ???? 1988.

CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Magill:1988:UTS

[720] K. D. Magill, Jr. Universal topological spaces. American Mathematical Monthly, 95(10):942–946, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See errata [817].

Gilbert:1988:CMI

[721] Richard C. Gilbert. Companion matrices with integer entries and integer eigenvalues and eigenvectors. American Mathematical Monthly, 95(10):947– 950, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Gerstein:1988:NAC

[722] Larry J. Gerstein. A new algorithm for computing the rank of a matrix. American Mathematical Monthly, 95(10):950– 952, ???? 1988. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1989:EPEb

[723] Donald E. Knuth. Elementary problem E3303, a binary summation. American Mathematical Monthly, 96(??):54, 1989. ISSN 0002-9890 (print), 1930-0972 (electronic). Solutions in [809].

Knuth:1989:EPEc

[724] Donald E. Knuth. Elementary problem E3309, a binomial coefficient inequality. American Mathematical Monthly, 96 (??):154, 1989. ISSN 0002-9890 (print), 1930-0972 (electronic). Solutions in

Knuth:1989:EPEa

[725] Donald E. Knuth. Elementary problem E3335, a deranged recurrence. American Mathematical Monthly, 96(??):525, 1989. ISSN 0002-9890 (print), 1930-0972 (electronic). Solutions in [811].

Knuth:1989:SEP

[726] Donald E. Knuth. Solution to elementary problem E2982, a double infinite sum for |x|. American Mathematical Monthly, 96(??):525–526, 1989. ISSN 0002-9890 (print), 1930-0972 (electronic). Original problem in [250].

Ross:1989:ADS

[727] Kenneth Ross. Award for distinguished service to Ivan Niven. American Mathematical Monthly, 96(1):3–4, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Busenberg:1989:MPD

[728] Stavros Busenberg, David Fisher, and Mario Martelli. Minimal periods of discrete and smooth orbits. American Mathematical Monthly, 96(1):5–17, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lazarus:1989:LED

[729] Andrew J. Lazarus. Letter to the editor: “Duality in nonnormal quartic fields” [Amer. Math. Monthly 94 (1987), no. 3, 279–284, MR 88j:11064 and errata, MR 89c:11156] by C. E. van der Ploeg. American Mathematical Monthly, 96(1): 17, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [592] and errata [641].

Gamelin:1989:IIR

[730] T. W. Gamelin and D. Khavinson. The isoperimetric inequality and rational approximation. American Mathematical Monthly, 96(1):18–30, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Hupert:1989:SRI

[731] Lillian E. Peters Hupert and Anne Leggett. On the square roots of infinite matrices. American Mathematical Monthly, 96(1):34–38, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pakula:1989:NVD

[732] Lewis Pakula. A note on Venn diagrams.

American Mathematical Monthly, 96(1): 38–39, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ligh:1989:DSR

[733] Steve Ligh and Jiang Luh. Direct sum of J-rings and zero rings. American Mathematical Monthly, 96(1):40– 41, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Patin:1989:VSP

[734] J. M. Patin. A very short proof of Stirling’s formula. American Mathematical Monthly, 96(1):41–42, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [770].

Mader:1989:EME

[735] Adolf Mader. A Euclidean model for Euclidean geometry. American Mathematical Monthly, 96(1):43–49, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Osborne:1989:OBI

[736] Anthony Osborne and Hans Liebeck. Orthogonal bases of R^{3} with integer coordinates and integer lengths. American Mathematical Monthly, 96(1):49– 53, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Strang:1989:PLA

[737] Gilbert Strang. Patterns in linear algebra. American Mathematical Monthly, 96(2):105–117, February 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cooper:1989:CIN

[738] Curtis N. Cooper and Robert E. Kennedy. Chebyshev’s inequality and natural density. American Mathematical Monthly, 96(2):118–124, February 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bateman:1989:NMC

[739] P. T. Bateman, J. L. Selfridge, and S. S. Wagstaff, Jr. The new Mersenne conjecture. American Mathematical Monthly, 96(2):125–128, February 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See letter to the editor [771]. The authors state: New Mersenne Conjecture. If two of the following statements about an odd positive integer p are true, then the third one is also true. (a) p = 2^{k} ±1 or p = 4^{k} ±3.

(b) M_{p}(= 2^{p} −1) is prime. (c) (2^{p} +1)/3 is prime.

Bockman:1989:GFA

[740] S. F. Bockman. Generalizing the formula for areas of polygons to moments. American Mathematical Monthly, 96(2): 131–132, February 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Kappe:1989:ETG

[741] Luise-Charlotte Kappe and Bette Warren. An elementary test for the Galois group of a quartic polynomial. American Mathematical Monthly, 96(2):133–137, February 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bapat:1989:CSR

[742] R. B. Bapat. Comparing the spectral radii of two nonnegative matrices. American Mathematical Monthly, 96(2): 137–139, February 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Borwein:1989:RME

[743] J. M. Borwein, P. B. Borwein, and D. H.

Bailey. Ramanujan, modular equations, and approximations to pi, or How to compute one billion digits of pi. American Mathematical Monthly, 96(3):201– 219, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See also [824] for a significance advance in this work, and [821] for further simplifications and derivations of families of series for π.

Lawrence:1989:EDR

[744] J. Lawrence and G. E. Simons. Equations in division rings — a survey. American Mathematical Monthly, 96(3):220– 232, ???? 1989. CODEN AMMYAE.

ISSN 0002-9890 (print), 1930-0972 (electronic).

Leibowitz:1989:LES

[745] Gerald Leibowitz. Letters to the editor: “Special integration techniques for trigonometric integrals” [Amer. Math. Monthly 95 (1988), no. 2, 126–130, MR 89e:26004] by A. K. Arora, S. K. Goel and D. M. Rodriguez. American Mathematical Monthly, 96(3):232, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [654].

Sangwine-Yager:1989:MBB

[746] J. R. Sangwine-Yager. The missing boundary of the Blaschke diagram. American Mathematical Monthly, 96(3): 233–237, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Blank:1989:GIP

[747] S. J. Blank, Nishan Krikorian, and David Spring. A geometrically inspired proof of the singular value decomposition. American Mathematical Monthly, 96(3):238–239, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bailey:1989:SZM

[748] Craig Bailey and R. Bruce Richter. Sum zero (mod n), size n subsets of integers. American Mathematical Monthly, 96(3):240–242, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Crowe:1989:OM

[749] John Crowe and Dominick Samperi. On open maps. American Mathematical Monthly, 96(3):242–243, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zeilberger:1989:CRJ

[750] Doron Zeilberger. On a conjecture of R. J. Simpson about exact covering congruences: “Disjoint covering systems of congruences” [Amer. Math. Monthly 94 (1987), no. 9, 865–868, MR 89b:11006]. American Mathematical Monthly, 96(3): 243, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [631].

Gupta:1989:GWE

[751] Narain Gupta. On groups in which every element has finite order. American Mathematical Monthly, 96(4):297– 308, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Adhikari:1989:SPA

[752] Ani Adhikari and Jim Pitman. The shortest planar arc of width 1. American Mathematical Monthly, 96(4):309– 327, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Botsko:1989:UFC

[753] Michael W. Botsko. The use of full covers in real analysis. American Mathematical Monthly, 96(4):328–333, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Diaconis:1989:FD

[754] Persi Diaconis and Joseph B. Keller. Fair dice. American Mathematical Monthly, 96(4):337–339, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cosgrave:1989:REP

[755] John B. Cosgrave. A remark on Euclid’s proof of the infinitude of primes. American Mathematical Monthly, 96(4):339– 341, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cucker:1989:APC

[756] Felipe Cucker and Antonio Gonzalez Corbalan. An alternate proof of the continuity of the roots of a polynomial. American Mathematical Monthly, 96(4): 342–345, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Thompson:1989:TTU

[757] H. B. Thompson. Taylor’s theorem using the generalized Riemann integral. American Mathematical Monthly, 96(4):346– 350, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Andrews:1989:MPR

[758] George E. Andrews and R. J. Baxter. A motivated proof of the Rogers– Ramanujan identities. American Mathematical Monthly, 96(5):401–409, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See comment [812].

McCleary:1989:HPF

[759] John McCleary. How not to prove Fermat’s last theorem. American Mathematical Monthly, 96(5):410–420, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rubel:1989:ECS

[760] Lee A. Rubel. The editor’s corner:

summability theory: a neglected tool of analysis. American Mathematical Monthly, 96(5):421–423, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

David:1989:PC

[761] Guy David and Carlos Tomei. The problem of the calissons. American Mathematical Monthly, 96(5):429–431, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rosay:1989:AAT

[762] Jean-Pierre Rosay and Walter Rudin.

Arakelian’s approximation theorem. American Mathematical Monthly, 96(5): 432–434, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Maddox:1989:NLF

[763] I. J. Maddox. The norm of a linear functional. American Mathematical Monthly, 96(5):434–436, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bradley:1989:ETR

[764] Richard C. Bradley. An elementary treatment of the Radon–Nikodým derivative. American Mathematical Monthly, 96(5):437–440, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilansky:1989:PRN

[765] Albert Wilansky. On the proof of the Radon–Nikodým theorem. American Mathematical Monthly, 96(5):441, ????

1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Thompson:1989:NCU

[766] Christopher L. Thompson. Nonstandard continuity and uniform convergence. American Mathematical Monthly, 96(5):443–444, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Anderson:1989:DBW

[767] Richard Anderson, László Lovász, Peter Shor, Joel Spencer, Éva Tardos, and Shmuel Winograd. Disks, balls, and walls: analysis of a combinatorial game. American Mathematical Monthly, 96(6): 481–493, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Goodman:1989:MCL

[768] Jacob E. Goodman, János Pach, and Chee-K. Yap. Mountain climbing, ladder moving, and the ring-width of a polygon. American Mathematical Monthly, 96(6):494–510, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Callan:1989:LEN

[769] David Callan. Letter to the editor: “A new approach to Bernoulli polynomials” [Amer. Math. Monthly 95 (1988), no. 10, 905–911, MR 90c:11014] by D. H. Lehmer. American Mathematical Monthly, 96(6):510, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [710].

Nelsen:1989:LEV

[770] Roger B. Nelsen. Letter to the editor: “A very short proof of Stirling’s formula” [Amer. Math. Monthly 96 (1989), no. 1, 41–42, MR 90e:33005a] by J. M. Patin. American Mathematical Monthly, 96(6):510–511, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [734].

Mullin:1989:LEN

[771] Albert A. Mullin. Letter to the editor: “The new Mersenne conjecture” [Amer. Math. Monthly 96 (1989), no. 2, 125–128, MR 90c:11009] by P. T. Bateman, J. L. Selfridge and S. S. Wagstaff, Jr. American Mathematical Monthly, 96(6):511, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [739]. Conjectures that “M_{n}(= 2^{n} − 1) is the product of two distinct primes only if n is either a prime p or the square of a prime q, in which case precisely one prime factor of M_{n} is Mersenne, vis. M_{q}.”.

Pinkham:1989:LES

[772] Roger Pinkham. Letter to the editor:

“A simple test for the nth term of a series to approach zero” [Amer. Math. Monthly 95 (1988), no. 10, 942] by J. Lewin and M. Lewin. American Mathematical Monthly, 96(6):511, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cohen:1989:MMF

[773] Joel M. Cohen. Monotone multiplicative functions. American Mathematical Monthly, 96(6):512–513, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wong:1989:PPD

[774] W. J. Wong. Powers of a prime dividing binomial coefficients. American Mathematical Monthly, 96(6):513–517, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wang:1989:PDM

[775] Derming Wang. The polar decomposition and a matrix inequality. American Mathematical Monthly, 96(6):517– 519, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Erdos:1989:PLM

[776] Paul Erdős, Dean Hickerson, and János Pach. A problem of Leo Moser about repeated distances on the sphere. American Mathematical Monthly, 96(7):569– 575, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Abi-Khuzam:1989:SRG

[777] Faruk F. Abi-Khuzam and Artin B. Boghossian. Some recent geometric inequalities. American Mathematical Monthly, 96(7):576–589, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zeilberger:1989:KOC

[778] Doron Zeilberger. Kathy O’Hara’s constructive proof of the unimodality of the Gaussian polynomials. American Mathematical Monthly, 96(7):590–602, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Arterburn:1989:CSN

[779] David R. Arterburn and William Dean Stone. A Cantor set of nonconvergence. American Mathematical Monthly, 96(7): 604–608, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Stock:1989:MMS

[780] Daniel L. Stock. Merlin’s magic square revisited. American Mathematical Monthly, 96(7):608–610, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Fisher:1989:NWL

[781] David C. Fisher. The number of words of length n in a graph monoid. American Mathematical Monthly, 96(7):610– 614, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Edelsbrunner:1989:NFN

[782] Herbert Edelsbrunner and Steven S.

Skiena. On the number of furthest neighbour pairs in a point set. American Mathematical Monthly, 96(7):614– 618, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lee:1989:RDD

[783] E. T. Y. Lee. A remark on divided differences. American Mathematical Monthly, 96(7):618–622, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Borwein:1989:PEN

[784] J. M. Borwein, P. B. Borwein, and K. Dilcher. Pi, Euler numbers, and asymptotic expansions. American Mathematical Monthly, 96(8):681–687, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Irwin:1989:GCF

[785] M. C. Irwin. Geometry of continued fractions. American Mathematical Monthly, 96(8):696–703, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Wilf:1989:ECW

[786] Herbert S. Wilf. The editor’s corner: the white screen problem. American Mathematical Monthly, 96(8):704–707, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Zoll:1989:LE

[787] Peter F. Zoll. Letter to the editor. American Mathematical Monthly, 96(8):709– 710, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Cusick:1989:FPT

[788] Larry W. Cusick and Peter Tannenbaum. Fixed points of the twisted cyclic shift operator. American Mathematical Monthly, 96(8):713–717, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Douwen:1989:FTN

[789] Eric K. van Douwen. Fubini’s theorem for null sets. American Mathematical Monthly, 96(8):718–721, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bassein:1989:OP

[790] Richard Bassein. An optimization problem. American Mathematical Monthly, 96(8):721–725, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lewkowicz:1989:CCC

[791] R. E. Lewkowicz. A characterization of a class of composition operators. American Mathematical Monthly, 96(8):725– 726, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rubel:1989:STT

[792] Lee A. Rubel. A survey of transcendentally transcendental functions. American Mathematical Monthly, 96(9):777– 788, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bezdek:1989:CCT

[793] K. Bezdek and R. Connelly. Covering curves by translates of a convex set. American Mathematical Monthly, 96(9): 789–806, ???? 1989. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Horwitz:1989:RFS

[794] Alan Horwitz. Reconstructing a function from its set of tangent lines. American Mathematical Monthly, 96(9):807– 813, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Thurston:1989:CGB

[795] Hugh Thurston. Can a graph be both continuous and discontinuous. American Mathematical Monthly, 96(9):814– 815, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rosset:1989:NSF

[796] Shmuel Rosset. Normalized symmetric functions, Newton’s inequalities and a new set of stronger inequalities. American Mathematical Monthly, 96(9):815– 819, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Alon:1989:RS

[797] N. Alon, I. Krasikov, and Y. Peres. Reflection sequences. American Mathematical Monthly, 96(9):820–823, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Sagher:1989:CR

[798] Yoram Sagher. Counting the rationals. American Mathematical Monthly, 96(9): 823, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Herron:1989:RCP

[799] Isom H. Herron. The radius of convergence of power series solutions to linear differential equations. American Mathematical Monthly, 96(9):824–827, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Epperson:1989:UIM

[800] James F. Epperson. On the use of iteration methods for approximating the natural logarithm. American Mathematical Monthly, 96(9):831–835, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Dowling:1989:TNS

[801] William F. Dowling. There are no safe virus tests. American Mathematical Monthly, 96(9):835–836, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Ash:1989:URT

[802] J. Marshall Ash. Uniqueness of representation by trigonometric series. American Mathematical Monthly, 96(10):873– 885, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Lew:1989:OIP

[803] John S. Lew and Donald A. Quarles, Jr. Optimal inscribed polygons in convex curves. American Mathematical Monthly, 96(10):886–902, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Tsarpalias:1989:VRT

[804] A. Tsarpalias. A version of Rouché’s theorem of continuous functions. American Mathematical Monthly, 96(10):911– 913, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Pambuccian:1989:AEE

[805] Victor Pambuccian. Another example of an exotic function. American Mathematical Monthly, 96(10):913–914, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Bogart:1989:FMT

[806] Kenneth P. Bogart. A fresh(man) treatment of determinants. American Mathematical Monthly, 96(10):915–920, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Rushanan:1989:VM

[807] Joseph J. Rushanan. On the Vandermonde matrix. American Mathematical Monthly, 96(10):921–924, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Leary:1989:RIR

[808] F. C. Leary. Rings with invertible regular elements. American Mathematical Monthly, 96(10):924–926, ???? 1989. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic).

Knuth:1990:SEPb

[809] Donald E. Knuth. Solution to elementary problem E3303, a binary summation. American Mathematical Monthly, 97(??):348–349, 1990. ISSN 0002-9890 (print), 1930-0972 (electronic). Original problem in [723].

Knuth:1990:SEPc

[810] Donald E. Knuth. Solution to elementary problem E3309, a binomial coefficient inequality. American Mathematical Monthly, 97(??):614, 1990. ISSN 0002-9890 (print), 1930-0972 (electronic). Original problem in [724].

Knuth:1990:SEPa

[811] Donald E. Knuth. Solution to elementary problem E3335, a deranged recurrence. American Mathematical Monthly, 97(??):927, 1990. ISSN 0002-9890 (print), 1930-0972 (electronic). Original problem in [725].

Robinson:1990:CMP

[812] Raphael M. Robinson. Comment to: “A motivated proof of the Rogers– Ramanujan identities” [Amer. Math.

Monthly 96 (1989), no. 5, 401–409, MR 90e:11147] by G. E. Andrews and R. J. Baxter. With a reply by Andrews. American Mathematical Monthly, 97(3): 214–215, March 1990. CODEN AM-MYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [758].

Boyd:1990:ADE

[813] David W. Boyd. Addendum: “The Diophantine equation x^{2} + y^{m} = z^{2n} ” [Amer. Math. Monthly 95 (1988), no. 6, 544–547, MR 89f:11046]. American Mathematical Monthly, 97(5):411– 412, May 1990. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [683].

Beebee:1990:EEI

[814] John Beebee. Errata: “Examples of infinite, incongruent exact covers” [Amer. Math. Monthly 95 (1988), no. 2, 121– 123, MR 89g:11013]. American Mathematical Monthly, 97(5):412, May 1990. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [652].

Benjamin:1990:EBM

[815] Arthur T. Benjamin. Errata: “The bisection method: which root?” [Amer. Math. Monthly 94 (1987), no. 9, 861– 863, MR 89c:26016]. American Mathematical Monthly, 97(5):412, May 1990. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [629].

Kleiner:1990:ECP

[816] Hans-J. Kleiner. Errata: “Coloring the Platonic solids” [Amer. Math. Monthly 93 (1986), no. 4, 288–292, MR 87e:05072] by D. H. Lehmer. American Mathematical Monthly, 97(5):412, May 1990. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [511].

Magill:1990:EUT

[817] K. D. Magill, Jr. Errata: “Universal topological spaces” [Amer. Math. Monthly 95 (1988), no. 10, 942–946, MR 89m:54018]. American Mathematical Monthly, 97(5):412, May 1990. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [720].

Wong:1990:EMV

[818] Jingcheng Wong. Errata: “On the mean value theorem for integrals” [Amer. Math. Monthly 89 (1982), no. 5, 300– 301, MR 83g:26002] by B. Jacobson. American Mathematical Monthly, 97(5): 412, May 1990. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). See [213].

Knuth:1990:SAP

[819] Donald E. Knuth. Solution to advanced problem 6581, the asymptotic expansion of the middle binomial coefficient. American Mathematical Monthly, 97(7):629–630, August/September 1990. ISSN 0002-9890 (print), 1930-0972 (electronic). Original problem in [700].

Nijenhuis:1993:SEP

[820] Albert Nijenhuis. Solution to elementary problem E3267, a solitaire game. American Mathematical Monthly, 100(3):292– 294, March 1993. ISSN 0002-9890 (print), 1930-0972 (electronic). Original problem in [674].

Adamchik:1997:SF

[821] Victor Adamchik and Stan Wagon.

A simple formula for π. American Mathematical Monthly, 104(9):852–855, November 1997. CODEN AMMYAE. ISSN 0002-9890 (print), 1930-0972 (electronic). The authors employ Mathematica to extend earlier work of Bailey, Borwein [743], and Plouffe, [824], done in 1995, but only just published, that discovered an amazing formula for π as is a power series in 16^{−k}, enabling any base-16 digit of π to be computed without knowledge of any prior digits. In this paper, Mathematica is used to find several simpler formulas having powers of 4^{−k}. They also note that it has been proven that their methods cannot be used to exhibit similar formulas in powers of 10^{−k}.

Ortega:1964:GTM

[822] James M. Ortega. Generation of test matrices by similarity transformations. Communications of the ACM, 7(6):377– 378, June 1964. CODEN CACMA2. ISSN 0001-0782 (print), 1557-7317 (electronic). See comment [454].

Knuth:1981:AMM

[823] Donald E. Knuth. Algorithms in modern mathematics and computer science. Lecture Notes in Computer Science, 122: 82–99, 1981. ISSN 0302-9743. Russian translation by G. S. Tseĭtin in Algoritmy v Sovremennoi Matematike i Ee Prilozheni�ıakh, Chast’ I (Novosibirsk: Akademi�ıa Nauk SSSR, Sibirskoe Otdelenie, Vychislitel’nyĭ Tsentr, 1982), 64– 98. Revised version in [407].

Bailey:1997:RCV

[824] David Bailey, Peter Borwein, and Simon Plouffe. On the rapid computation of various polylogarithmic constants. Mathematics of Computation, 66(218):903–913, April 1997. CODEN MCMPAF. ISSN 0025-5718 (print), 1088-6842 (electronic). URL http://

                                        www.ams.org/mcom/1997-66-218. See

[821, 743].