Last update:
Thu Nov 30 06:43:41 MST 2023
K. Fan and
G. G. Lorentz An integral inequality . . . . . . . . . 626--631
Anonymous Semitopological groups . . . . . . . . . 996--998
A. E. Livingston and
M. L. Livingston The congruence $a^{r+s}\equiv a^{r}
\pmod {m}$ . . . . . . . . . . . . . . . 97--100
R. L. Wilder Evolution of the topological concept of
``connected'' . . . . . . . . . . . . . 720--726
Solomon W. Golomb Cyclotomic polynomials and factorization
theorems . . . . . . . . . . . . . . . . 734--737
Malcolm Murrill On a hyperanalytic geometry for complex
functions . . . . . . . . . . . . . . . 8--25
Yu Ting Shen A ``natural'' enumeration of nonnegative
rational numbers---an informal
discussion . . . . . . . . . . . . . . . 25--29
R. L. Wilder Correction and addendum to: ``Evolution
of the topological concept of
`connected'\thinspace '' [Amer. Math.
Monthly \bf 85 (1978), no. 9, 720--726,
MR 80f:01019a] . . . . . . . . . . . . . 31--32
K. W. Thompson and
T. Schonbek A problem of the Pompeiu type . . . . . 32--36
A. M. Russell A commutative Banach algebra of
functions of bounded variation . . . . . 39--40
D. Kirby Concurrences for a triangle . . . . . . 45--47
Richard S. Millman The upper half plane model for
hyperbolic geometry . . . . . . . . . . 48--53
Harry Dym On the absolute convergence of a
multiple integral of ${\rm sin}\,x/x$ 53--54
R. W. Hamming The unreasonable effectiveness of
mathematics . . . . . . . . . . . . . . 81--90
Robert M. MacGregor Generalizing the notion of a periodic
sequence . . . . . . . . . . . . . . . . 90--102
Duane W. DeTemple A geometric method of phase plane
analysis . . . . . . . . . . . . . . . . 102--112
Neal Koblitz The $p$-adic approach to solutions of
equations over finite fields . . . . . . 115--118
J. W. Nienhuys Uniform continuity of derivatives in
convex sets . . . . . . . . . . . . . . 118--120
V. L. N. Sarma and
Nand Lal and
V. K. Singh An example of a locally finite family 121--122
David P. Robbins The probability that neighbors remain
neighbors after random rearrangements 122--124
Edward Rozema Estimating the error in the trapezoidal
rule . . . . . . . . . . . . . . . . . . 124--128
Gabriel Klambauer Summation of series . . . . . . . . . . 128--130
Lawrence Zalcman Offbeat integral geometry . . . . . . . 161--175
David D. Bleecker Infinitesimal deformations of portions
of the standard sphere in $E^{3}$ . . . 175--182
Calvin H. Wilcox Positive temperatures with prescribed
initial heat distributions . . . . . . . 183--186
Antonio Steiner Plancherel's theorem and the Shannon
series derived simultaneously . . . . . 193--197
Dixon Jones Quadrangles, butterflies, Pascal's
hexagon, and projective fixed points . . 197--200
Eric C. Nummela Cayley's theorem for topological groups 202--203
I. Netuka and
J. Vesel\'y Regions of harmonicity . . . . . . . . . 203--205
George Miel Calculator calculus and roundoff errors 243--252
R. E. Rice and
B. Schweizer and
A. Sklar When is $f(f(z))=az^{2}+bz+c$ . . . . . 252--263
Michael A. B. Deakin Euler's version of the Laplace transform 264--269
Carlo H. Sequin Twisted prismatic Klein bottles . . . . 269--277
J. Cobb and
W. Voxman Dispersion points and fixed points . . . 278--281
G. H. Meisters Principal vertices, exposed points, and
ears . . . . . . . . . . . . . . . . . . 284--285
Richard B. Darst The connection between lim sup and
uniform integrability . . . . . . . . . 285--286
H. Groemer On finite classes of convex sets that
permit space coverings . . . . . . . . . 286--288
L. C. Martins and
P. Podio-Guidugli An elementary proof of the polar
decomposition theorem . . . . . . . . . 288--290
Khursheed Alam Bounds on the negative exponential
function . . . . . . . . . . . . . . . . 290--292
James H. Foster and
Jean J. Pedersen On the reflective property of ellipses 294--297
William Watkins Similarity of matrices . . . . . . . . . 300--300
R. Creighton Buck Sherlock Holmes in Babylon . . . . . . . 335--345
Richard Askey Ramanujan's extensions of the gamma and
beta functions . . . . . . . . . . . . . 346--359
Stuart S. Antman The equations for large vibrations of
strings . . . . . . . . . . . . . . . . 359--370
Lee Rubel and
Kenneth Stolarsky Subseries of the power series for
$e^{x}$ . . . . . . . . . . . . . . . . 371--376
Albert Nijenhuis Correction to: ``A minimal-path
algorithm for the `money changing
problem' '' . . . . . . . . . . . . . . 377--377
Alan Dow and
John Ginsburg Integration on $[0,\,1]^{\omega }$ . . . 378--380
D. R. Brown and
M. J. O'Malley On $n$th roots of positive operators . . 380--382
Wulf Rehder On the volume of unions of translates of
a convex set . . . . . . . . . . . . . . 382--384
Péter Kiss A method for solving Diophantine
equations . . . . . . . . . . . . . . . 384--387
Ray Redheffer and
Carey Smith On a surprising inequality of Goldberg
and Straus . . . . . . . . . . . . . . . 387--390
Charles Vanden Eynden Proofs that $\sum 1/p$ diverges . . . . 394--397
Joel Spencer Counting magic squares . . . . . . . . . 397--399
Paul R. Chernoff Pointwise convergence of Fourier series 399--400
B. H. Pourciau Modern multiplier rules . . . . . . . . 433--452
Michael A. Penna Total torsion . . . . . . . . . . . . . 452--461
S. N. Maitra A simple application of the theorem of
composition of accelerations . . . . . . 466--468
M. S. Klamkin Inequalities for inscribed and
circumscribed polygons . . . . . . . . . 469--473
Gebhard Greiter Nonunique factorization in subsemigroups
of semigroups with unique prime
factorization . . . . . . . . . . . . . 473--474
U. V. Satyanarayana A note on Riemann-Stieltjes integrals 477--478
Henry J. Schultz The sum of the $k$th powers of the first
$n$ integers . . . . . . . . . . . . . . 478--481
Donald W. Robinson A proof of the Frobenius rank equality 481--482
Hubert Kennedy The first written examinations at
Harvard College . . . . . . . . . . . . 483--486
P. R. Halmos The heart of mathematics . . . . . . . . 519--524
C. A. Rogers A less strange version of Milnor's proof
of Brouwer's fixed-point theorem . . . . 525--527
András Prékopa On the development of optimization
theory . . . . . . . . . . . . . . . . . 527--542
I. M. Isaacs Roots of polynomials in algebraic
extensions of fields . . . . . . . . . . 543--544
Kenneth B. Stolarsky The power and generalized logarithmic
means . . . . . . . . . . . . . . . . . 545--548
James R. Schatz On the weight distributions of cosets of
a linear code . . . . . . . . . . . . . 548--551
Shinji Yamashita Cowling's theorem on a Dirichlet finite
holomorphic function in the disk . . . . 551--552
J. C. Lagarias and
A. M. Odlyzko Divisibility properties of some
cyclotomic sequences . . . . . . . . . . 561--564
M. A. Golberg and
H. Bowman Mikusi\'nski operators without the
Titchmarsh theorem . . . . . . . . . . . 564--567
George D. Parker A metric model of plane Euclidean
geometry . . . . . . . . . . . . . . . . 567--572
Mina Rees The mathematical sciences and World War
II . . . . . . . . . . . . . . . . . . . 607--621
Ivan Netuka The Dirichlet problem for harmonic
functions . . . . . . . . . . . . . . . 621--628
Robert G. Bartle An extension of Egorov's theorem . . . . 628--633
Walter Stromquist How to cut a cake fairly . . . . . . . . 640--644
Leon Gerber Napoleon's theorem and the parallelogram
inequality for affine-regular polygons 644--648
Joan P. Hutchinson and
Paul B. Trow Some pigeonhole principle results
extended . . . . . . . . . . . . . . . . 648--651
M. S. Klamkin and
A. Liu Note on a result of Niven on impossible
tessellations . . . . . . . . . . . . . 651--653
William J. Knight Functions with zero right derivatives
are constant . . . . . . . . . . . . . . 657--658
Albert Nijenhuis Complete solutions of linear difference
equations . . . . . . . . . . . . . . . 658--660
Kenneth A. Ross Another approach to Riemann-Stieltjes
integrals . . . . . . . . . . . . . . . 660--662
D. J. Newman Simple analytic proof of the prime
number theorem . . . . . . . . . . . . . 693--696
E. R. Swart The philosophical implications of the
four-color problem . . . . . . . . . . . 697--707
M. D. Fox Formulae for the curvatures of circles
in chains . . . . . . . . . . . . . . . 708--715
Frank Boesch and
Ralph Tindell Robbins's theorem for mixed multigraphs 716--719
Solomon W. Golomb Iterated binomial coefficients . . . . . 719--727
A. Galperin and
Z. Waksman An elementary approach to Jordan theory 728--732
János Pintz On Legendre's prime number formula . . . 733--735
Zensho Nakao Polynomial group laws . . . . . . . . . 735--736
Miguel de Guzmán A change-of-variables formula without
continuity . . . . . . . . . . . . . . . 736--739
Ronald E. Prather Generating the $k$-subsets of an $n$-set 740--743
Thomas Whaley and
Judson Williford Differentiability and permutations of
quantifiers . . . . . . . . . . . . . . 745--748
D. R. Smart When does $T^{n+1}x-T^{n}x\rightarrow 0$
imply convergence . . . . . . . . . . . 748--749
B. R. Johnson An elementary proof of
inclusion-exclusion formulas . . . . . . 750--751
Duane W. DeTemple and
Jack M. Robertson Constructing Buffon curves from their
distributions . . . . . . . . . . . . . 779--784
Steven Roman The formula of Fa\`a di Bruno . . . . . 805--809
Israel Halperin and
Peter Rosenthal Burnside's theorem on algebras of
matrices . . . . . . . . . . . . . . . . 810--810
A. Ecker Comment on the note: ``The congruence
$a^{r+s}\equiv a^{r} \pmod {m}$'' [Amer.
Math. Monthly 85 (1978), no. 2, 97--100,
MR 57 #12355] by A. E. Livingston and M.
L. Livingston . . . . . . . . . . . . . 811--814
J. M. Henle Functions with arbitrarily small periods 816--816
C. C. Cowen and
K. R. Davidson and
R. P. Kaufman Rearranging the alternating harmonic
series . . . . . . . . . . . . . . . . . 817--819
R. B. Burckel A strong converse to Gauss's mean-value
theorem . . . . . . . . . . . . . . . . 819--820
Bernard Grofman Fair apportionment and the Banzhaf index 1--5
B. Roth Rigid and flexible frameworks . . . . . 6--21
J. R. Quine Plücker equations for curves . . . . . . 21--29
Kenneth R. Meyer An application of Poincaré's recurrence
theorem to academic administration . . . 32--33
Paul Schaefer Sum-preserving rearrangements of
infinite series . . . . . . . . . . . . 33--40
C. G. Méndez On the law of large numbers, infinite
games, and category . . . . . . . . . . 40--42
Richard A. Dean A rational polynomial whose group is the
quaternions . . . . . . . . . . . . . . 42--45
Douglas S. Bridges On Montel's proof of the great Picard
theorem . . . . . . . . . . . . . . . . 45--47
Tudor Zamfirescu Most monotone functions are singular . . 47--49
Herbert S. Wilf An algorithm-inspired proof of the
spectral theorem in $E^{n}$ . . . . . . 49--50
Mark D. Meyerson Every power series is a Taylor series 51--52
John Isbell Submodules of free modules . . . . . . . 53--53
Thomas Zaslavsky The geometry of root systems and signed
graphs . . . . . . . . . . . . . . . . . 88--105
Chester J. Salwach Planes, biplanes, and their codes . . . 106--125
Hans Willi Siegberg Some historical remarks concerning
degree theory . . . . . . . . . . . . . 125--139
R. Creighton Buck Characterization of classes of functions 139--142
Lindsay N. Childs and
Morris Orzech On modular group rings, normal bases,
and fixed points . . . . . . . . . . . . 142--145
G. M. Phillips Archimedes the numerical analyst . . . . 165--169
L. J. Ratliff, Jr. A brief history and survey of the
catenary chain conjectures . . . . . . . 169--178
Russell Merris Pólya's counting theorem via tensors . . 179--185
Marcus B. Feldman A proof of Lusin's theorem . . . . . . . 191--192
Adolf Cusmariu A proof of the arithmetic mean-geometric
mean inequality . . . . . . . . . . . . 192--194
S. M. Gagola, Jr. and
S. C. Garrison and
M. R. Pettet On a vanishing product in the integral
group ring . . . . . . . . . . . . . . . 195--196
Ernst Snapper An affine generalization of the Euler
line . . . . . . . . . . . . . . . . . . 196--198
Charles Riley A note on strict convexity . . . . . . . 198--199
Stanley Kertzner The linear Diophantine equation . . . . 200--203
Hermann Hueber On uniform continuity and compactness in
metric spaces . . . . . . . . . . . . . 204--205
Emeric Deutsch Bounds for the zeros of polynomials . . 205--206
R. Arthur Knoebel Exponentials reiterated . . . . . . . . 235--252
J. L. Brenner and
R. C. Lyndon Proof of the fundamental theorem of
algebra . . . . . . . . . . . . . . . . 253--256
Ezra Brown The first proof of the quadratic
reciprocity law, revisited . . . . . . . 257--264
Yakar Kannai An elementary proof of the no-retraction
theorem . . . . . . . . . . . . . . . . 264--268
James Kraft and
Michael Rosen Eisenstein reciprocity and $n$th-power
residues . . . . . . . . . . . . . . . . 269--270
John A. Ewell An easy proof of the triple-product
identity . . . . . . . . . . . . . . . . 270--272
W. A. Sentance Occurrences of consecutive odd powerful
numbers . . . . . . . . . . . . . . . . 272--274
Josip E. Pe\vcari\'c Note on: ``An integral inequality''
[Amer. Math. Monthly \bf 61 (1954),
626--631, MR \bf 16, 342] by K. Fan and
G. G. Lorentz . . . . . . . . . . . . . 275--276
Daniel A. Marcus Classroom Notes: An Alternative to
Euclid's Algorithm . . . . . . . . . . . 280--283
Arthur H. Copeland, Jr. and
Albert O. Shar Constructing loops from groups . . . . . 283--285
G. J. Porter New angles on an old game . . . . . . . 285--286
Philip J. Davis Are there coincidences in mathematics 311--320
W. Hrusa and
J. L. Troutman Elementary characterization of classical
minima . . . . . . . . . . . . . . . . . 321--327
H. B. Griffiths Cayley's version of the resultant of two
polynomials . . . . . . . . . . . . . . 328--338
Solomon W. Golomb Corrections to: ``Cyclotomic polynomials
and factorization theorems'' [Amer.
Math. Monthly \bf 85 (1978), no. 9,
734--737, MR 80e:10011] . . . . . . . . 338--339
Duane Boes and
Richard Darst and
Paul Erd\Hos Fat, symmetric, irrational Cantor sets 340--341
Thomas P. Dence On the monotonicity of a class of
exponential sequences . . . . . . . . . 341--344
Michael Rosen Abel's theorem on the lemniscate . . . . 387--395
R. B. Burckel Iterating analytic self-maps of discs 396--407
Frank D. Grosshans Rigid motions of conics: an introduction
to invariant theory . . . . . . . . . . 407--413
Edith H. Luchins Women and mathematics: fact and fiction 413--419
John Bloom and
Lee Whitt The geometry of rolling curves . . . . . 420--426
John A. R. Holbrook Stochastic independence and
space-filling curves . . . . . . . . . . 426--432
Y. Sternfeld Homeomorphisms of cubes into Euclidean
spaces . . . . . . . . . . . . . . . . . 436--439
Robert D. Small Modified convergence of Taylor series 439--441
Andrew Sobczyk Equivalence of an identity in vector
analysis to quaternion associativity,
and ramifications . . . . . . . . . . . 441--443
Saunders Mac Lane Mathematical models: a sketch for the
philosophy of mathematics . . . . . . . 462--472
L. E. Dubins and
D. A. Freedman Machiavelli and the Gale--Shapley
algorithm . . . . . . . . . . . . . . . 485--494
I. Grattan-Guinness On the development of logics between the
two World Wars . . . . . . . . . . . . . 495--509
Edward T. Wong Polygons, circulant matrices, and
Moore--Penrose inverses . . . . . . . . 509--515
Roger L. Cooke Almost-periodic functions . . . . . . . 515--526
D. J. Newman Differentiation of asymptotic formulas 526--527
Alexander Abian Generalizing the generalized mean-value
theorem . . . . . . . . . . . . . . . . 528--530
G. Alefeld On the convergence of Halley's method 530--536
M. Katchalski and
M. S. Klamkin and
A. Liu An experience in problem solving . . . . 551--556
W. B. Arthur Why a population converges to stability 557--563
Karen D. Rappaport S. Kovalevsky: a mathematical lesson . . 564--574
William Abikoff The uniformization theorem . . . . . . . 574--592
Patricia C. Kenschaft Black women in mathematics in the United
States . . . . . . . . . . . . . . . . . 592--604
Cyril W. L. Garner and
Agnes M. Herzberg On McCarty's queen squares . . . . . . . 612--613
Walter Stromquist Addendum to: ``How to cut a cake
fairly'' [Amer. Math. Monthly \bf 87
(1980), no. 8, 640--644, MR 81m:05016] 613--614
Chantal Shafroth A generalization of the formula for
computing the inverse of a matrix . . . 614--616
I. J. Schoenberg A direct derivation of a Jacobian
identity from elliptic functions . . . . 616--618
Bhama Srinivasan Characters of finite groups: some uses
and mathematical applications . . . . . 639--646
J.-P. Delahaye The set of periodic points . . . . . . . 646--651
J. W. Bruce and
P. J. Giblin and
C. G. Gibson On caustics of plane curves . . . . . . 651--667
Lawrence Narici and
Edward Beckenstein Strange terrain --- non-Archimedean
spaces . . . . . . . . . . . . . . . . . 667--676
Eldon Hansen Sums of functions satisfying recursion
relations . . . . . . . . . . . . . . . 676--679
Solomon W. Golomb Normed division domains . . . . . . . . 680--686
Jozef Dodziuk Eigenvalues of the Laplacian and the
heat equation . . . . . . . . . . . . . 686--695
Richard Johnsonbaugh The trapezoid rule, Stirling's formula,
and Euler's constant . . . . . . . . . . 696--698
Elon Kohlberg and
Abraham Neyman Asymptotic behavior of nonexpansive
mappings in uniformly convex Banach
spaces . . . . . . . . . . . . . . . . . 698--700
Donald E. Knuth A permanent inequality . . . . . . . . . 731--740, 798
Geoffrey C. Berresford Cauchy's theorem . . . . . . . . . . . . 741--744
Heinrich Guggenheimer The Hilbert model of hyperbolic geometry 744--748
Edwin Buchman The impossibility of tiling a convex
region with unequal equilateral
triangles . . . . . . . . . . . . . . . 748--753
Katherine E. McLain and
Hugh M. Edgar A note on S. W. Golomb's: ``Cyclotomic
polynomials and factorization theorems''
[Amer. Math. Monthly \bf 85 (1978), no.
9, 734--737, MR 80e:10011] . . . . . . . 753--753
Tibor \vSalát On functions that are monotone on no
interval . . . . . . . . . . . . . . . . 754--755
Richard A. Davis More on similarity of matrices . . . . . 761--762
F. F. Bonsall A down-to-earth view of mathematics . . 8--15
A. J. W. Duijvestijn and
P. J. Federico and
P. Leeuw Compound perfect squares . . . . . . . . 15--32
John Wavrik Computers and the multiplicity of
polynomial roots . . . . . . . . . . . . 34--36, 45--56
Charles Small A simple proof of the four-squares
theorem . . . . . . . . . . . . . . . . 59--61
G. Baley Price Award for distinguished service to Dr.
Thornton Carl Fry . . . . . . . . . . . 81--83 (1 plate)
Tony Rothman Genius and biographers: the
fictionalization of Évariste Galois . . . 84--106
F. H. Norwood Long proofs . . . . . . . . . . . . . . 110--112
Andrew Simoson An ``Archimedean'' paradox . . . . . . . 114--116, 125
M. Nair On Chebyshev-type inequalities for
primes . . . . . . . . . . . . . . . . . 126--129
Desmond Fearnley-Sander Hermann Grassmann and the prehistory of
universal algebra . . . . . . . . . . . 161--166
Carmen Chicone and
Jing Huang Tian On general properties of quadratic
systems . . . . . . . . . . . . . . . . 167--178
Robert C. Reilly Mean curvature, the Laplacian, and soap
bubbles . . . . . . . . . . . . . . . . 180--188, 197--198
Hong Xiang Li Elementary quadratures of ordinary
differential equations . . . . . . . . . 198--208
Mau Hsiang Shih An analog of Bolzano's theorem for
functions of a complex variable . . . . 210--211
Wolfgang Walter Old and new approaches to Euler's
trigonometric expansions . . . . . . . . 225--230
Azriel Rosenfeld How a digital computer can tell whether
a line is straight . . . . . . . . . . . 231--235
F. K. Hwang New concepts in seeding knockout
tournaments . . . . . . . . . . . . . . 235--239
Andreana S. Madguerova On Bridges' proof of the great Picard
theorem . . . . . . . . . . . . . . . . 239--239
Walter Rudin Nonuniqueness and growth in first-order
differential equations . . . . . . . . . 241--244
A. K. Bose Linear differential equations on the
complex plane . . . . . . . . . . . . . 244--249
Harley Flanders On the Fresnel integrals . . . . . . . . 264--266
Herbert S. Wilf What is an answer . . . . . . . . . . . 289--292
Bernard Jacobson On the mean value theorem for integrals 300--301
David Challener and
Lee Rubel A converse to Rouché's theorem . . . . . 302--305
Pablo M. Salzberg A reflection principle for calculating
the derivatives of a polynomial . . . . 305--307
Brian M. Scott and
Zachary Robinson The boundary topology of a space . . . . 307--309
E. S. Wolk On the inadequacy of subnets and
transfinite sequences . . . . . . . . . 310--311
Alfonso G. Azpeitia On the Lagrange remainder of the Taylor
formula . . . . . . . . . . . . . . . . 311--312
Norman M. Rice On $n$th roots of positive operators . . 313--314
Achim Clausing Kantorovich-type inequalities . . . . . 314, 327--330
Aviezri S. Fraenkel How to beat your Wythoff games' opponent
on three fronts . . . . . . . . . . . . 353--361
William S. Hatcher Calculus is algebra . . . . . . . . . . 362--370
Edwin O. Buchman and
Frederick A. Valentine Any new Helly numbers . . . . . . . . . 370--375
Robert S. Strichartz Radon inversion --- variations on a
theme . . . . . . . . . . . . . . . . . 377--384, 420--423
Fred Richman Meaning and information in constructive
mathematics . . . . . . . . . . . . . . 385--388
Raymond G. Ayoub On the nonsolvability of the general
polynomial . . . . . . . . . . . . . . . 397--401
Dan Kalman Central functions and fixed points . . . 401--402
Renfrey B. Potts Differential and difference equations 402--407
Gerald Janusz and
Joseph Rotman Outer automorphisms of $S_{6}$ . . . . . 407--410
Amitava Bagchi and
Edward M. Reingold A naturally occurring function
continuous only at irrationals . . . . . 411--417
G. P. Wene A little color in abstract algebra . . . 417--419
Dean S. Clark On some abstract properties of binomial
coefficients . . . . . . . . . . . . . . 433--443
Dawn Fisher Extending functions to infinitesimals of
finite order . . . . . . . . . . . . . . 443--449
W. M. Snyder Factoring repunits . . . . . . . . . . . 462--466
F. S. Cater Most monotone functions are not singular 466--469
Gilbert Strang The width of a chair . . . . . . . . . . 529--534
Robert L. Devaney Blowing up singularities in classical
mechanical systems . . . . . . . . . . . 535--552
Richard Johnsonbaugh and
Tadao Murata Petri nets and marked graphs ---
mathematical models of concurrent
computation . . . . . . . . . . . . . . 552--566
Gregory A. Fredricks Sylvester's theorem for matrices with
smooth entries . . . . . . . . . . . . . 586--587
Jean-Pierre Rosay Injective holomorphic mappings . . . . . 587--588
Robert C. James Bases in Banach spaces . . . . . . . . . 625--640
Yung Chow Wong and
Kai Man Tsang A strong converse of Morley's trisector
theorem . . . . . . . . . . . . . . . . 642--653
Robert F. Brown The fixed point property and Cartesian
products . . . . . . . . . . . . . . . . 654--678
A. W. Marshall and
I. Olkin A convexity proof of Hadamard's
inequality . . . . . . . . . . . . . . . 687--688
Abraham Ungar Generalized hyperbolic functions . . . . 688--691
Donald Duncan and
William Barnier On trisection, quintisection, \ldots,
etc. . . . . . . . . . . . . . . . . . . 693--693
Robert A. Proctor Solution of two difficult combinatorial
problems with linear algebra . . . . . . 721--734
Charles Small On the equation $xyz=x+y+z=1$ . . . . . 736--749
Murray Bell and
John Ginsburg A space which will not go where its
proper subspaces want it to go . . . . . 749--751
Donald E. Knuth Elementary problem E2982, a double
infinite sum for $\vert x\vert$ . . . . 54--54
E. L. Ortiz and
T. J. Rivlin Another look at the Chebyshev
polynomials . . . . . . . . . . . . . . 3--10
R. Fletcher and
D. C. Sorensen An algorithmic derivation of the Jordan
canonical form . . . . . . . . . . . . . 12--16
George Miel Of calculations past and present: the
Archimedean algorithm . . . . . . . . . 17--35
Walter Rudin Well-distributed measurable sets . . . . 41--42
Bernard R. Gelbaum An algorithm for the minimal polynomial
of a matrix . . . . . . . . . . . . . . 43--44
Cleve Moler and
Donald Morrison Singular value analysis of cryptograms 78--87
Roger Fenn What is the geometry of a surface . . . 87--98
Richard McIntosh A necessary and sufficient condition for
the primality of Fermat numbers . . . . 98--99
Quentin F. Stout and
Patricia A. Woodworth Relational databases . . . . . . . . . . 101--118
J. A. Guthrie A continuous modulus of continuity . . . 126--127
Melvin Hausner Applications of a simple counting
technique . . . . . . . . . . . . . . . 127--129
Jan Mycielski The meaning of the conjecture ${\rm
P}\not={\rm NP}$ for mathematical logic 129--130
Keith M. Kendig Algebra, geometry, and algebraic
geometry: some interconnections . . . . 161--174
Uri Leron Structuring mathematical proofs . . . . 174--185
Judith V. Grabiner Who gave you the epsilon? Cauchy and the
origins of rigorous calculus . . . . . . 185--194
L. Richard Duffy An elementary proof of the isomorphism
${\bf C}^{*} \approx S^{1}$ . . . . . . 201--202
J.-C. Renaud Matrices with integer entries and
integer eigenvalues . . . . . . . . . . 202--203
Juan L. Romero When is $L^p(\mu)$ contained in
$L^q(\mu)$? . . . . . . . . . . . . . . 203--206
J.-B. Hiriart-Urruty A short proof of the variational
principle for approximate solutions of a
minimization problem . . . . . . . . . . 206--207
Joel Franklin Mathematical methods of economics . . . 229--244
Thomas Jech The ranking of incomplete tournaments: a
mathematician's guide to popular sports 246--266
Morris Marden Conjectures on the critical points of a
polynomial . . . . . . . . . . . . . . . 267--276
Donald G. Hartig The Riesz representation theorem
revisited . . . . . . . . . . . . . . . 277--280
E. E. Posey and
J. E. Vaughan Functions with a proper local maximum in
each interval . . . . . . . . . . . . . 281--282
Liu Wen A space filling curve . . . . . . . . . 283--283
Man Duen Choi Tricks or treats with the Hilbert matrix 301--312
R. Hirshon A group with constant growth rate . . . 312--317
Charles W. Schelin Calculator function approximation . . . 317--325
Allen J. Schwenk and
J. Ian Munro How small can the mean shadow of a set
be . . . . . . . . . . . . . . . . . . . 325--329
Charles Blair and
Lee A. Rubel A universal entire function . . . . . . 331--332
John Milnor On the geometry of the Kepler problem 353--365
Joel Spencer Short theorems with long proofs . . . . 365--366
P. C. Fishburn and
H. O. Pollak Fixed-route cost allocation . . . . . . 366--378
William C. Waterhouse Do symmetric problems have symmetric
solutions . . . . . . . . . . . . . . . 378--387
Kenneth R. Davidson Pointwise limits of analytic functions 391--394
Lee A. Rubel and
Aristomenis Siskakis A net of exponentials converging to a
nonmeasurable function . . . . . . . . . 394--396
Jürgen Kindler A simple proof of the Daniell-Stone
representation theorem . . . . . . . . . 396--397
A. Keith Austin An elementary approach to
NP-completeness . . . . . . . . . . . . 398--399
Geng Zhe Chang and
Philip J. Davis Iterative processes in elementary
geometry . . . . . . . . . . . . . . . . 421--431
Theodore P. Hill Determining a fair border . . . . . . . 438--442
Harry Appelgate and
Hironori Onishi The slow continued fraction algorithm
via $2\times 2$ integer matrices . . . . 443--455
W. A. Coppel An interesting Cantor set . . . . . . . 456--460
Lance L. Littlejohn Symmetry factors for differential
equations . . . . . . . . . . . . . . . 462--464
H. Haruki and
S. Haruki Euler's integrals . . . . . . . . . . . 464--466
James W. Walker A homology version of the Borsuk-Ulam
theorem . . . . . . . . . . . . . . . . 466--468
John F. Hughes and
J. O. Shallit On the number of multiplicative
partitions . . . . . . . . . . . . . . . 468--471
Deborah Tepper Haimo and
Franklin Tepper Haimo Comments and complements . . . . . . . . 472--478
Bruce C. Berndt The quarterly reports of S. Ramanujan 505--516
James T. Cross The Euler $\varphi$-function in the
Gaussian integers . . . . . . . . . . . 518--528
J. W. Bruce and
P. J. Giblin Generic geometry . . . . . . . . . . . . 529--545
Steven G. Krantz Characterization of smooth domains in
${\bf C}$ by their biholomorphic
self-maps . . . . . . . . . . . . . . . 555--557
Michael J. Hoffman and
Richard Katz The sequence of derivatives of a
$C^{\infty }$ function . . . . . . . . . 557--560
P. S. Bullen An inequality for variations . . . . . . 560--560
Z. Kominek Measure, category, and the sums of sets 561--562
George K. Francis Drawing Seifert surfaces that fiber the
figure-$8$ knot complement in $S^{3}$
over $S^{1}$ . . . . . . . . . . . . . . 589--599
Roger Howe Very basic Lie theory . . . . . . . . . 600--623
Steven C. Althoen and
Lawrence D. Kugler When is ${\bf R}^{2}$ a division algebra 625--635
John A. Ewell A simple proof of Fermat's two-square
theorem . . . . . . . . . . . . . . . . 635--637
G. Ladas and
Y. G. Sficas and
I. P. Stavroulakis Necessary and sufficient conditions for
oscillations . . . . . . . . . . . . . . 637--640
Andrzej Szulkin ${\bf R}^{3}$ is the union of disjoint
circles . . . . . . . . . . . . . . . . 640--641
Robert C. Thompson Author vs. referee: a case history for
middle level mathematicians . . . . . . 661--668
Joel Spencer Large numbers and unprovable theorems 669--675
Michael E. Mays Functions which parametrize means . . . 677--683
K. J. Falconer Applications of a result on spherical
integration to the theory of convex sets 690--693
Denis Higgs Iterating the derived set function . . . 693--697
W. S. Massey Cross products of vectors in
higher-dimensional Euclidean spaces . . 697--701
Elgin Johnston A ``counterexample'' for the
Schwarz--Christoffel transform . . . . . 701--703
Donald G. Saari and
John B. Urenko Newton's method, circle maps, and
chaotic motion . . . . . . . . . . . . . 3--17
Harvey Diamond and
Gregory Gell\`es Relations among some classes of subsets
of ${\bf R}$ . . . . . . . . . . . . . . 19--22
R. B. Burckel Bishop's Stone-Weierstrass theorem . . . 22--32
Brad Jackson and
Gerhard Ringel Colorings of circles . . . . . . . . . . 42--49
R. Fuster and
A. Marquina Geometric series in incomplete normed
algebras . . . . . . . . . . . . . . . . 49--51
C. R. MacCluer A simple proof of the fundamental
theorem on finite abelian groups . . . . 52--52
Joseph Kupka and
Karel Prikry The measurability of uncountable unions 85--97
Daniel B. Shapiro A periodicity problem in plane geometry 97--108
George M. Phillips Archimedes and the complex plane . . . . 108--114
P. G. Laird and
R. McCann On some characterizations of polynomials 114--116
Timothy C. Brown Poisson approximations and the
definition of the Poisson process . . . 116--123
Joseph MacDonnell A ruled Moebius band which
self-intersects in a straight line . . . 125--127
Thomas L. Miller and
Robert F. Olin Analytic curves . . . . . . . . . . . . 127--130
G. W. Johnson An unsymmetric Fubini theorem . . . . . 131--133
Joseph A. Gallian Another proof that $A_{5}$ is simple . . 134--135
Hung C. Li A generalized problem of least squares 135--137
Claude Christen and
Frank K. Hwang Detection of a defective coin with
partial weight information . . . . . . . 173--179
Robert S. Boyer and
J. Strother Moore Proof checking the RSA public key
encryption algorithm . . . . . . . . . . 181--189
Andrew Simoson On two halves being two wholes . . . . . 190--193
Marvin Jay Greenberg Note on the Cayley--Hamilton theorem . . 193--195
Josip E. Pe\vcari\'c A simple proof of the Jensen-Steffensen
inequality . . . . . . . . . . . . . . . 195--196
Joseph A. Gallian and
James Van Buskirk The number of homomorphisms from $Z_{m}$
into $Z_{n}$ . . . . . . . . . . . . . . 196--197
J. B. Wilker Möbius equivalence and Euclidean symmetry 225--247
Roger Howe Correction to: ``Very basic Lie theory'' 247--247
Kenneth M. Levasseur A probabilistic proof of the Weierstrass
approximation theorem . . . . . . . . . 249--250
Michael Stob A supplement to: ``A mathematician's
guide to popular sports'' [Amer. Math.
Monthly \bf 90 (1983), no. 4, 246--266,
MR 85i:05122a] by T. Jech . . . . . . . 277--282
Kurt Eisemann Number-theoretic analysis and extensions
of ``the most complicated and fantastic
card trick ever invented'' . . . . . . . 284--289
Andrew P. Guinand Euler lines, tritangent centers, and
their triangles . . . . . . . . . . . . 290--300
Walter Rudin The inner function problem . . . . . . . 301--302
Mohsen Pourahmadi Taylor expansion of ${\rm exp}(\sum
^{\infty }_{k=0}a_{k}z^{k})$ and some
applications . . . . . . . . . . . . . . 303--307
F. S. Cater On van der Waerden's nowhere
differentiable function . . . . . . . . 307--308
John D. Dixon Factorization and primality tests . . . 333--352
G. M. Phillips Aitken sequences and Fibonacci numbers 354--357
Zoltán Magyar A recursion on quadruples . . . . . . . 360--362
I. Bárány and
M. Katchalski and
János Pach Helly's theorem with volumes . . . . . . 362--365
R. J. Stroeker How to solve a Diophantine equation ---
a number-theoretic excursion . . . . . . 385--392
B. L. Burrows and
R. F. Talbot Sums of powers of integers . . . . . . . 394--403
John V. Baxley and
John C. Moorhouse Lagrange multiplier problems in
economics . . . . . . . . . . . . . . . 404--412
David Avis The number of furthest neighbour pairs
of a finite planar set . . . . . . . . . 417--420
R. P. Lewis A combinatorial proof of the triple
product identity . . . . . . . . . . . . 420--423
Doris J. Schattschneider The taxicab group . . . . . . . . . . . 423--428
B. J. Ball Arcwise connectedness and the
persistence of errors . . . . . . . . . 431--433
J. M. Henle Tangent planes with infinitesimals . . . 433--435
Kenneth S. Williams Letter to the editor: ``Euler's
integrals'' [Amer. Math. Monthly \bf 90
(1983), no. 7, 464--466, MR 84k:26012],
by H. Haruki and S. Haruki . . . . . . . 455--455
Donald E. Knuth The toilet paper problem . . . . . . . . 465--470
George Boolos The logic of provability . . . . . . . . 470--480
Karl Scherer Some new types of closure properties in
the plane . . . . . . . . . . . . . . . 480--487
Myron S. Henry Approximation by polynomials:
interpolation and optimal nodes . . . . 497--499
R. Spigler Double limits and matched asymptotic
expansions . . . . . . . . . . . . . . . 501--505
Nam Kiu Tsing Infinite-dimensional Banach spaces must
have uncountable basis---an elementary
proof . . . . . . . . . . . . . . . . . 505--506
Avraham Feintuch and
Matatyahu Rubin The matrix equation $AX-XB=C$ . . . . . 506--507
H. G. ter Morsche and
G. W. Veltkamp A discrete Landau problem . . . . . . . 508--509
André Weil Euler . . . . . . . . . . . . . . . . . 537--542
Graciela S. Birman and
Katsumi Nomizu Trigonometry in Lorentzian geometry . . 543--549
H. J. ter Horst Riemann-Stieltjes and Lebesgue-Stieltjes
integrability . . . . . . . . . . . . . 551--559
Sidney A. Morris An elementary proof that the Hilbert
cube is compact . . . . . . . . . . . . 563--564
F. S. Cater A partition of the unit interval . . . . 564--566
Stephen Wolfram Geometry of binomial coefficients . . . 566--571
I. M. Richards A remark on the number of cyclic
subgroups of a finite group . . . . . . 571--572
Richard Koch Matrix invariants . . . . . . . . . . . 573--575
Angus E. Taylor A life in mathematics remembered . . . . 605--618
F. S. Cater Differentiable, nowhere analytic
functions . . . . . . . . . . . . . . . 618--624
Murray Schechter Summation of divergent series by
computer . . . . . . . . . . . . . . . . 629--632
Geng Zhe Chang Bernstein polynomials via the shifting
operator . . . . . . . . . . . . . . . . 634--638
Frederick Solomon A theorem concerning Lorentz
transformations . . . . . . . . . . . . 638--641
Ryuji Maehara The Jordan curve theorem via the Brouwer
fixed point theorem . . . . . . . . . . 641--643
Hans U. Gerber Wronski's formula and the resultant of
two polynomials . . . . . . . . . . . . 644--646
Bruce R. Johnson An elementary approach for extending
Poisson processes to the nonstationary
case . . . . . . . . . . . . . . . . . . 646--648
Donald E. Knuth Problem E3106, A curious sum for Euler's
totient function . . . . . . . . . . . . 590
Emma Lehmer On square-separable primes . . . . . . . 719--720
Jeffrey C. Lagarias The $3x+1$ problem and its
generalizations . . . . . . . . . . . . 3--23
J. Chris Fisher and
D. Ruoff and
J. Shilleto Perpendicular polygons . . . . . . . . . 23--37
W. G. Bardsley and
R. M. W. Wood Critical points and sigmoidicity of
positive rational functions . . . . . . 37--48
Ingram Olkin A probabilistic proof of a theorem of
Schur . . . . . . . . . . . . . . . . . 50--51
David L. Reiner Enumeration in music theory . . . . . . 51--54
David M. Bressoud and
Doron Zeilberger Bijecting Euler's partitions-recurrence 54--55
L. Wos Automated reasoning . . . . . . . . . . 85--92
Alexander Abian Solvability of infinite systems of
polynomial equations over the field of
complex numbers . . . . . . . . . . . . 94--98
A. O. Pittenger The logarithmic mean in $n$ variables 99--104
Aviezri S. Fraenkel Systems of numeration . . . . . . . . . 105--114
Wolfgang Walter An elementary proof of the
Cauchy-Kowalevsky theorem . . . . . . . 115--126
Bruce C. Berndt The gamma function and the Hurwitz
zeta-function . . . . . . . . . . . . . 126--130
Walter Gander On Halley's iteration method . . . . . . 131--134
Carmen Chicone and
N. J. Kalton and
Ira J. Papick A converse for the Cayley--Hamilton
theorem . . . . . . . . . . . . . . . . 134--136
Jerry Johnson An elementary characterization of weak
convergence of measures . . . . . . . . 136--137
Harvey Diamond and
Gregory Gelles Interlaced second category sets . . . . 138--140
Ernst Snapper An ingrained error concerning resultants 141--141
M. Cosnard and
C. Masse Letter to the editor: ``Newton's method,
circle maps, and chaotic motion'' [Amer.
Math. Monthly \bf 91 (1984), no. 1,
3--17, MR 85a:58060] by D. Saari and J.
Urenko . . . . . . . . . . . . . . . . . 157--158
David Roselle Award for distinguished service to
Professor Everett Pitcher . . . . . . . 169--170
Donald E. Knuth Algorithmic thinking and mathematical
thinking . . . . . . . . . . . . . . . . 170--181
Jonathan Britt The anatomy of low-dimensional stable
singularities . . . . . . . . . . . . . 183--201
F. J. Craveiro de Carvalho Characterizing maximally looped closed
curves . . . . . . . . . . . . . . . . . 202--207
Ronald J. Leach On Gelbaum's algorithm for computing the
minimal polynomial of a matrix . . . . . 208--209
Vladimir Drobot and
Micha\l Morayne Continuous functions with a dense set of
proper local maxima . . . . . . . . . . 209--211
Frank Harary and
Robert W. Robinson The diameter of a graph and its
complement . . . . . . . . . . . . . . . 211--212
Kenneth M. Levasseur Letter to the editor: ``A probabilistic
proof of the Weierstrass approximation
theorem'' [Amer. Math. Monthly \bf 91
(1984), no. 4, 249--250, MR 85h:41016] 227--227
Ethan Akin and
Morton Davis Bulgarian solitaire . . . . . . . . . . 237--250
Herbert S. Wilf Some examples of combinatorial averaging 250--261
David Gale and
Marilda Sotomayor Ms. Machiavelli and the stable matching
problem . . . . . . . . . . . . . . . . 261--268
William C. Waterhouse When one equation solves them all . . . 270--273
F. J. Papp The d'Alembert functional equation . . . 273--275
L. K. Arnold and
S. J. Benkoski and
B. J. McCabe The discriminator (a simple application
of Bertrand's postulate) . . . . . . . . 275--277
Seymour Lipschutz Notes on graphs and matrix inequalities 277--280
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 . . . . . . 303--303
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] . . . . . . . . . . . . . . . 303--304
F. J. Bloore and
H. R. Morton Advice on hanging pictures . . . . . . . 309--321
B. van Rootselaar How to solve the system $x'=Ax$ . . . . 321--327
A. H. Stone Trees and power-sums . . . . . . . . . . 328--331
Robert Osserman The four-or-more vertex theorem . . . . 332--337
Solomon Leader The inclusion-exclusion probability
formulas by Taylor's theorem . . . . . . 343--345
A. Charnow and
E. Charnow On transcendental linear operators . . . 345--347
Piotr Biler Dini type theorems on positive series 347--349
C. E. Burgess Classification of surfaces . . . . . . . 349--354
Boris Kimelfeld An inequality concerning minors of a
semidefinite matrix . . . . . . . . . . 354--355
Paul R. Chernoff Letter to the editor: ``Pointwise
convergence of Fourier series'' [Amer.
Math. Monthly \bf 87 (1980), no. 5,
399--400, MR 81b:42028] . . . . . . . . 373--374
Mogens Esrom Larsen Rubik's revenge: the group theoretical
solution . . . . . . . . . . . . . . . . 381--390
T. H. MacGregor Linear methods in geometric function
theory . . . . . . . . . . . . . . . . . 392--406
Paul Cull and
E. F. Ecklund, Jr. Towers of Hanoi and analysis of
algorithms . . . . . . . . . . . . . . . 407--420
Jeff Connor A short proof of Steinhaus' theorem on
summability . . . . . . . . . . . . . . 420--421
Robin Thomas A combinatorial construction of a
nonmeasurable set . . . . . . . . . . . 421--422
Paul Bankston and
Ralph Fox Topological partitions of Euclidean
space by spheres . . . . . . . . . . . . 423--424
John D. Dixon Letter to the editor: ``Factorization
and primality tests'' . . . . . . . . . 444--444
D. H. Lehmer Interesting series involving the central
binomial coefficient . . . . . . . . . . 449--457
T. A. McKee The logic of graph-theoretic duality . . 457--464
Marc Rogalski and
Jean Saint-Raymond Inequalities about symmetric compact
convex sets in the plane . . . . . . . . 466--480
Lawrence J. Wallen Modified iteration and probability . . . 481--485
Alfonso Villani Another note on the inclusion
$L^p(\mu)\subset L^q(\mu)$ . . . . . . . 485--487
M. Arala Chaves Spaces where all continuity is uniform 487--489
Walter Rudin Unique right inverses are two-sided . . 489--490
Gunnar Blom A simple property of exchangeable random
variables . . . . . . . . . . . . . . . 491--492
N. J. Lord Simultaneous complements in
finite-dimensional vector spaces . . . . 492--493
N. Costa Pereira A short proof of Chebyshev's theorem . . 494--495
Geng Zhe Chang Planar metric inequalities derived from
the Vandermonde determinant . . . . . . 495--499
Jerome L. Paul Combinatorial proofs of Pascal's formula
for sums of powers of the integers . . . 499--501
I. N. Baker and
P. J. Rippon A note on complex iteration . . . . . . 501--504
Warren Page Compactness and closedness in locally
compact Hausdorff spaces . . . . . . . . 504--506
James M. Ortega Comment on: ``Matrices with integer
entries and integer eigenvalues'' by
J.-C. Renaud [Amer. Math. Monthly \bf 90
(1983), no. 3, 202--203, MR 84c:15024 ]
and ``Generation of test matrices by
similarity transformations'' by Ortega
[Comm. ACM \bf 7 (1964), 377--378, MR
\bf 29 #5375] . . . . . . . . . . . . . 526--526
N. N. Chan and
Man Kam Kwong Hermitian matrix inequalities and a
conjecture . . . . . . . . . . . . . . . 533--541
R. J. MacG. Dawson Monostatic simplexes . . . . . . . . . . 541--546
G. R. Veldkamp The isoperimetric point and the point(s)
of equal detour in a triangle . . . . . 546--558
I. M. Isaacs Solution of polynomials by real radicals 571--575
Haragauri N. Gupta A theorem in combinatorics and Wilson's
theorem . . . . . . . . . . . . . . . . 575--576
Roger C. Alperin $p$-adic binomial coefficients mod $p$ 576--578
Michael D. Hirschhorn A simple proof of Jacobi's two-square
theorem . . . . . . . . . . . . . . . . 579--580
Donald P. Minassian A simple structure theorem for
two-generator, one-relation groups . . . 580--583
Marvin Jay Greenberg Correction to: ``Note on the
Cayley--Hamilton theorem'' [Amer. Math.
Monthly \bf 91 (1984), no. 3, 193--195,
MR 85c:15023] . . . . . . . . . . . . . 583--583
Dale E. Varberg Pick's theorem revisited . . . . . . . . 584--587
Charles R. Wall Unbounded sequences of Euler-Dedekind
means . . . . . . . . . . . . . . . . . 587--587
Edward C. Turner and
Karen F. Gold Rubik's groups . . . . . . . . . . . . . 617--629
D. Spring On the second derivative test for
constrained local extrema . . . . . . . 631--643
Morris Marden The search for a Rolle's theorem in the
complex domain . . . . . . . . . . . . . 643--650
Peter Hilton On all sorts of automorphisms . . . . . 650--656
Alan Shuchat Generalized least squares and
eigenvalues . . . . . . . . . . . . . . 656--659
James C. Owings, Jr. A combinatorial proof of a criterion for
normality . . . . . . . . . . . . . . . 662--663
P. J. Giblin and
S. A. Brassett Local symmetry of plane curves . . . . . 689--707
G. Gerla and
R. Volpe Geometry without points . . . . . . . . 707--711
James R. Weaver Centrosymmetric (cross-symmetric)
matrices, their basic properties,
eigenvalues, and eigenvectors . . . . . 711--717
Dean S. Clark A combinatorial theorem on circulant
matrices . . . . . . . . . . . . . . . . 725--729
David E. Penney and
Carl Pomerance Multiplicative relations for sums of
initial $k$th powers . . . . . . . . . . 729--731
Eric L. Grinberg On the smoothness hypothesis in Sard's
theorem . . . . . . . . . . . . . . . . 733--734
I. J. Schoenberg A conjectured analogue of Rolle's
theorem for polynomials with real or
complex coefficients . . . . . . . . . . 8--13
J. M. De Villiers and
P. N. Robinson The interval of convergence and limiting
functions of a hyperpower sequence . . . 13--23
Victor Namias A simple derivation of Stirling's
asymptotic series . . . . . . . . . . . 25--29
Albrecht Beutelspacher $21-6=15$: a connection between two
distinguished geometries . . . . . . . . 29--41
Steven G. Krantz and
T. D. Parsons Antisocial subcovers of self-centered
coverings . . . . . . . . . . . . . . . 45--48
Edwin H. Kaufman, Jr. and
Terry D. Lenker Linear convergence and the bisection
algorithm . . . . . . . . . . . . . . . 48--51
Ibrahim A. Salama and
Lawrence L. Kupper A geometric interpretation for the
Eulerian numbers . . . . . . . . . . . . 51--52
Philip D. Straffin, Jr. Letter to the editor: ``The diameter of
a graph and its complement'' [Amer.
Math. Monthly \bf 92 (1985), no. 3,
211--212, MR 87j:05139a] by F. Harary
and R. W. Robinson . . . . . . . . . . . 76--76
Andrea Laforgia and
Martin E. Muldoon Some consequences of the Sturm
comparison theorem . . . . . . . . . . . 89--94
William A. Chance A geometric derivation of the
distribution of the correlation
coefficient $\vert r\vert $ when
$\rho=0$ . . . . . . . . . . . . . . . . 94--98
Thomas Tracy Allen Pólya's orchard problem . . . . . . . . . 98--104
Philip A. Leonard Cyclic relative difference sets . . . . 106--111
T. L. McCoy On ``${\rm cos}\,f(x)=f({\rm sin}\,x)$'' 111--115
Jack M. Robertson and
Andrew F. Siegel Designing Buffon's needle for a given
crossing distribution . . . . . . . . . 116--119
Mícheál Ó Searcóid and
Desmond MacHale Two elementary generalisations of
Boolean rings . . . . . . . . . . . . . 121--122
P. Diaconis and
D. Freedman An elementary proof of Stirling's
formula . . . . . . . . . . . . . . . . 123--125
L. E. Mattics and
F. W. Dodd A bound for the number of multiplicative
partitions . . . . . . . . . . . . . . . 125--126
Curtis Cooper Geometric series and a probability
problem . . . . . . . . . . . . . . . . 126--127
J. A. Eidswick Cubelike puzzles --- what are they and
how do you solve them . . . . . . . . . 157--176
E. J. P. Georg Schmidt An alternative approach to canonical
forms of matrices . . . . . . . . . . . 176--184
Sandy Grabiner The Tietze extension theorem and the
open mapping theorem . . . . . . . . . . 190--191
Joseph B. Keller The probability of heads . . . . . . . . 191--197
T. D. Parsons Ancestors, cardinals, and
representatives . . . . . . . . . . . . 197--200
A. Lenard A note on Liouville's theorem . . . . . 200--201
Kurt Eisemann A self-dual card trick based on
congruences and $k$-shuffles . . . . . . 201--205
Donald E. Knuth Solution to problem 6480, A Catalonian
sum . . . . . . . . . . . . . . . . . . 220--220
Peter Ungar Review of three calculus textbooks . . . 221--230
Sheldon Axler Harmonic functions from a complex
analysis viewpoint . . . . . . . . . . . 246--258
Joan Cleary and
Sidney A. Morris and
David Yost Numerical geometry --- numbers for
shapes . . . . . . . . . . . . . . . . . 260--275
Charles Small Sums of three squares and levels of
quadratic number fields . . . . . . . . 276--279
Georges A. Lion A simple proof of the Dirichlet--Jordan
convergence test . . . . . . . . . . . . 281--282
Jan Turk The fixed divisor of a polynomial . . . 282--286
Rolf Brandl Integer polynomials that are reducible
modulo all primes . . . . . . . . . . . 286--288
D. H. Lehmer Coloring the Platonic solids . . . . . . 288--292
Ira Gessel Letter to the editor: ``Trees and
power-sums'' [Amer. Math. Monthly \bf 92
(1985), no. 5, 328--331, MR 87e:05016a]
by A. H. Stone . . . . . . . . . . . . . 323--324
Steven H. Weintraub Letter to the editor: ``Tricks or treats
with the Hilbert matrix'' [Amer. Math.
Monthly \bf 90 (1983), no. 5, 301--312,
MR 84h:47031] by M. D. Choi . . . . . . 324--324
David Aldous and
Persi Diaconis Shuffling cards and stopping times . . . 333--348
Solomon Leader What is a differential? A new answer
from the generalized Riemann integral 348--356
Alan C. Wilde Transformations leaving the determinant
of circulant matrices invariant . . . . 356--361
Jaroslav Han\vcl A simple proof of the irrationality of
$\pi^4$ . . . . . . . . . . . . . . . . 374--375
Thomas E. Cecil and
Patrick J. Ryan The principal curvatures of the monkey
saddle . . . . . . . . . . . . . . . . . 380--382
Robert Gilmer Zero divisors in commutative rings . . . 382--387
Yasuhiko Ikebe and
Toshiyuki Inagaki An elementary approach to the functional
calculus for matrices . . . . . . . . . 390--392
Sylvan Burgstahler An algorithm for solving polynomial
equations . . . . . . . . . . . . . . . 421--430
Benjamin Kedem A stochastic characterization of the
sine function . . . . . . . . . . . . . 430--440
I. D. Macdonald Commutators and their products . . . . . 440--444
R. Farwig and
D. Zwick A variation on the Landau problem . . . 444--451
A. W. F. Edwards A quick route to sums of powers . . . . 451--455
Gary L. Walls Automorphism groups . . . . . . . . . . 459--462
A. J. Bosch The factorization of a square matrix
into two symmetric matrices . . . . . . 462--464
Tomás Domínguez Benavides How many zeros does a continuous
function have . . . . . . . . . . . . . 464--466
Jet Wimp Quadrature with generalized means . . . 466--468
C. J. Smyth A coloring proof of a generalisation of
Fermat's little theorem . . . . . . . . 469--471
A. H. M. Hoare An involution of blocks in the
partitions of $n$ . . . . . . . . . . . 475--476
David F. Anderson Letter to the editor: ``Solvability of
infinite systems of polynomial equations
over the field of complex numbers''
[Amer. Math. Monthly \bf 92 (1985), no.
2, 94--98, MR 86c:12004] by A. Abian . . 496--497
M. J. Pelling Letter to the editor: ``Dini type
theorems on positive series'' [Amer.
Math. Monthly \bf 92 (1985), no. 5,
347--349, MR 86m:40001] by P. Biler . . 497--498
J. Korevaar Ludwig Bieberbach's conjecture and its
proof by Louis de Branges . . . . . . . 505--514
Kenneth P. Bogart and
Peter G. Doyle Nonsexist solution of the ménage problem 514--519
David Borwein and
Jonathan M. Borwein A note on alternating series in several
dimensions . . . . . . . . . . . . . . . 531--539
Rade T. \vZivaljevi\'c Infinitesimals, microsimplexes and
elementary homology theory . . . . . . . 540--544
S. Barnett Forms of the resultant of two
polynomials . . . . . . . . . . . . . . 551--552
Eliot T. Jacobson and
Alan E. Parks Infinite branches of the phi-tree . . . 552--554
Richard M. Aron and
Gerd H. Fricke Homomorphisms on $C({\bf R})$ . . . . . 555--555
Ka-Lam Kueh A note on Kronecker's approximation
theorem . . . . . . . . . . . . . . . . 555--556
J.-B. Hiriart-Urruty When is a point $x$ satisfying $\nabla
f(x)=0$ a global minimum of $f$ . . . . 556--558
Everett Howe A new proof of Erd\Hos' theorem on
monotone multiplicative functions . . . 593--595
Richard P. Savage, Jr. Graphical constructions of means . . . . 595--603
David Farnsworth and
Richard Orr Gini means . . . . . . . . . . . . . . . 603--607
Robert L. Long Remarks on the history and philosophy of
mathematics . . . . . . . . . . . . . . 609--619
George Maltese A simple proof of the fundamental
theorem of finite Markov chains . . . . 629--630
Charles S. Allen A characterization of dimension . . . . 635--636
G. B. Folland On characterizations of analyticity . . 640--641
Richard D. Byrd Simultaneous complements in
finite-dimensional vector spaces . . . . 641--642
Thomas L. Markham Oppenheim's inequality for positive
definite matrices . . . . . . . . . . . 642--644
Colin R. Blyth Convolutions of Cauchy distributions . . 645--647
M. Carchidi A method for finding the eigenvectors of
an $n\times n$ matrix corresponding to
eigenvalues of multiplicity one . . . . 647--649
H. P. Williams Fourier's method of linear programming
and its dual . . . . . . . . . . . . . . 681--695
John Clough and
Gerald Myerson Musical scales and the generalized
circle of fifths . . . . . . . . . . . . 695--701
James E. Simpson More trees and power sums . . . . . . . 701--708
H. Väliaho An elementary approach to the Jordan
form of a matrix . . . . . . . . . . . . 711--714
Beda Chan An application of finite difference
algebra . . . . . . . . . . . . . . . . 716--717
David Benson and
Walter Feit and
Roger Howe Finite linear groups, the Commodore 64,
Euler and Sylvester . . . . . . . . . . 717--719
Erwin Kleinfeld A class of rings which are very nearly
associative . . . . . . . . . . . . . . 720--722
Alan E. Parks $\pi$, and $e$, and other irrational
numbers . . . . . . . . . . . . . . . . 722--723
Michael W. Botsko An easy generalization of the Riemann
integral . . . . . . . . . . . . . . . . 728--732
Howard Hiller Crystallography and cohomology of groups 765--779
Barry W. Brunson The partial order of iterated
exponentials . . . . . . . . . . . . . . 779--786
Joseph H. Silverman Points of finite order on elliptic
curves . . . . . . . . . . . . . . . . . 793--795
V. Faber and
J. Mycielski The shortest curve that meets all the
lines that meet a convex body . . . . . 796--801
Donald E. Knuth Problem 86-2, a random knockout
tournament (with solution) . . . . . . . 127--129
Herbert S. Wilf A greeting: and a view of Riemann's
hypothesis . . . . . . . . . . . . . . . 3--6
Edward A. Bender The number of three-dimensional convex
polyhedra . . . . . . . . . . . . . . . 7--21
Dan Kalman and
Abraham Ungar Combinatorial and functional identities
in one-parameter matrices . . . . . . . 21--35
Ranjan Roy Binomial identities and hypergeometric
series . . . . . . . . . . . . . . . . . 36--46
Alan F. Beardon Curvature, circles, and conformal maps 48--53
William C. Calhoun Counting the subgroups of some finite
groups . . . . . . . . . . . . . . . . . 54--59
Wells Johnson The Diophantine equation $X^2+7=2^n$ . . 59--62
Susan Jane Colley The tumbling box . . . . . . . . . . . . 62--68
Donald Sarason The multiplication theorem for Fredholm
operators . . . . . . . . . . . . . . . 68--70
F. K. Hwang A tale of two coins . . . . . . . . . . 121--129
Steven C. Althoen and
Renate McLaughlin Gauss--Jordan reduction: a brief history 130--142
Don Pelletier Merlin's magic square . . . . . . . . . 143--150
Joseph Zaks Neighborly families of congruent convex
polytopes . . . . . . . . . . . . . . . 151--155
Anatole Beck Constructing a fair border . . . . . . . 157--162
Desmond MacHale An anticommutativity consequence of a
ring commutativity theorem of Herstein 162--165
Mícheál Ó Searcóid A reordering of the Sylow theorems . . . 165--168
P. Erd\Hos and
P. P. Pálfy and
M. Szegedy $a\pmod {p}\leq b\pmod {p}$ for all
primes $p$ implies $a=b$ . . . . . . . . 169--170
E. B. Saff and
Jon C. Snader The error for quadrature methods: a
complex variables approach . . . . . . . 175--180
Donald E. Knuth Solution to problem E3061, Empty cells 189
Steven G. Krantz What is several complex variables . . . 236--256
Richard A. Brualdi The Jordan canonical form: an old proof 257--267
Herbert S. Wilf Finite lists of obstructions . . . . . . 267--271
Takayuki Furuta A counterexample to a conjectured
Hermitian matrix inequality . . . . . . 271--272
R. B. Paris An asymptotic approximation connected
with the golden number . . . . . . . . . 272--278
C. E. van der Ploeg Duality in nonnormal quartic fields . . 279--284
Edward R. Rozema Romberg integration by Taylor series . . 284--288
James Rovnyak Note on characteristic polynomials . . . 289--290
I. N. Herstein A remark on finite fields . . . . . . . 290--291
Robert Lee Taylor and
Tien Chung Hu Sub-Gaussian techniques in proving
strong laws of large numbers . . . . . . 295--299
James F. Epperson On the Runge example . . . . . . . . . . 329--341
Peter Rosenthal The remarkable theorem of Lévy and
Steinitz . . . . . . . . . . . . . . . . 342--351
Yasuhiko Ikebe and
Toshiyuki Inagaki and
Sadaaki Miyamoto The monotonicity theorem, Cauchy's
interlace theorem, and the
Courant-Fischer theorem . . . . . . . . 352--354
J. B. Wilker The $n$th derivative as a limit . . . . 354--356
Bong Dae Choi Limiting distribution for the
generalized matching problem . . . . . . 356--360
Nina M. Roy Extreme points of convex sets in
infinite-dimensional spaces . . . . . . 409--422
J. G. Mauldon A matrix with applications to random
walk, Brownian motion, and ring theory 423--436
Lawrence J. Wallen All the way with Wirtinger: a short
proof of Bonnesen's inequality . . . . . 440--442
Gerald Beer and
Luzviminda Villar When is a free union of regular measures
regular . . . . . . . . . . . . . . . . 443--445
John Petro Real division algebras of dimension $>1$
contain ${\bf C}$ . . . . . . . . . . . 445--449
William Miller The maximum order of an element of a
finite symmetric group . . . . . . . . . 497--506
William S. Zwicker Playing games with games: the hypergame
paradox . . . . . . . . . . . . . . . . 507--514
John McKay On computing discriminants . . . . . . . 523--527
D. Zwick Best approximation by convex functions 528--534
Detlef Laugwitz and
Bernd Rodewald A simple characterization of the gamma
function . . . . . . . . . . . . . . . . 534--536
Stan Wagon Fourteen proofs of a result about tiling
a rectangle . . . . . . . . . . . . . . 601--617
Mark E. Kidwell and
R. Bruce Richter Trees and Euler tours in a planar graph
and its relatives . . . . . . . . . . . 618--630
Peter M. Maurer A rose is a rose$\ldots$ . . . . . . . . 631--645
Susan Jane Colley Correction: ``The tumbling box'' [Amer.
Math. Monthly \bf 94 (1987), no. 1,
62--68, MR 88b:53010] . . . . . . . . . 646--646
Lyle E. Pursell Comment: ``Homomorphisms on $C({\bf
R})$'' [Amer. Math. Monthly 93 (1986),
no. 7, 555, MR 87i:46109] by R. M. Aron
and G. H. Fricke . . . . . . . . . . . . 646--646
Helaman Ferguson Generalization of some algorithms of
Euler . . . . . . . . . . . . . . . . . 647--652
Charles Vanden Eynden Applications of a product identity to
sums of squares and partitions . . . . . 652--656
T. M. Cronin The construction of matrices with
required properties over the integers 656--662
Boo Rim Choe An elementary proof of
$\sum^\infty_{n=1}1/n^2=\pi^2/6$ . . . . 662--663
Michael Hoffman An invariant of finite abelian groups 664--666
Arthur T. White Ringing the cosets . . . . . . . . . . . 721--746
Paul R. Scott The fascination of the elementary . . . 759--768
Melvyn B. Nathanson A generalization of the
Goldbach-Shnirel\cprimeman theorem . . . 768--771
I. Korec and
\vS. Znám A note on the $3x+1$ problem . . . . . . 771--772
Claudio Martins Mendes and
Maria Aparecida Soares Ruas Hyperbolic motions of conics . . . . . . 825--845
Dennis Kletzing Rational representations of finite
groups: the story of $\gamma$ . . . . . 846--854
Herbert S. Wilf The editor's corner: strings,
substrings, and the ``nearest integer''
function . . . . . . . . . . . . . . . . 855--860
Arthur Benjamin The bisection method: which root . . . . 861--863
Alfonso Villani Spaces with locally compact completions
are compact . . . . . . . . . . . . . . 863--865
R. J. Simpson Disjoint covering systems of congruences 865--868
C. Johnson and
G. Wolkowicz and
H. Wolkowicz Elem. Prob. E. 3234 . . . . . . . . . . 877
Barry A. Cipra An introduction to the Ising model . . . 937--959
David E. Freund Selecting estimators for the standard
deviation of a normal distribution . . . 971--975
Philippe Tondeur Barycentric representation for the
incenter and excenters of a triangle . . 975--976
Donald P. Minassian The arithmetic-geometric mean inequality
revisited: elementary calculus and
negative numbers . . . . . . . . . . . . 977--978
Henry Heatherly Matrices satisfying $AB-BA=I$ . . . . . 979--980
Roger B. Nelsen Consequences of the memoryless property
for random variables . . . . . . . . . . 981--984
Edward A. Bender Errata: ``The number of
three-dimensional convex polyhedra''
[Amer. Math. Monthly \bf 94 (1987), no.
1, 7--21, MR 88b:52010] . . . . . . . . 994--994
S. Elwood Bohn and
Jong Lee Errata: ``Semitopological groups''
[Amer. Math. Monthly \bf 72 (1965),
996--998, MR \bf 32 #7672] . . . . . . . 994--994
C. E. van der Ploeg Errata: ``Duality in nonnormal quartic
fields'' [Amer. Math. Monthly \bf 94
(1987), no. 3, 279--284] . . . . . . . . 994--994
Gerald L. Alexanderson Award for distinguished service to
Professor Murray Klamkim . . . . . . . . 1--4
Branko Grünbaum and
G. C. Shephard Isonemal fabrics . . . . . . . . . . . . 5--30
Gary S. Bloom and
John W. Kennedy and
Louis V. Quintas A characterization of graphs of diameter
two . . . . . . . . . . . . . . . . . . 37--38
Elon L. Lima The Jordan-Brouwer separation theorem
for smooth hypersurfaces . . . . . . . . 39--42
Peter A. Fowler The Königsberg bridges---250 years later 42--43
Donald J. Newman and
T. D. Parsons On monotone subsequences . . . . . . . . 44--45
Ralph Kopperman All topologies come from generalized
metrics . . . . . . . . . . . . . . . . 89--97
George W. Polites Prime desert $n$-tuplets . . . . . . . . 98--104
Klaus E. Eldridge and
Seok Sagong The determination of Kaprekar
convergence and loop convergence of all
three-digit numbers . . . . . . . . . . 105--112
I. Bouwer and
Z. Star A question of protocol . . . . . . . . . 118--121
John Beebee Examples of infinite, incongruent exact
covers . . . . . . . . . . . . . . . . . 121--123
David J. Hallenbeck and
Katarzyna Tkaczy\'nska The absolute and uniform convergence of
infinite improper integrals . . . . . . 124--126
Ashok K. Arora and
Sudhir K. Goel and
Dennis M. Rodriguez Special integration techniques for
trigonometric integrals . . . . . . . . 126--130
Andrew M. Gleason Angle trisection, the heptagon, and the
triskaidecagon . . . . . . . . . . . . . 185--194
Louis H. Kauffman New invariants in the theory of knots 195--242
Joseph A. Gallian and
Douglas S. Jungreis Homomorphisms from $Z_m[i]$ into
$Z_n[i]$ and $Z_m[\rho]$ into
$Z_n[\rho],$ where $i^2+1=0$ and
$\rho^2+\rho+1=0$ . . . . . . . . . . . 247--249
Michael W. Botsko An elementary proof that a bounded a.e.
continuous function is Riemann
integrable . . . . . . . . . . . . . . . 249--252
Jon Froemke and
Jerrold W. Grossman An algebraic approach to some
number-theoretic problems arising from
paper-folding regular polygons . . . . . 289--307
Ilan Vardi Integrals, an introduction to analytic
number theory . . . . . . . . . . . . . 308--315
Lewis C. Robertson and
Rae Michael Shortt and
Stephen G. Landry Dice with fair sums . . . . . . . . . . 316--328
Lawrence Neff Stout Two discrete forms of the Jordan curve
theorem . . . . . . . . . . . . . . . . 332--336
Mohd. Ashraf and
Murtaza A. Quadri and
Daniel Zelinsky Some polynomial identities that imply
commutativity for rings . . . . . . . . 336--339
Hale F. Trotter An overlooked example of nonunique
factorization . . . . . . . . . . . . . 339--342
P. V. Krishnaiah Two counterexamples in general topology 342--343
Benno Artmann A simple proof for the simplicity of
$A_5$ . . . . . . . . . . . . . . . . . 344--349
S. P. Lalley The ``prime number theorem'' for the
periodic orbits of a Bernoulli flow . . 385--398
Wm. Douglas Withers Folding polynomials and their dynamics 399--413
I. E. Leonard More on Fresnel integrals . . . . . . . 431--433
Gary A. Martin A class of abelian groups arising from
an analysis of a proof . . . . . . . . . 433--436
John Schue The Wedderburn theorem of finite
division rings . . . . . . . . . . . . . 436--437
Theodore P. Hill Common hyperplane medians for random
vectors . . . . . . . . . . . . . . . . 437--441
David A. Cox Quadratic reciprocity: its conjecture
and application . . . . . . . . . . . . 442--448
Barry Hayes and
Donald E. Knuth and
Carlos Subi Elementary problem E3267, a solitaire
game . . . . . . . . . . . . . . . . . . 456--457
Jane Day and
Brian Peterson Growth in Gaussian elimination . . . . . 489--513
Stephen D. Fisher The Möbius group and invariant spaces of
analytic functions . . . . . . . . . . . 514--527
Brian Conrey and
Amit Ghosh On the zeros of the Taylor polynomials
associated with the exponential function 528--533
J. G. Wendel Shanks' identity is elementary . . . . . 534--534
M. J. Pelling Letter to the editor . . . . . . . . . . 535--536
J. Fabrykowski On continued fractions and a certain
example of a sequence of continuous
functions . . . . . . . . . . . . . . . 537--539
W. S. Anglin Using Pythagorean triangles to
approximate angles . . . . . . . . . . . 540--541
Gerald Wildenberg Convergence-preserving functions . . . . 542--544
David W. Boyd The Diophantine equation
$x^2+y^m=z^{2n}$ . . . . . . . . . . . . 544--547
Gert Almkvist and
Bruce Berndt Gauss, Landen, Ramanujan, the
arithmetic-geometric mean, ellipses,
$\pi$, and the Ladies diary . . . . . . 585--608
John G. Kingston and
John L. Synge The sequence of pedal triangles . . . . 609--620
Charles Small Magic squares over fields . . . . . . . 621--625
Janet Crandell Tremain The Jerusalem ticket problem . . . . . . 626--630
Kiran B. Chilakamarri Decomposition of bipartite graphs into
paths . . . . . . . . . . . . . . . . . 634--636
W. V. Quine Fermat's last theorem in combinatorial
form . . . . . . . . . . . . . . . . . . 636--636
Andrew Simoson A difference equation for strings of
ones . . . . . . . . . . . . . . . . . . 636--638
Alec Norton Continued fractions and
differentiability of functions . . . . . 639--643
Donald E. Knuth Solution to problem E3166, A polynomial
identity . . . . . . . . . . . . . . . . 662--663
Nicholas D. Kazarinoff Special functions and the Bieberbach
conjecture . . . . . . . . . . . . . . . 689--696
Richard K. Guy The strong law of small numbers . . . . 697--712
John Mitchell and
Lee A. Rubel Every smooth map of Euclidean space into
itself is an expansion followed by a
contraction . . . . . . . . . . . . . . 713--716
G. L. Cohen and
G. H. Smith A simple verification of Ilieff's
conjecture for polynomials with three
zeros . . . . . . . . . . . . . . . . . 734--737
Gerald Beer UC spaces revisited . . . . . . . . . . 737--739
G. N. Hile and
R. Z. Yeh Line integrals of higher-order
derivatives . . . . . . . . . . . . . . 739--744
James Chew A note on closure continuity . . . . . . 744--745
Donald E. Knuth and
Ilan Vardi Advanced problem 6581, the asymptotic
expansion of the middle binomial
coefficient . . . . . . . . . . . . . . 774
Olga Taussky How I became a torchbearer for matrix
theory . . . . . . . . . . . . . . . . . 801--812
Frank Morgan Area-minimizing surfaces, faces of
Grassmannians, and calibrations . . . . 813--822
Robert Brooks Constructing isospectral manifolds . . . 823--839
V. J. Baston and
F. A. Bostock A simple cover-up game . . . . . . . . . 850--854
Fa Sheng Liu A note on probabilities in proofreading 854--854
Michael I. Rosen A proof of the Lucas-Lehmer test . . . . 855--856
J. Aczél and
Zs. Páles The behaviour of means under equal
increments of their variables . . . . . 856--860
Peter Andrews The classification of surfaces . . . . . 861--867
Oscar A. Cámpoli A principal ideal domain that is not a
Euclidean domain . . . . . . . . . . . . 868--871
D. H. Lehmer A new approach to Bernoulli polynomials 905--911
Andrew M. Gleason Addenda: ``Angle trisection, the
heptagon, and the triskaidecagon''
[Amer. Math. Monthly \bf 95 (1988), no.
3, 185--194, MR 89d:51028] . . . . . . . 911--911
Doug Hensley Errata: ``On continued fractions and a
certain example of a sequence of
continuous functions'' [Amer. Math.
Monthly \bf 95 (1988), no. 6, 537--539,
MR 89i:40001] by J. Fabrykowski . . . . 911--911
Donna Crystal Llewellyn and
Craig Tovey and
Michael Trick Finding saddlepoints of two-person, zero
sum games . . . . . . . . . . . . . . . 912--918
Ronald V. Book Dehn's algorithm and the complexity of
word problems . . . . . . . . . . . . . 919--925
X.-B. Lin Another brief proof of the Sylvester
theorem . . . . . . . . . . . . . . . . 932--933
Takayuki Furuta $A\geq B\geq 0$ ensures
$(BA^2B)^{1/2}\geq B^2$---solution to a
conjecture on operator inequalities . . 933--934
Steven Landy A generalization of Ceva's theorem to
higher dimensions . . . . . . . . . . . 936--939
S. Ramakrishnan and
W. D. Sudderth A sequence of coin toss variables for
which the strong law fails . . . . . . . 939--941
Jonathan Lewin and
Myrtle Lewin A simple test for the $n$th term of a
series to approach zero . . . . . . . . 942--942
K. D. Magill, Jr. Universal topological spaces . . . . . . 942--946
Richard C. Gilbert Companion matrices with integer entries
and integer eigenvalues and eigenvectors 947--950
Larry J. Gerstein A new algorithm for computing the rank
of a matrix . . . . . . . . . . . . . . 950--952
Donald E. Knuth Elementary problem E3303, a binary
summation . . . . . . . . . . . . . . . 54
Donald E. Knuth Elementary problem E3309, a binomial
coefficient inequality . . . . . . . . . 154
Donald E. Knuth Elementary problem E3335, a deranged
recurrence . . . . . . . . . . . . . . . 525
Donald E. Knuth Solution to Elementary problem E2982, a
double infinite sum for $\vert x\vert$ 525--526
Kenneth Ross Award for distinguished service to Ivan
Niven . . . . . . . . . . . . . . . . . 3--4
Stavros Busenberg and
David Fisher and
Mario Martelli Minimal periods of discrete and smooth
orbits . . . . . . . . . . . . . . . . . 5--17
Andrew J. Lazarus Letter to the editor: ``Duality in
nonnormal quartic fields'' [Amer. Math.
Monthly \bf 94 (1987), no. 3, 279--284,
MR 88j:11064 and errata, MR 89c:11156]
by C. E. van der Ploeg . . . . . . . . . 17--17
T. W. Gamelin and
D. Khavinson The isoperimetric inequality and
rational approximation . . . . . . . . . 18--30
Lillian E. Peters Hupert and
Anne Leggett On the square roots of infinite matrices 34--38
Lewis Pakula A note on Venn diagrams . . . . . . . . 38--39
Steve Ligh and
Jiang Luh Direct sum of $J$-rings and zero rings 40--41
J. M. Patin A very short proof of Stirling's formula 41--42
Adolf Mader A Euclidean model for Euclidean geometry 43--49
Anthony Osborne and
Hans Liebeck Orthogonal bases of ${\bf {R}}^3$ with
integer coordinates and integer lengths 49--53
Gilbert Strang Patterns in linear algebra . . . . . . . 105--117
Curtis N. Cooper and
Robert E. Kennedy Chebyshev's inequality and natural
density . . . . . . . . . . . . . . . . 118--124
P. T. Bateman and
J. L. Selfridge and
S. S. Wagstaff, Jr. The new Mersenne conjecture . . . . . . 125--128
S. F. Bockman Generalizing the formula for areas of
polygons to moments . . . . . . . . . . 131--132
Luise-Charlotte Kappe and
Bette Warren An elementary test for the Galois group
of a quartic polynomial . . . . . . . . 133--137
R. B. Bapat Comparing the spectral radii of two
nonnegative matrices . . . . . . . . . . 137--139
J. M. Borwein and
P. B. Borwein and
D. H. Bailey Ramanujan, modular equations, and
approximations to pi, or How to compute
one billion digits of pi . . . . . . . . 201--219
J. Lawrence and
G. E. Simons Equations in division rings --- a survey 220--232
Gerald Leibowitz Letters to the editor: ``Special
integration techniques for trigonometric
integrals'' [Amer. Math. Monthly \bf 95
(1988), no. 2, 126--130, MR 89e:26004]
by A. K. Arora, S. K. Goel and D. M.
Rodriguez . . . . . . . . . . . . . . . 232--232
J. R. Sangwine-Yager The missing boundary of the Blaschke
diagram . . . . . . . . . . . . . . . . 233--237
S. J. Blank and
Nishan Krikorian and
David Spring A geometrically inspired proof of the
singular value decomposition . . . . . . 238--239
Craig Bailey and
R. Bruce Richter Sum zero (mod $n$), size $n$ subsets of
integers . . . . . . . . . . . . . . . . 240--242
John Crowe and
Dominick Samperi On open maps . . . . . . . . . . . . . . 242--243
Doron Zeilberger On a conjecture of R. J. Simpson about
exact covering congruences: ``Disjoint
covering systems of congruences'' [Amer.
Math. Monthly \bf 94 (1987), no. 9,
865--868, MR 89b:11006] . . . . . . . . 243--243
Narain Gupta On groups in which every element has
finite order . . . . . . . . . . . . . . 297--308
Ani Adhikari and
Jim Pitman The shortest planar arc of width $1$ . . 309--327
Michael W. Botsko The use of full covers in real analysis 328--333
Persi Diaconis and
Joseph B. Keller Fair dice . . . . . . . . . . . . . . . 337--339
John B. Cosgrave A remark on Euclid's proof of the
infinitude of primes . . . . . . . . . . 339--341
Felipe Cucker and
Antonio Gonzalez Corbalan An alternate proof of the continuity of
the roots of a polynomial . . . . . . . 342--345
H. B. Thompson Taylor's theorem using the generalized
Riemann integral . . . . . . . . . . . . 346--350
George E. Andrews and
R. J. Baxter A motivated proof of the
Rogers--Ramanujan identities . . . . . . 401--409
John McCleary How not to prove Fermat's last theorem 410--420
Lee A. Rubel The editor's corner: summability theory:
a neglected tool of analysis . . . . . . 421--423
Guy David and
Carlos Tomei The problem of the calissons . . . . . . 429--431
Jean-Pierre Rosay and
Walter Rudin Arakelian's approximation theorem . . . 432--434
I. J. Maddox The norm of a linear functional . . . . 434--436
Richard C. Bradley An elementary treatment of the
Radon--Nikodým derivative . . . . . . . . 437--440
Albert Wilansky On the proof of the Radon--Nikodým
theorem . . . . . . . . . . . . . . . . 441--441
Christopher L. Thompson Nonstandard continuity and uniform
convergence . . . . . . . . . . . . . . 443--444
Richard Anderson and
László Lovász and
Peter Shor and
Joel Spencer and
Éva Tardos and
Shmuel Winograd Disks, balls, and walls: analysis of a
combinatorial game . . . . . . . . . . . 481--493
Jacob E. Goodman and
János Pach and
Chee-K. Yap Mountain climbing, ladder moving, and
the ring-width of a polygon . . . . . . 494--510
David Callan Letter to the editor: ``A new approach
to Bernoulli polynomials'' [Amer. Math.
Monthly \bf 95 (1988), no. 10, 905--911,
MR 90c:11014] by D. H. Lehmer . . . . . 510--510
Roger B. Nelsen Letter to the editor: ``A very short
proof of Stirling's formula'' [Amer.
Math. Monthly \bf 96 (1989), no. 1,
41--42, MR 90e:33005a] by J. M. Patin 510--511
Albert A. Mullin Letter to the editor: ``The new Mersenne
conjecture'' [Amer. Math. Monthly \bf 96
(1989), no. 2, 125--128, MR 90c:11009]
by P. T. Bateman, J. L. Selfridge and S.
S. Wagstaff, Jr . . . . . . . . . . . . 511--511
Roger Pinkham Letter to the editor: ``A simple test
for the $n$th term of a series to
approach zero'' [Amer. Math. Monthly \bf
95 (1988), no. 10, 942] by J. Lewin and
M. Lewin . . . . . . . . . . . . . . . . 511--511
Joel M. Cohen Monotone multiplicative functions . . . 512--513
W. J. Wong Powers of a prime dividing binomial
coefficients . . . . . . . . . . . . . . 513--517
Derming Wang The polar decomposition and a matrix
inequality . . . . . . . . . . . . . . . 517--519
Paul Erd\Hos and
Dean Hickerson and
János Pach A problem of Leo Moser about repeated
distances on the sphere . . . . . . . . 569--575
Faruk F. Abi-Khuzam and
Artin B. Boghossian Some recent geometric inequalities . . . 576--589
Doron Zeilberger Kathy O'Hara's constructive proof of the
unimodality of the Gaussian polynomials 590--602
David R. Arterburn and
William Dean Stone A Cantor set of nonconvergence . . . . . 604--608
Daniel L. Stock Merlin's magic square revisited . . . . 608--610
David C. Fisher The number of words of length $n$ in a
graph monoid . . . . . . . . . . . . . . 610--614
Herbert Edelsbrunner and
Steven S. Skiena On the number of furthest neighbour
pairs in a point set . . . . . . . . . . 614--618
E. T. Y. Lee A remark on divided differences . . . . 618--622
J. M. Borwein and
P. B. Borwein and
K. Dilcher Pi, Euler numbers, and asymptotic
expansions . . . . . . . . . . . . . . . 681--687
M. C. Irwin Geometry of continued fractions . . . . 696--703
Herbert S. Wilf The editor's corner: the white screen
problem . . . . . . . . . . . . . . . . 704--707
Peter F. Zoll Letter to the editor . . . . . . . . . . 709--710
Larry W. Cusick and
Peter Tannenbaum Fixed points of the twisted cyclic shift
operator . . . . . . . . . . . . . . . . 713--717
Eric K. van Douwen Fubini's theorem for null sets . . . . . 718--721
Richard Bassein An optimization problem . . . . . . . . 721--725
R. E. Lewkowicz A characterization of a class of
composition operators . . . . . . . . . 725--726
Lee A. Rubel A survey of transcendentally
transcendental functions . . . . . . . . 777--788
K. Bezdek and
R. Connelly Covering curves by translates of a
convex set . . . . . . . . . . . . . . . 789--806
Alan Horwitz Reconstructing a function from its set
of tangent lines . . . . . . . . . . . . 807--813
Hugh Thurston Can a graph be both continuous and
discontinuous . . . . . . . . . . . . . 814--815
Shmuel Rosset Normalized symmetric functions, Newton's
inequalities and a new set of stronger
inequalities . . . . . . . . . . . . . . 815--819
N. Alon and
I. Krasikov and
Y. Peres Reflection sequences . . . . . . . . . . 820--823
Yoram Sagher Counting the rationals . . . . . . . . . 823--823
Isom H. Herron The radius of convergence of power
series solutions to linear differential
equations . . . . . . . . . . . . . . . 824--827
James F. Epperson On the use of iteration methods for
approximating the natural logarithm . . 831--835
William F. Dowling There are no safe virus tests . . . . . 835--836
J. Marshall Ash Uniqueness of representation by
trigonometric series . . . . . . . . . . 873--885
John S. Lew and
Donald A. Quarles, Jr. Optimal inscribed polygons in convex
curves . . . . . . . . . . . . . . . . . 886--902
A. Tsarpalias A version of Rouché's theorem of
continuous functions . . . . . . . . . . 911--913
Victor Pambuccian Another example of an exotic function 913--914
Kenneth P. Bogart A fresh(man) treatment of determinants 915--920
Joseph J. Rushanan On the Vandermonde matrix . . . . . . . 921--924
F. C. Leary Rings with invertible regular elements 924--926
Donald E. Knuth Solution to Elementary problem E3303, a
binary summation . . . . . . . . . . . . 348--349
Donald E. Knuth Solution to Elementary problem E3309, a
binomial coefficient inequality . . . . 614
Donald E. Knuth Solution to Elementary problem E3335, a
deranged recurrence . . . . . . . . . . 927--927
Raphael M. Robinson Comment to: ``A motivated proof of the
Rogers--Ramanujan identities'' [Amer.
Math. Monthly \bf 96 (1989), no. 5,
401--409, MR 90e:11147] by G. E. Andrews
and R. J. Baxter. With a reply by
Andrews . . . . . . . . . . . . . . . . 214--215
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] . . . . . . . . . . . . . . . 411--412
John Beebee Errata: ``Examples of infinite,
incongruent exact covers'' [Amer. Math.
Monthly \bf 95 (1988), no. 2, 121--123,
MR 89g:11013] . . . . . . . . . . . . . 412--412
Arthur T. Benjamin Errata: ``The bisection method: which
root?'' [Amer. Math. Monthly \bf 94
(1987), no. 9, 861--863, MR 89c:26016] 412--412
Hans-J. Kleiner Errata: ``Coloring the Platonic solids''
[Amer. Math. Monthly \bf 93 (1986), no.
4, 288--292, MR 87e:05072] by D. H.
Lehmer . . . . . . . . . . . . . . . . . 412--412
K. D. Magill, Jr. Errata: ``Universal topological spaces''
[Amer. Math. Monthly \bf 95 (1988), no.
10, 942--946, MR 89m:54018] . . . . . . 412--412
Jingcheng Wong Errata: ``On the mean value theorem for
integrals'' [Amer. Math. Monthly \bf 89
(1982), no. 5, 300--301, MR 83g:26002]
by B. Jacobson . . . . . . . . . . . . . 412--412
Donald E. Knuth Solution to Advanced problem 6581, the
asymptotic expansion of the middle
binomial coefficient . . . . . . . . . . 629--630
Albert Nijenhuis Solution to Elementary problem E3267, a
solitaire game . . . . . . . . . . . . . 292--294
Victor Adamchik and
Stan Wagon A Simple Formula for $\pi$ . . . . . . . 852--855
James M. Ortega Generation of test matrices by
similarity transformations . . . . . . . 377--378
Donald E. Knuth Algorithms in modern mathematics and
computer science . . . . . . . . . . . . 82--99
David Bailey and
Peter Borwein and
Simon Plouffe On the rapid computation of various
polylogarithmic constants . . . . . . . 903--913