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Wed Nov 8 12:32:52 MST 2023
Donald E. Knuth Sequences with precisely $k+1$
$k$-blocks: Solution to Problem E2307 773--774
Donald E. Knuth Schröder's problem: Solution to Problem
E2315 . . . . . . . . . . . . . . . . . 910
Donald E. Knuth Groups: Solution to Problem E2328 . . . 1138--1139
Donald E. Knuth Computer Science and its Relation to
Mathematics . . . . . . . . . . . . . . 323--343
Donald E. Knuth Elementary Problem E2492 (binomial
coefficients and mods) . . . . . . . . . 902
Donald E. Knuth Solution to Elementary Problem E2492
(binomial coefficients and mods) . . . . 855
Donald E. Knuth Problem 6049 (cyclic permutation
generators) . . . . . . . . . . . . . . 856
Donald E. Knuth Problem 6050 (random maximization) . . . 856
Donald E. Knuth Elementary Problem E2613 (compact sets) 656
Donald E. Knuth Elementary Problem E2636 (diphages and
triphages) . . . . . . . . . . . . . . . 134
Donald E. Knuth Solution to Problem 6049 (cyclic
permutation generators) . . . . . . . . 397
Donald E. Knuth Solution to Elementary Problem E2613
(compact sets) . . . . . . . . . . . . . 827--828
Lajos Takács An increasing continuous singular
function . . . . . . . . . . . . . . . . 35--37
Anonymous Extended mean values . . . . . . . . . . 84--90
P. R. Halmos Schauder bases . . . . . . . . . . . . . 256--257
H. S. Bear and
G. N. Hile Gradient characterizations of
analyticity . . . . . . . . . . . . . . 333--337
Michael J. Norris and
William Yslas Vélez A characterization of the splitting of
inseparable algebraic extensions . . . . 338--341
J. E. Humphreys Hilbert's fourteenth problem . . . . . . 341--353
Donald E. Knuth Elementary Problem E2636 (diphages and
triphages) . . . . . . . . . . . . . . . 385--386
R. P. Boas Extremal problems for polynomials . . . 473--475
John Milnor Analytic proofs of the ``hairy ball
theorem'' and the Brouwer fixed-point
theorem . . . . . . . . . . . . . . . . 521--524
Kenneth I. Gross On the evolution of noncommutative
harmonic analysis . . . . . . . . . . . 525--548
L. Carlitz Some product-sum identities . . . . . . 570--572
R. Cignoli and
J. Hounie Functions with arbitrarily small periods 582--584
Martha Zelinka Edward Griffith Begle . . . . . . . . . 629--631
Heinz Bauer Approximation and abstract boundaries 632--647
John E. Wetzel On the division of the plane by lines 647--656
E. B. Leach and
M. C. Sholander Corrections to: ``Extended mean values''
[Amer. Math. Monthly \bf 85 (1978), no.
2, 84--90, MR \bf 58 #22428] . . . . . . 656--656
Calvin C. Moore Approximately finite von Neumann
algebras . . . . . . . . . . . . . . . . 657--659
John E. Wetzel Dissections of a simply-connected plane
domain . . . . . . . . . . . . . . . . . 660--661
A. D. Wadhwa Some convergent subseries of the
harmonic series . . . . . . . . . . . . 661--663
Gérard Letac Cauchy functional equation again . . . . 663--664
Donald E. Knuth Solution to Problem 6050 (random
maximization) . . . . . . . . . . . . . 686--688
R. L. Wilder Evolution of the topological concept of
``connected'' . . . . . . . . . . . . . 720--726
J. C. Alexander Matrices, eigenvalues, and complex
projective space . . . . . . . . . . . . 727--733
Solomon W. Golomb Cyclotomic polynomials and factorization
theorems . . . . . . . . . . . . . . . . 734--737
Cletus O. Oakley and
Justine C. Baker The Morley trisector theorem . . . . . . 737--745
L. Carlitz and
Jo Ann Lutz A characterization of permutation
polynomials over a finite field . . . . 746--748
R. P. Boas and
H. Pollard and
D. V. Widder The asymptotic behavior of derivatives 749--750
Barry Powell Proof of a special case of Fermat's last
theorem . . . . . . . . . . . . . . . . 750--751
H. Guggenheimer The Jordan and Schoenflies theorems in
axiomatic geometry . . . . . . . . . . . 753--756
Gebhard Greiter A simple proof for a theorem of
Kronecker . . . . . . . . . . . . . . . 756--757
Ivan Niven Convex polygons that cannot tile the
plane . . . . . . . . . . . . . . . . . 785--792
Donald G. Saari Apportionment methods and the House of
Representatives . . . . . . . . . . . . 792--802
Leon Gerber A simple improvement on the binomial
series . . . . . . . . . . . . . . . . . 808--809
K. Athreya and
D. McDonald and
P. Ney Coupling and the renewal theorem . . . . 809--814
Patrick J. O'Hara and
Rene S. Rodriguez Polynomials with zeros uniformly
distributed on the unit circle . . . . . 814--817
A. E. Livingston and
M. L. Livingston The congruence $a^{r+s}\equiv a^{r}
\pmod {m}$ . . . . . . . . . . . . . . . 97--100
Emma Lehmer Rational reciprocity laws . . . . . . . 467--472
Robert Osserman Bonnesen-style isoperimetric
inequalities . . . . . . . . . . . . . . 1--29
David Gale Tone perception and decomposition of
periodic functions . . . . . . . . . . . 36--42
R. Daniel Mauldin The existence of non-measurable sets . . 45--46
B. G. Basmaji Complex representations of metacyclic
groups . . . . . . . . . . . . . . . . . 47--48
R. P. Boas Award for distinguished service to Otto
Neugebauer . . . . . . . . . . . . . . . 77--78
David P. Roselle Award of the Chauvenet Prize to Dr. Neil
J. A. Sloane . . . . . . . . . . . . . . 79--79
Steven J. Brams and
Philip D. Straffin, Jr. Prisoner's dilemma and professional
sports drafts . . . . . . . . . . . . . 80--88
George E. Andrews An introduction to Ramanujan's ``lost''
notebook . . . . . . . . . . . . . . . . 89--108
James K. Knowles Universal states of finite anti-plane
shear: Ericksen's problem in miniature 109--113
Heiko Harborth Divisibility of $(^{m}_{k})$ by
$m(m-1)\cdots (m-h+1)$ . . . . . . . . . 115--117
S. A. Kenton and
S. D. Shore The Pixley-Roy space is continuously
semimetrizable . . . . . . . . . . . . . 117--119
Edward T. H. Wang When is the permanent function convex on
the set of doubly stochastic matrices 119--121
C. L. Belna and
M. J. Evans and
P. D. Humke Symmetric and strong differentiation . . 121--123
Karl Stromberg The Banach-Tarski paradox . . . . . . . 151--161
D. B. Oulton and
D. J. Wollkind and
R. N. Maurer A stability analysis of a prototype
moving boundary problem in heat flow and
diffusion . . . . . . . . . . . . . . . 175--186
Andrew P. Guinand The umbral method: a survey of
elementary mnemonic and manipulative
uses . . . . . . . . . . . . . . . . . . 187--195
Salomon Bochner Fourier series came first . . . . . . . 197--199
Scott Garten Corrections to: ``Irregular integers''
(Amer. Math. Monthly \bf 85 (1978), no.
3, 165--172) by M. Schreiber . . . . . . 199--199
T. M. K. Davison A generalization of regulated functions 202--204
Robert Sine and
Vladislav Kre\uìnovi\vc Remarks on billiards . . . . . . . . . . 204--206
Emad El-Neweihi and
Frank Proschan Unified treatment of inequalities of the
Weierstrass product type . . . . . . . . 206--208
William C. Waterhouse The normal basis theorem . . . . . . . . 212--212
G. J. Miel The Kantorovich theorem with optimal
error bounds . . . . . . . . . . . . . . 212--215
Dorothy L. Bernstein The role of applications in pure
mathematics . . . . . . . . . . . . . . 245--253
Keith Harrow Theoretical and applied computer
science: antagonism or symbiosis . . . . 253--260
J. C. Fisher Geometry according to Euclid . . . . . . 260--270
D. V. Widder The Airy transform . . . . . . . . . . . 271--277
Ronald J. Evans Silverman's game on intervals . . . . . 277--281
Erwin Turdza The solutions of an inequality for the
$n$th iterate of a function . . . . . . 281--283
Paul D. Humke and
Lawrence L. Krajewski A characterization of circles which
contain rational points . . . . . . . . 287--290
Y. H. Wang Dependent random variables with
independent subsets . . . . . . . . . . 290--292
David H. Anderson The application of a classical
inequality to population mathematics . . 294--296
Robert M. Young An elementary proof of a trigonometric
identity . . . . . . . . . . . . . . . . 296--297
Lud\vek Zají\vcek An elementary proof of the
one-dimensional density theorem . . . . 297--298
Shiing Shen Chern From triangles to manifolds . . . . . . 339--349
J. L. Brenner Student days---1930 . . . . . . . . . . 350--356
E. J. Barbeau Euler subdues a very obstreperous series 356--372
Robert Baillie Sums of reciprocals of integers missing
a given digit . . . . . . . . . . . . . 372--374
Patrick Morton A generalization of Zolotarev's theorem 374--375
Denis Higgs and
Paul de Witte On products of transpositions and their
graphs . . . . . . . . . . . . . . . . . 376--380
R. Výborn\'y On the use of a differentiable homotopy
in the proof of the Cauchy theorem . . . 380--382
Steven H. Schot Geometrical properties of the
penosculating conics of a plane curve 449--457
T. Bruce McLean ${V}$-flexing the hexahexaflexagon . . . 457--466
Trevor Evans Universal algebra and Euler's officer
problem . . . . . . . . . . . . . . . . 466--473
E. Lutwak On isoperimetric inequalities related to
a problem of Moser . . . . . . . . . . . 476--477
George E. Andrews A note on partitions and triangles with
integer sides . . . . . . . . . . . . . 477--478
Dan Eustice and
M. S. Klamkin On the coefficients of a partial
fraction decomposition . . . . . . . . . 478--480
A. M. Russell Further comments on the variation
function . . . . . . . . . . . . . . . . 480--482
Alexander Abian An ultimate proof of Rolle's theorem . . 484--485
A. Day Bradley Prismatoid, prismoid, generalized
prismoid . . . . . . . . . . . . . . . . 486--490
Bertram Walsh More on gradient characterizations of
analyticity . . . . . . . . . . . . . . 490--491
Bernard O. Koopman Search and its optimization . . . . . . 527--540
Nicolas D. Goodman Mathematics as an objective science . . 540--551
Ernst Snapper What is mathematics . . . . . . . . . . 551--557
R. L. Cooke The Cantor-Lebesgue theorem . . . . . . 558--565
William H. Ruckle The bounded consistency theorem . . . . 566--571
Murray Eisenberg and
Robert Guy A proof of the hairy ball theorem . . . 572--574
John Ginsburg and
Bill Sands Minimal infinite topological spaces . . 574--576
Shigeru Haruki A property of quadratic polynomials . . 577--579
Samuel S. Wagstaff, Jr. Some questions about arithmetic
progressions . . . . . . . . . . . . . . 579--582
Ira Rosenholtz There is no differentiable metric for
${\bf R}^{n}$ . . . . . . . . . . . . . 585--586
Azriel Rosenfeld Digital topology . . . . . . . . . . . . 621--630
John W. Pratt Finding how many roots a polynomial has
in $(0,\,1)$ or $(0,\,\infty )$ . . . . 630--637
Richard Johnsonbaugh Summing an alternating series . . . . . 637--648
Emil Grosswald Recent applications of some old work of
Laguerre . . . . . . . . . . . . . . . . 648--658
Karel Hrbacek Nonstandard set theory . . . . . . . . . 659--677
J. R. Nurcombe A sequence of convergence tests . . . . 679--681
Richard J. Bagby Taylor polynomials and difference
quotients . . . . . . . . . . . . . . . 681--684
C. David Minda Conformal automorphisms of circular
regions . . . . . . . . . . . . . . . . 684--686
J. H. Jordan and
Ray Walch and
R. J. Wisner Triangles with integer sides . . . . . . 686--689
Walter Leighton A useful lemma in the theory of
second-order linear differential
equations . . . . . . . . . . . . . . . 693--694
George Miel An algorithm for the calculation of
$\pi$ . . . . . . . . . . . . . . . . . 694--697
D. H. Lehmer and
Emma Lehmer Picturesque exponential sums. I . . . . 725--733
Wendell Mills and
Boris Weisfeiler and
Allan M. Krall Discovering theorems with a computer:
the case of $y^{\prime} ={\rm sin}(xy)$ 733--739
John Dawson The Gödel incompleteness theorem from a
length-of-proof perspective . . . . . . 740--747
Marvin Jay Greenberg Euclidean and non-Euclidean geometries
without continuity . . . . . . . . . . . 757--764
I. J. Schoenberg On a problem of Steinhaus on lattice
points . . . . . . . . . . . . . . . . . 765--766
A. L. Brown The Borsuk-Ulam theorem and
orthogonality in normed linear spaces 766--767
C. H. Heiberg Extrema for functions of several
variables . . . . . . . . . . . . . . . 767--770
Phyllis Joan Cassidy Products of commutators are not always
commutators: an example . . . . . . . . 772--772
Desmond Fearnley-Sander Hermann Grassmann and the creation of
linear algebra . . . . . . . . . . . . . 809--817
David Gale The game of Hex and the Brouwer
fixed-point theorem . . . . . . . . . . 818--827
Marvin Jay Greenberg The ``real'' projective plane without
continuity . . . . . . . . . . . . . . . 827--832
Albert Nijenhuis A minimal-path algorithm for the ``money
changing problem'' . . . . . . . . . . . 832--835
Deborah Tepper Haimo and
Franklin Tepper Haimo Comments and complements . . . . . . . . 836--841
David W. Kammler and
Robert J. McGlinn Local conditioning of parametric forms
used to approximate continuous functions 841--845
R. D. Nelson Perfect quadrilaterals . . . . . . . . . 845--847
James M. Briggs and
Thomas Schaffter Measure and cardinality . . . . . . . . 852--855
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
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
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
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