BOOKS:
JOURNAL ARTICLES “Mathematicians’ Proof, Established Mathematics, and Warranted Assertibility”, to appear in “From a Heuristic Point of View,” ed. E. Ippoliti, Cambridge Scholars “Paul Cohen in 1963,” The Mathematical Intelligencer, 24 (3) 38-40, 2011 “Dialogo fra un matematico de succeso e uno studente testardo”, Archimede (Firenze, Italia) ottobre-dicembre 2010 4/2010, 202--205 “Alvin White,” Journal of Humanistic Mathematics, 2011 “Under-represented Then over-represented: A Memoir of Jews in American Mathematics,” College Mathematics Journal, January 2010, pp. 2-9 “Refuge from Misery and Suffering,” Mathematical Intelligencer, Winter, 2008, 30 (1) 22-26 “Clarence Stephens and the Potsdam Model,” Math Horizons, February 2010, pp 18-21, 29 Introduction to “Report on programs for minorities in mathematics” , Newsletter of SW region of MAA, 1988; Focus Obituary of Nicholas Kazarinoff, SIAM News “Proof is convincing and explaining,” Ed Stud in Math vol 24 pp 389-399 1993 “What is humanistic mathematics?”, Mathematics in College, 1990 49-50 “Humanistic mathematics and the real world,” in “Szeged in 1934,” (edited from manuscripts of Edgar Lorch) Amer Math Monthly 100(3) Winner of Ford Prize “Math lingo vs. plain English: double entendre”, Amer Math Monthly January 1997 Biographies of David Blackwell and Solomon Lefschetz, “Mathematical menopause, or, a young man’s game?” The Mathematical Intelligencer 23(3) 2001 52-60 “Form and function in mathematical modeling,” talk at Budapest meeting of Santa Fe Institute “The Origin of Chaos,” talk at Santa Fe Institute “Mathematics and Ethics,” The Mathematical Intelligencer 12(3) 1990 12-15 “Ethics for Mathematicians,” in Philosophy of Math Education, P. Ernest ed., 2007
“Mixed problems in several variables,” J Math Mech 12(3) 1963 “Boundary conditions for equations of evolution,” Arch Rat Mech Anal 16(4) 1964 “On surface waves with finite and infinite speed of propagation,” Arch Rat Mech Anal 19(4) 1965 “On vibration, diffusion or equilibrium across a plane interface,” Arch Rat Mech Anal 21(5)1966 “The three-dimensional wave equation in a characteristic quarter-space,” with Y W Chen, J Math and Mech, November 1967 “Finite difference approximations for mixed initial-boundary value problems of general type,” SIAM J on Numer Anal 5(2) June 1968 “On the general theory of mixed problems,” “Direct solution of general one-dimensional parabolic equations via an abstract Plancherel formula,” Proc Nat Acad Sci July 1969 “The method of reflection for two-sided problems of general
type,” in “A perturbation series for Cauchy’s problem for higher-order abstract parabolic equations” (with J Donaldson) Proc Nat Acad Sci vol 67 September 1970, pp 41-44 “How to classify differential polynomials,” Amer Math Monthly June-July 1973 pp 641-654 “The method of transmutations,” “Stochastic solutions of hyperbolic equations”, ibid, pp 283-301 “Hyperbolic equations with coefficients in an enveloping algebra” (with S Steinberg) J Diff Eq 34(3) December 1979 pp 405-426
“Random semigroups, Markov chains, and systems of partial differential equations” (with Richard J Griego) Proc Nat Acad Sci February 1969 “Theory of random evolutions with applications to partial differential equations” (with R J Griego) Trans Amer Math Soc vol 156 May 1971 pp 405-418 “Random evolutions are asymptotically Gaussian” (with M Pinsky) Comm Pure & Appl Math vol 25 1972 pp 33-44 “Non-commuting random evolutions, and an operator-valued Feynman-Kac formula” (with G Papanicolaou) Comm Pure & Appl Math vol 25 1972 pp 337-367 “Two limit theorems for random differential equations” (with R Cogburn) Indiana U Math J vol 22 1973 pp 1067-1089 “Random evolutions, a survey of results and problems,” Rocky Mt J Math, Summer 1974 pp 443-477 “Weyl’s theorem for certain operator-valued potentials” (with R. Griego) Indiana Univ Math J 1978 27(2) pp 195-209 “The birth of random evolutions,” The Mathematical Intelligencer 25(1) 2003 53-60
“A class of central limit theorems for convolution products of generalized functions,” Trans Amer Math Soc June 1969 “Some limit theorems for stochastic equations and applications” (with G Papanicolaou) Indiana U Math J vol 21 1972 pp 815-840 “Maxwell’s coefficients are conditional probabilities” Proc Amer Math Soc June 1974 pp 449-453 “Introduction to a special issue on stochastic differential equations,” Rocky Mt J Math Summer 1974 “Quasi-standard random variables and stochastic
differentials” (with P. Greenwood) Brownian motion and nonstandard analysis, University of New Mexico Technical Report No. 277, May 1973.
“Explicit solution of a class of abstract Cauchy problems,” J Diff Eqs vol 8 1970 570- 579 “Perturbation and approximation theory for higher-order abstract Cauchy problems” (with L Bobisud) Rocky Mt J Math vol 2 1972 pp 57-73 “On the invariance principle of scattering theory” (with J A Donaldson and A G Gibson) J Func Anal October 1973 14(2) pp131-145 “High-accuracy stable difference schemes for well-posed initial-value problems” (with T.Kato) SIAM J Numer Anal 1979 pp670-682
“Why Faulhaber Polynomials are Powers of (n + 1/2)”, College Math J., 2011 “From counting to quaternions”, Journal of Humanistic Mathematics, Vol 1, No. 1, 2011 “Mathematical Intuition:
Poincare, Polya, Dewey”, in “Mathematical
discourse: the link from
pre-mathematical to fully mathematical thinking,”
(with KristinUmland) in Philosophy and Education 19 “Mathematical practice as a scientific
problem,” in “Definition of
mathematics” in “On Platonism,” Newsletter of the European Mathematical Society, June, 2008 “On von Glasersfeld’s Radical Constructivism,” Constructivist Notes, 2008 “What I would like my freshman students to know about
proof”, in “Wings, not foundations!”, in G. Sica ed., Foreword to “On the
interdisciplinary study of mathematical practice,” in B. v. Kerkhove & J.P.v.Bendegem, “Independent Thinking” College Math J. 34 (2) 2003 “Sines and cosines are just exponentials,” Math Rev (England) 2(4) April 1992 22-25 “The classroom encounter,” Humanistic Math Newsletter “Reply to Martin Gardner,” The Mathematical Intelligencer 23 (1) 2001, 3-5 “The origin of geometry,” College Math J 33(3) May 2002 207-211 “A nifty derivation of Heron’s area formula by 11 “Heron’s area formula: what about a tetrahedron?” College Math J 35(2) March 2004 112-114 “A simple derivation of Heron’s area formula,” Wiskunde & Onderweis 2003 “Some proposals for reviving the philosophy of mathematics,” Advance in Mathematics 31(1) January 1979 pp 31-50 “Introducing Imre Lakatos,” Mathematical Intelligencer 1(3) 1978 pp 148-151 “Rhetoric and mathematics” (with P J Davis) in “Mathematics has a front and a back,” Eureka 1988, Synthese 88(2) August 1991 “Introduction to special issue,” Synthese 88(2) August 1991 “A mathematician’s “Let’s teach philosophy of math!” College Math J 21(2) March 1990 105-111 “Inner knowledge, outer truth,” in “A visit to Hungarian mathematics,” (with V. John-Steiner) The Mathematical Intelligencer Spring 1993 “Fresh breezes in the philosophy of mathematics,” NY Acad of
Sci December 2, 1993; in Amer Math Monthly and in
Non-Cantorian set theory (with Paul Cohen) Scientific American December 1967 Brownian motion and potential theory (with Richard Griego) Scientific American March 1969 Nonstandard analysis (with M Davis) Scientific American June 1972 pp 78-86 Hilbert’s tenth problem (with M Davis) Scientific American November 1973 pp 84-91 Winner of the Chauvenet Prize Brownian motion, Infinity.
“Freud on math,” The Mathematical Intelligencer 1995 “How to do and write math research”, The Mathematical Intelligencer September 1997 “Follow-up on math lingo,” MAA Online “Independent thinking,” College Math J 34(2) March 2003 112-115 “The wedding,” The Mathematical Intelligencer, 2006
Kees van Deemter, “Not Exactly…in praise of vagueness” SIAM Review Peter Lax, “Selected Papers,” AMS Bulletin William Byers, “How mathematicians think,” Notices of the AMS, 54 (11) December, 2007 Neal Koblitz, “Random Curves,” College Math J., 40 (2), March, 2009 Alain Badiou, “Number and numbers,” Nordisk Matematisk Tidskrift, 2009 George Szpiro, “Poincare’s Prize,” College Math J., September, 2009 Alain Badiou, “Number and numbers,” The Mathematical Intelligencer, 2009, #3 Masha Gessen, “Perfect Rigor,” The Mathematical Intelligencer, 2010 Roland Omnes, “Converging Realities,” American Scientist Jonathan Borwein and David Bailey, “Mathematics by experiment” and “Experimentation in mathematics,” SIAM Review (with R. Frye) Harold Edwards, “Essays in constructive mathematics,” Springer Verlag Stanislaw Ulam,”Sets, numbers and universes,” “Analogies between analogies,” “Science, computers and people” The Mathematical Intelligencer 14 (4) 1992, 71-73 R. Utton, “The Social Life of Numbers” J Anthropological Res. Paul Hoffman, “Archimedes Revenge”, American Scientist 77(5) sept-oct 1989, 500-501 Mark Kac, “Enigmas of chance,” Advances in Mathematics September 1986 p 305 Gian-Carlo Rota, “Indiscrete Thoughts,” College Math Journal Zalman Usiskin et al., “Mathematics for high school teachers,” Prentice Hall Alberto Martinez, “Negative Math,” Princeton U. Press Morris Kline, “Mathematics and the search for knowledge,” American Mathematical Monthly 94 (3) March 1987, 314-315 Imre Lakatos, “Proofs and Refutations,” Advances in mathematics July 1978, 131-133 Philip Kitcher & W. Asprey, “History and philosophy of modern mathematics Vol XI Minnesota Studies in the Philosophy of Science,” Historia Mathematica vol.18, 288-291 John Casti, “Alternate realities—mathematical models of nature and man,” UMAP Journal, November 4, 359-361 Paul Ernest, “Philosophy of Mathematics Education,” Philosophia Mathematica, May1994, 172--176 L. Salem et al. “The most beautiful mathematical formulas,” UMAP Journal Marcia Ascher, “Ethnomathematics,” SIAM Review 35 (1) March 1993, 151-153 Clifford A. Pickover, “Mazes for the Mind,” IEEE Spectrum, April 1993, pp 7. 12 David Darling, “Equations of Infinity,” IEEE Spectrum Mark Kac, G.-C. Rota and J. Schwartz, “Discrete Thoughts,” Review of Mathematics Books and Software Jacot & Hudson, “The way men think,” w. V. John-Steiner, Journal of Gender Studies Keith Devlin, “The math gene,” The Mathematical Intelligencer Stanislas Dehaene, “The Number Sense,” American Mathematical Monthly Marcus du Sautoy, “The music of the primes,” London Times John Derbyshire, “Prime obsession,” London Times Keith Ball, “Strange curves, counting rabbits…” London Times Thomas A. Garrity, “All the mathematics you missed,” UMAP Journal Amir Aczel, “Geometrical landscapes,” American Scientist David Corfield, “Towards a philosophy of real mathematics,” SIAM Review Donald Estep, “Practical analysis in one variable,” SIAM Review
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