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European Mathematical Society
CONTENTS EDITORIAL TEAM EUROPEAN MATHEMATICAL SOCIETY EDITOR-IN-CHIEF MARTIN RAUSSEN Department of Mathematical Sciences, Aalborg University Fredrik Bajers Vej 7G DK-9220 Aalborg, Denmark e-mail: [email protected] ASSOCIATE EDITORS VASILE BERINDE Department of Mathematics, University of Baia Mare, Romania NEWSLETTER No. 52 e-mail: [email protected] KRZYSZTOF CIESIELSKI Mathematics Institute June 2004 Jagiellonian University Reymonta 4, 30-059 Kraków, Poland EMS Agenda ........................................................................................................... 2 e-mail: [email protected] STEEN MARKVORSEN Editorial by Ari Laptev ........................................................................................... 3 Department of Mathematics, Technical University of Denmark, Building 303 EMS Summer Schools.............................................................................................. 6 DK-2800 Kgs. Lyngby, Denmark EC Meeting in Helsinki ........................................................................................... 6 e-mail: [email protected] ROBIN WILSON On powers of 2 by Pawel Strzelecki ........................................................................ 7 Department of Pure Mathematics The Open University A forgotten mathematician by Robert Fokkink ..................................................... 9 Milton Keynes MK7 6AA, UK e-mail: [email protected] Quantum Cryptography by Nuno Crato ............................................................ 15 COPY EDITOR: KELLY -
R Mathematics Esearch Eports
Mathematics r research reports M r Boris Hasselblatt, Svetlana Katok, Michele Benzi, Dmitry Burago, Alessandra Celletti, Tobias Holck Colding, Brian Conrey, Josselin Garnier, Timothy Gowers, Robert Griess, Linus Kramer, Barry Mazur, Walter Neumann, Alexander Olshanskii, Christopher Sogge, Benjamin Sudakov, Hugh Woodin, Yuri Zarhin, Tamar Ziegler Editorial Volume 1 (2020), p. 1-3. <http://mrr.centre-mersenne.org/item/MRR_2020__1__1_0> © The journal and the authors, 2020. Some rights reserved. This article is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/ Mathematics Research Reports is member of the Centre Mersenne for Open Scientific Publishing www.centre-mersenne.org Mathema tics research reports Volume 1 (2020), 1–3 Editorial This is the inaugural volume of Mathematics Research Reports, a journal owned by mathematicians, and dedicated to the principles of fair open access and academic self- determination. Articles in Mathematics Research Reports are freely available for a world-wide audi- ence, with no author publication charges (diamond open access) but high production value, thanks to financial support from the Anatole Katok Center for Dynamical Sys- tems and Geometry at the Pennsylvania State University and to the infrastructure of the Centre Mersenne. The articles in MRR are research announcements of significant ad- vances in all branches of mathematics, short complete papers of original research (up to about 15 journal pages), and review articles (up to about 30 journal pages). They communicate their contents to a broad mathematical audience and should meet high standards for mathematical content and clarity. The entire Editorial Board approves the acceptance of any paper for publication, and appointments to the board are made by the board itself. -
Positional Notation Or Trigonometry [2, 13]
The Greatest Mathematical Discovery? David H. Bailey∗ Jonathan M. Borweiny April 24, 2011 1 Introduction Question: What mathematical discovery more than 1500 years ago: • Is one of the greatest, if not the greatest, single discovery in the field of mathematics? • Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? • Was fiercely resisted in Europe for hundreds of years after its discovery? • Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, to- gether with the basic arithmetic computational schemes, which were discov- ered in India prior to 500 CE. ∗Bailey: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Email: [email protected]. This work was supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. yCentre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Email: [email protected]. 1 2 Why? As the 19th century mathematician Pierre-Simon Laplace explained: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very sim- plicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appre- ciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity. -
The Bibliography
Referenced Books [Ach92] N. I. Achieser. Theory of Approximation. Dover Publications Inc., New York, 1992. Reprint of the 1956 English translation of the 1st Rus- sian edition; the 2nd augmented Russian edition is available, Moscow, Nauka, 1965. [AH05] Kendall Atkinson and Weimin Han. Theoretical Numerical Analysis: A Functional Analysis Framework, volume 39 of Texts in Applied Mathe- matics. Springer, New York, second edition, 2005. [Atk89] Kendall E. Atkinson. An Introduction to Numerical Analysis. John Wiley & Sons Inc., New York, second edition, 1989. [Axe94] Owe Axelsson. Iterative Solution Methods. Cambridge University Press, Cambridge, 1994. [Bab86] K. I. Babenko. Foundations of Numerical Analysis [Osnovy chislennogo analiza]. Nauka, Moscow, 1986. [Russian]. [BD92] C. A. Brebbia and J. Dominguez. Boundary Elements: An Introductory Course. Computational Mechanics Publications, Southampton, second edition, 1992. [Ber52] S. N. Bernstein. Collected Works. Vol. I. The Constructive Theory of Functions [1905–1930]. Izdat. Akad. Nauk SSSR, Moscow, 1952. [Russian]. [Ber54] S. N. Bernstein. Collected Works. Vol. II. The Constructive Theory of Functions [1931–1953]. Izdat. Akad. Nauk SSSR, Moscow, 1954. [Russian]. [BH02] K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction, volume 80 of Springer Series in Solid-State Sciences. Springer-Verlag, Berlin, fourth edition, 2002. [BHM00] William L. Briggs, Van Emden Henson, and Steve F. McCormick. A Multigrid Tutorial. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition, 2000. [Boy01] John P. Boyd. Chebyshev and Fourier Spectral Methods. Dover Publi- cations Inc., Mineola, NY, second edition, 2001. [Bra84] Achi Brandt. Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, volume 85 of GMD-Studien [GMD Studies]. -
Hyberbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves CBMS-NSF REGIONAL CONFERENCE SERIES in APPLIED MATHEMATICS
Hyberbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS A series of lectures on topics of current research interest in applied mathematics under the direction of the Conference Board of the Mathematical Sciences, supported by the National Science Foundation and published by SIAM. GARRETT BIRKHOFF, The Numerical Solution of Elliptic Equations D. V. LINDLEY, Bayesian Statistics, A Review R. S. VARGA, Functional Analysis and Approximation Theory in Numerical Analysis R. R. BAHADUR, Some Limit Theorems in Statistics PATRICK BILLINGSLEY, Weak Convergence of Measures: Applications in Probability J. L. LIONS, Some Aspects of the Optimal Control of Distributed Parameter Systems ROGER PENROSE, Techniques of Differential Topology in Relativity HERMAN CHERNOFF, Sequential Analysis and Optimal Design J. DURBIN, Distribution Theory for Tests Based on the Sample Distribution Function SOL I. RUBINOW, Mathematical Problems in the Biological Sciences P. D. LAX, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves I. J. SCHOENBERG, Cardinal Spline Interpolation IVAN SINGER, The Theory of Best Approximation and Functional Analysis WERNER C. RHEINBOLDT, Methods of Solving Systems of Nonlinear Equations HANS F. WEINBERGER, Variational Methods for Eigenvalue Approximation R. TYRRELL ROCKAFELLAR, Conjugate Duality and Optimization SIR JAMES LIGHTHILL, Mathematical Biofluiddynamics GERARD SALTON, Theory of Indexing CATHLEEN S. MORAWETZ, Notes on Time Decay and Scattering for Some Hyperbolic Problems F. HOPPENSTEADT, Mathematical Theories of Populations: Demographics, Genetics and Epidemics RICHARD ASKEY, Orthogonal Polynomials and Special Functions L. E. PAYNE, Improperly Posed Problems in Partial Differential Equations S. ROSEN, Lectures on the Measurement and Evaluation of the Performance of Computing Systems HERBERT B. -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
A Complete Bibliography of Publications in SIAM Journal on Mathematical Analysis, 1970–1999
A Complete Bibliography of Publications in SIAM Journal on Mathematical Analysis, 1970{1999 Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 13 March 2018 Version 3.14 ∗ Title word cross-reference aK(at);a! 0 [Log79b]. B [Rei79]. BC1 [Ask82]. β [HT87]. BV (Ω) [AK99]. C1 [Coh89]. C3 [McC97]. Cα [YL94]. Cα(Ω) [XA91]. Cp [Rea86b]. C [Yao95]. C (T ) #11889 [Spe79]. 0 0 [Wu90]. C` [Mil94]. A [FM99]. D [Har80]. D O(2) [ML93]. Dr u(x; t)=D u(x; t) (−1; 1) [LS93]. (−∞; 1)[Pas74]. n x t 0 0 [Kem82a]. (m(t)x (t)) + A(t)x(t)=0[Ede79]. k ∗ 0 0 0 D U(X1; ···;Xr)=DX U(X1; ···;Xr) (p(x)u (x)) + g(x)u (x)+qu(x)=f [Whi79]. X1 k [Kem85]. DA [Har80]. δ [Lan83b]. ∆2u = λu (φ(y0)) = qf(t; y; y0); 0 <t<1[O'R93]. [Cof82]. ∆ u(x)+F (x)u(x)=0[CG71]. (r(t) (x)x0)0 + a(t)f(x) = 0 [MR79a]. p+2 ∆ + K2 = 0 [Kal75]. 0 <p(x) 2 L1[a; b] [Whi79]. 0 ≤ x ≤ l − ∆u + K(jxj)jujp 1u = 0 [Yan96]. [CL73]. 2 [AJV94, CW99]. 2m + 1 [Sho70]. − − ∆u + jujp 1u −|ujq 1u = 0 [Tro90]. E3 2π [FR91]. 2π/m [FR91]. 3 [KoM98]. -
Writing the History of Dynamical Systems and Chaos
Historia Mathematica 29 (2002), 273–339 doi:10.1006/hmat.2002.2351 Writing the History of Dynamical Systems and Chaos: View metadata, citation and similar papersLongue at core.ac.uk Dur´ee and Revolution, Disciplines and Cultures1 brought to you by CORE provided by Elsevier - Publisher Connector David Aubin Max-Planck Institut fur¨ Wissenschaftsgeschichte, Berlin, Germany E-mail: [email protected] and Amy Dahan Dalmedico Centre national de la recherche scientifique and Centre Alexandre-Koyre,´ Paris, France E-mail: [email protected] Between the late 1960s and the beginning of the 1980s, the wide recognition that simple dynamical laws could give rise to complex behaviors was sometimes hailed as a true scientific revolution impacting several disciplines, for which a striking label was coined—“chaos.” Mathematicians quickly pointed out that the purported revolution was relying on the abstract theory of dynamical systems founded in the late 19th century by Henri Poincar´e who had already reached a similar conclusion. In this paper, we flesh out the historiographical tensions arising from these confrontations: longue-duree´ history and revolution; abstract mathematics and the use of mathematical techniques in various other domains. After reviewing the historiography of dynamical systems theory from Poincar´e to the 1960s, we highlight the pioneering work of a few individuals (Steve Smale, Edward Lorenz, David Ruelle). We then go on to discuss the nature of the chaos phenomenon, which, we argue, was a conceptual reconfiguration as -
Prizes and Awards Session
PRIZES AND AWARDS SESSION Wednesday, July 12, 2021 9:00 AM EDT 2021 SIAM Annual Meeting July 19 – 23, 2021 Held in Virtual Format 1 Table of Contents AWM-SIAM Sonia Kovalevsky Lecture ................................................................................................... 3 George B. Dantzig Prize ............................................................................................................................. 5 George Pólya Prize for Mathematical Exposition .................................................................................... 7 George Pólya Prize in Applied Combinatorics ......................................................................................... 8 I.E. Block Community Lecture .................................................................................................................. 9 John von Neumann Prize ......................................................................................................................... 11 Lagrange Prize in Continuous Optimization .......................................................................................... 13 Ralph E. Kleinman Prize .......................................................................................................................... 15 SIAM Prize for Distinguished Service to the Profession ....................................................................... 17 SIAM Student Paper Prizes .................................................................................................................... -
From the Collections of the Seeley G. Mudd Manuscript Library, Princeton, NJ
From the collections of the Seeley G. Mudd Manuscript Library, Princeton, NJ These documents can only be used for educational and research purposes (“Fair use”) as per U.S. Copyright law (text below). By accessing this file, all users agree that their use falls within fair use as defined by the copyright law. They further agree to request permission of the Princeton University Library (and pay any fees, if applicable) if they plan to publish, broadcast, or otherwise disseminate this material. This includes all forms of electronic distribution. Inquiries about this material can be directed to: Seeley G. Mudd Manuscript Library 65 Olden Street Princeton, NJ 08540 609-258-6345 609-258-3385 (fax) [email protected] U.S. Copyright law test The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or other reproduction is not to be “used for any purpose other than private study, scholarship or research.” If a user makes a request for, or later uses, a photocopy or other reproduction for purposes in excess of “fair use,” that user may be liable for copyright infringement. The Princeton Mathematics Community in the 1930s Transcript Number 11 (PMC11) © The Trustees of Princeton University, 1985 MERRILL FLOOD (with ALBERT TUCKER) This is an interview of Merrill Flood in San Francisco on 14 May 1984. The interviewer is Albert Tucker. -
A Complete Bibliography of Publications in Nordisk Tidskrift for Informationsbehandling, BIT, and BIT Numerical Mathematics
A Complete Bibliography of Publications in Nordisk Tidskrift for Informationsbehandling, BIT,andBIT Numerical Mathematics Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 09 June 2021 Version 3.54 Title word cross-reference [3105, 328, 469, 655, 896, 524, 873, 455, 779, 946, 2944, 297, 1752, 670, 2582, 1409, 1987, 915, 808, 761, 916, 2071, 2198, 1449, 780, 959, 1105, 1021, 497, 2589]. A(α) #24873 [1089]. [896, 2594, 333]. A∗ [2013]. A∗Ax = b [2369]. n A [1640, 566, 947, 1580, 1460]. A = a2 +1 − 0 n (3) [2450]. (A λB) [1414]. 0=1 [1242]. 1 [334]. α [824, 1580]. AN [1622]. A(#) [3439]. − 12 [3037, 2711]. 1 2 [1097]. 1:0 [3043]. 10 AX − XB = C [2195, 2006]. [838]. 11 [1311]. 2 AXD − BXC = E [1101]. B [2144, 1953, 2291, 2162, 3047, 886, 2551, 957, [2187, 1575, 1267, 1409, 1489, 1991, 1191, 2007, 2552, 1832, 949, 3024, 3219, 2194]. 2; 3 979, 1819, 1597, 1823, 1773]. β [824]. BN n − p − − [1490]. 2 1 [320]. 2 1 [100]. 2m 4 [1181]. BS [1773]. BSI [1446]. C0 [2906]. C1 [1105]. 3 [2119, 1953, 2531, 1351, 2551, 1292, [3202]. C2 [3108, 2422, 3000, 2036]. χ2 1793, 949, 1356, 2711, 2227, 570]. [30, 31]. Cln(θ); (n ≥ 2) [2929]. cos [228]. D 3; 000; 000; 000 [575, 637]. -
The Book Review Column1 by William Gasarch Department of Computer Science University of Maryland at College Park College Park, MD, 20742 Email: [email protected]
The Book Review Column1 by William Gasarch Department of Computer Science University of Maryland at College Park College Park, MD, 20742 email: [email protected] In this column we review the following books. 1. We review four collections of papers by Donald Knuth. There is a large variety of types of papers in all four collections: long, short, published, unpublished, “serious” and “fun”, though the last two categories overlap quite a bit. The titles are self explanatory. (a) Selected Papers on Discrete Mathematics by Donald E. Knuth. Review by Daniel Apon. (b) Selected Papers on Design of Algorithms by Donald E. Knuth. Review by Daniel Apon (c) Selected Papers on Fun & Games by Donald E. Knuth. Review by William Gasarch. (d) Companion to the Papers of Donald Knuth by Donald E. Knuth. Review by William Gasarch. 2. We review jointly four books from the Bolyai Society of Math Studies. The books in this series are usually collections of article in combinatorics that arise from a conference or workshop. This is the case for the four we review. The articles here vary tremendously in terms of length and if they include proofs. Most of the articles are surveys, not original work. The joint review if by William Gasarch. (a) Horizons of Combinatorics (Conference on Combinatorics Edited by Ervin Gyori,¨ Gyula Katona, Laszl´ o´ Lovasz.´ (b) Building Bridges (In honor of Laszl´ o´ Lovasz’s´ 60th birthday-Vol 1) Edited by Martin Grotschel¨ and Gyula Katona. (c) Fete of Combinatorics and Computer Science (In honor of Laszl´ o´ Lovasz’s´ 60th birthday- Vol 2) Edited by Gyula Katona, Alexander Schrijver, and Tamas.´ (d) Erdos˝ Centennial (In honor of Paul Erdos’s˝ 100th birthday) Edited by Laszl´ o´ Lovasz,´ Imre Ruzsa, Vera Sos.´ 3.