An Interview with Martin Davis
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The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary
The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary i Reproduction. The work may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents. In any reproduction, the original publication by the Publisher must be credited in the following manner: “First published in The William Lowell Putnam Mathematical Competition 1985–2000: Problems, Solutions, and Commen- tary, c 2002 by the Mathematical Association of America,” and the copyright notice in proper form must be placed on all copies. Ravi Vakil’s photo on p. 337 is courtesy of Gabrielle Vogel. c 2002 by The Mathematical Association of America (Incorporated) Library of Congress Catalog Card Number 2002107972 ISBN 0-88385-807-X Printed in the United States of America Current Printing (last digit): 10987654321 ii The William Lowell Putnam Mathematical Competition 1985–2000 Problems, Solutions, and Commentary Kiran S. Kedlaya University of California, Berkeley Bjorn Poonen University of California, Berkeley Ravi Vakil Stanford University Published and distributed by The Mathematical Association of America iii MAA PROBLEM BOOKS SERIES Problem Books is a series of the Mathematical Association of America consisting of collections of problems and solutions from annual mathematical competitions; compilations of problems (including unsolved problems) specific to particular branches of mathematics; books on the art and practice of problem solving, etc. Committee on Publications Gerald Alexanderson, Chair Roger Nelsen Editor Irl Bivens Clayton Dodge Richard Gibbs George Gilbert Art Grainger Gerald Heuer Elgin Johnston Kiran Kedlaya Loren Larson Margaret Robinson The Inquisitive Problem Solver, Paul Vaderlind, Richard K. -
The Association for Women in Mathematics: How and Why It Was
Mathematical Communities t’s 2011 and the Association for Women in Mathematics The Association (AWM) is celebrating 40 years of supporting and II promoting female students, teachers, and researchers. It’s a joyous occasion filled with good food, warm for Women conversation, and great mathematics—four plenary lectures and eighteen special sessions. There’s even a song for the conference, titled ‘‘((3 + 1) 9 3 + 1) 9 3 + 1 Anniversary in Mathematics: How of the AWM’’ and sung (robustly!) to the tune of ‘‘This Land is Your Land’’ [ICERM 2011]. The spirit of community and and Why It Was the beautiful mathematics on display during ‘‘40 Years and Counting: AWM’s Celebration of Women in Mathematics’’ are truly a triumph for the organization and for women in Founded, and Why mathematics. It’s Still Needed in the 21st Century SARAH J. GREENWALD,ANNE M. LEGGETT, AND JILL E. THOMLEY This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of ‘‘mathematical community’’ is Participants from the Special Session in Number Theory at the broadest: ‘‘schools’’ of mathematics, circles of AWM’s 40th Anniversary Celebration. Back row: Cristina Ballantine, Melanie Matchett Wood, Jackie Anderson, Alina correspondence, mathematical societies, student Bucur, Ekin Ozman, Adriana Salerno, Laura Hall-Seelig, Li-Mei organizations, extra-curricular educational activities Lim, Michelle Manes, Kristin Lauter; Middle row: Brooke Feigon, Jessica Libertini-Mikhaylov, Jen Balakrishnan, Renate (math camps, math museums, math clubs), and more. Scheidler; Front row: Lola Thompson, Hatice Sahinoglu, Bianca Viray, Alice Silverberg, Nadia Heninger. (Photo Cour- What we say about the communities is just as tesy of Kiran Kedlaya.) unrestricted. -
Hilbert Constance Reid
Hilbert Constance Reid Hilbert c COPERNICUS AN IMPRINT OF SPRINGER-VERLAG © 1996 Springer Science+Business Media New York Originally published by Springer-Verlag New York, Inc in 1996 All rights reserved. No part ofthis publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Library ofCongress Cataloging·in-Publication Data Reid, Constance. Hilbert/Constance Reid. p. Ctn. Originally published: Berlin; New York: Springer-Verlag, 1970. Includes bibliographical references and index. ISBN 978-0-387-94674-0 ISBN 978-1-4612-0739-9 (eBook) DOI 10.1007/978-1-4612-0739-9 I. Hilbert, David, 1862-1943. 2. Mathematicians-Germany Biography. 1. Title. QA29.HsR4 1996 SIO'.92-dc20 [B] 96-33753 Manufactured in the United States of America. Printed on acid-free paper. 9 8 7 6 543 2 1 ISBN 978-0-387-94674-0 SPIN 10524543 Questions upon Rereading Hilbert By 1965 I had written several popular books, such as From liro to Infinity and A Long Way from Euclid, in which I had attempted to explain certain easily grasped, although often quite sophisticated, mathematical ideas for readers very much like myself-interested in mathematics but essentially untrained. At this point, with almost no mathematical training and never having done any bio graphical writing, I became determined to write the life of David Hilbert, whom many considered the profoundest mathematician of the early part of the 20th century. Now, thirty years later, rereading Hilbert, certain questions come to my mind. -
“Gödel's Modernism: on Set-Theoretic Incompleteness,” Revisited
“G¨odel'sModernism: on Set-Theoretic Incompleteness," revisited∗ Mark van Atten and Juliette Kennedy As to problems with the answer Yes or No, the con- viction that they are always decidable remains un- touched by these results. —G¨odel Contents 1 Introduction 1.1 Questions of incompleteness On Friday, November 15, 1940, Kurt G¨odelgave a talk on set theory at Brown University.1 The topic was his recent proof of the consistency of Cantor's Con- tinuum Hypothesis, henceforth CH,2 with the axiomatic system for set theory ZFC.3 His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness:4 (Remarks I planned to make, but did not) Discussion on G¨odel'slecture on the Continuum Hypothesis, November 14,5 1940 There seems to be a difference: between the undecidable propo- sitions of the kind of his example [i.e., 1931] and propositions such as the Axiom of Choice, and the Axiom of the Continuum [CH ]. We used to ask: \When these two have been decided, is then everything decided?" (The Poles, Tarski I think, suspected that this would be the case.) Now we know that (on the basis of the usual finitary rules) there will always remain undecided propositions. ∗An earlier version of this paper appeared as ‘G¨odel'smodernism: on set-theoretic incom- pleteness', Graduate Faculty Philosophy Journal, 25(2), 2004, pp.289{349. Erratum facing page of contents in 26(1), 2005. 1 1. Can we nevertheless still ask an analogous question? I.e. -
I. Overview of Activities, April, 2005-March, 2006 …
MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 …......……………………. 2 Innovations ………………………………………………………..... 2 Scientific Highlights …..…………………………………………… 4 MSRI Experiences ….……………………………………………… 6 II. Programs …………………………………………………………………….. 13 III. Workshops ……………………………………………………………………. 17 IV. Postdoctoral Fellows …………………………………………………………. 19 Papers by Postdoctoral Fellows …………………………………… 21 V. Mathematics Education and Awareness …...………………………………. 23 VI. Industrial Participation ...…………………………………………………… 26 VII. Future Programs …………………………………………………………….. 28 VIII. Collaborations ………………………………………………………………… 30 IX. Papers Reported by Members ………………………………………………. 35 X. Appendix - Final Reports ……………………………………………………. 45 Programs Workshops Summer Graduate Workshops MSRI Network Conferences MATHEMATICAL SCIENCES RESEARCH INSTITUTE ANNUAL REPORT FOR 2005-2006 I. Overview of Activities, April, 2005-March, 2006 This annual report covers MSRI projects and activities that have been concluded since the submission of the last report in May, 2005. This includes the Spring, 2005 semester programs, the 2005 summer graduate workshops, the Fall, 2005 programs and the January and February workshops of Spring, 2006. This report does not contain fiscal or demographic data. Those data will be submitted in the Fall, 2006 final report covering the completed fiscal 2006 year, based on audited financial reports. This report begins with a discussion of MSRI innovations undertaken this year, followed by highlights -
2019 Symposium Schedule of Events and Abstracts
2019 AWM Research Symposium Schedule Rice University, Houston Texas Friday, April 5, 2019 5:00-8:00pm Informal Opening Reception Outside Valhalla Hall | Rice University Saturday, April 6, 2019 8:00-8:30am Registration and Continental Breakfast (Duncan Hall) 8:30-8.45am Welcoming Remarks: Ruth Haas, AWM President, and Ami Radunskaya, AWM Past-President (McMurtry Auditorium, Duncan Hall) 8:45-9:30am Plenary Lecture: Chelsea Walton, University of Illinois Title: Quantum Symmetry Location: McMurtry Auditorium, Duncan Hall 9:30-10:15 Exhibits and Coffee (Martel Atrium, Duncan Hall) 10:15-12:15 Research Sessions (expanded below) ACxx: Women in Algebraic Combinatorics, I (Keck 105) Analysis and Numerical Methods for Kinetic Transport and Related Models, I (Duncan Hall 1046) Applied and Computational Harmonic Analysis, I (Duncan Hall 1075) Combinatorial Commutative Algebra, I (Hermann Brown 227) WICA: Women in Commutative Algebra, I (Herzstein 212) Education Partnerships: University Mathematics Faculty and K-12 Mathematics Teachers (Herzstein 210) New Advances in Symplectic and Contact Topology, I (Hermann Brown 423) Topology of 3- and 4-Manifolds, I (Hermann Brown 427) WIC: Women in Control, I (Duncan Hall 1042) WIMM: Women in Mathematics of Materials, I (Herzstein 211) WINASC: Women in Numerical Analysis and Scientific Computing, I (Duncan Hall 1064) WinCompTop: Women in Computational Topology, I (Keck 100) WINART: Women in Noncommutative Algebra and Representation Theory, I (Keck 107) WIN: Women in Numbers, I (Herman Brown 453) WiSh: -
Alfred Tarski and a Watershed Meeting in Logic: Cornell, 1957 Solomon Feferman1
Alfred Tarski and a watershed meeting in logic: Cornell, 1957 Solomon Feferman1 For Jan Wolenski, on the occasion of his 60th birthday2 In the summer of 1957 at Cornell University the first of a cavalcade of large-scale meetings partially or completely devoted to logic took place--the five-week long Summer Institute for Symbolic Logic. That meeting turned out to be a watershed event in the development of logic: it was unique in bringing together for such an extended period researchers at every level in all parts of the subject, and the synergetic connections established there would thenceforth change the face of mathematical logic both qualitatively and quantitatively. Prior to the Cornell meeting there had been nothing remotely like it for logicians. Previously, with the growing importance in the twentieth century of their subject both in mathematics and philosophy, it had been natural for many of the broadly representative meetings of mathematicians and of philosophers to include lectures by logicians or even have special sections devoted to logic. Only with the establishment of the Association for Symbolic Logic in 1936 did logicians begin to meet regularly by themselves, but until the 1950s these occasions were usually relatively short in duration, never more than a day or two. Alfred Tarski was one of the principal organizers of the Cornell institute and of some of the major meetings to follow on its heels. Before the outbreak of World War II, outside of Poland Tarski had primarily been involved in several Unity of Science Congresses, including the first, in Paris in 1935, and the fifth, at Harvard in September, 1939. -
Constance Reid
Constance Reid John Ewing, former director of the American Mathematical Society, says this of Constance Reid: “ She has a special talent for understanding mathematicians and their culture. She understands us. She is the Boswell for mathematics – a biographer who has made the mathematical life understandable to the general public and to mathematicians themselves. Her work has enriched our profession.” The “autobiography” of her sister Julia Robinson has been a source of inspiration for many young women contemplating careers in mathematics, and her biography of David Hilbert stands as one of the best mathematical biographies ever written. It is no exaggeration to say that publication of Hilbert made her a star among mathematical biographers. Her five lively and penetrating biographies of mathematicians have been highly praised and constitute a great contribution to the world of mathematics. She has set a high standard for future biographers. We are proud that she was a member of our section. Although the formal mathematical education of Constance Reid concluded with high school algebra and geometry, she was able to understand mathematical ideas well enough to write three best - selling popularizations of mathematics: From Zero to Infinity (1955), Introduction to Higher Mathematics (1959), and A Long Way From Euclid (1963). Several mathematicians have commented on the influence of From Zero to Infinity on their development. Her writing ability was early demonstrated in her book Slacks and Calluses(1944), an account of her working for a summer on a bomber factory assembly line in World War II. At the time she was a high school English teacher in San Diego and only twenty - six. -
1914 Martin Gardner
ΠME Journal, Vol. 13, No. 10, pp 577–609, 2014. 577 THE PI MU EPSILON 100TH ANNIVERSARY PROBLEMS: PART II STEVEN J. MILLER∗, JAMES M. ANDREWS†, AND AVERY T. CARR‡ As 2014 marks the 100th anniversary of Pi Mu Epsilon, we thought it would be fun to celebrate with 100 problems related to important mathematics milestones of the past century. The problems and notes below are meant to provide a brief tour through some of the most exciting and influential moments in recent mathematics. No list can be complete, and of course there are far too many items to celebrate. This list must painfully miss many people’s favorites. As the goal is to introduce students to some of the history of mathematics, ac- cessibility counted far more than importance in breaking ties, and thus the list below is populated with many problems that are more recreational. Many others are well known and extensively studied in the literature; however, as our goal is to introduce people to what can be done in and with mathematics, we’ve decided to include many of these as exercises since attacking them is a great way to learn. We have tried to include some background text before each problem framing it, and references for further reading. This has led to a very long document, so for space issues we split it into four parts (based on the congruence of the year modulo 4). That said: Enjoy! 1914 Martin Gardner Few twentieth-century mathematical authors have written on such diverse sub- jects as Martin Gardner (1914–2010), whose books, numbering over seventy, cover not only numerous fields of mathematics but also literature, philosophy, pseudoscience, religion, and magic. -
Institute for Pure and Applied Mathematics, UCLA Award/Institution #0439872-013151000 Annual Progress Report for 2009-2010 August 1, 2011
Institute for Pure and Applied Mathematics, UCLA Award/Institution #0439872-013151000 Annual Progress Report for 2009-2010 August 1, 2011 TABLE OF CONTENTS EXECUTIVE SUMMARY 2 A. PARTICIPANT LIST 3 B. FINANCIAL SUPPORT LIST 4 C. INCOME AND EXPENDITURE REPORT 4 D. POSTDOCTORAL PLACEMENT LIST 5 E. INSTITUTE DIRECTORS‘ MEETING REPORT 6 F. PARTICIPANT SUMMARY 12 G. POSTDOCTORAL PROGRAM SUMMARY 13 H. GRADUATE STUDENT PROGRAM SUMMARY 14 I. UNDERGRADUATE STUDENT PROGRAM SUMMARY 15 J. PROGRAM DESCRIPTION 15 K. PROGRAM CONSULTANT LIST 38 L. PUBLICATIONS LIST 50 M. INDUSTRIAL AND GOVERNMENTAL INVOLVEMENT 51 N. EXTERNAL SUPPORT 52 O. COMMITTEE MEMBERSHIP 53 P. CONTINUING IMPACT OF PAST IPAM PROGRAMS 54 APPENDIX 1: PUBLICATIONS (SELF-REPORTED) 2009-2010 58 Institute for Pure and Applied Mathematics, UCLA Award/Institution #0439872-013151000 Annual Progress Report for 2009-2010 August 1, 2011 EXECUTIVE SUMMARY Highlights of IPAM‘s accomplishments and activities of the fiscal year 2009-2010 include: IPAM held two long programs during 2009-2010: o Combinatorics (fall 2009) o Climate Modeling (spring 2010) IPAM‘s 2010 winter workshops continued the tradition of focusing on emerging topics where Mathematics plays an important role: o New Directions in Financial Mathematics o Metamaterials: Applications, Analysis and Modeling o Mathematical Problems, Models and Methods in Biomedical Imaging o Statistical and Learning-Theoretic Challenges in Data Privacy IPAM sponsored reunion conferences for four long programs: Optimal Transport, Random Shapes, Search Engines and Internet MRA IPAM sponsored three public lectures since August. Noga Alon presented ―The Combinatorics of Voting Paradoxes‖ on October 5, 2009. Pierre-Louis Lions presented ―On Mean Field Games‖ on January 5, 2010. -
UCLA UCLA Electronic Theses and Dissertations
UCLA UCLA Electronic Theses and Dissertations Title Automorphy Lifting Theorems Permalink https://escholarship.org/uc/item/5br5g0fq Author Kalyanswamy, Sudesh Publication Date 2017 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Los Angeles Automorphy Lifting Theorems A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics by Sudesh Kalyanswamy 2017 c Copyright by Sudesh Kalyanswamy 2017 ABSTRACT OF THE DISSERTATION Automorphy Lifting Theorems by Sudesh Kalyanswamy Doctor of Philosophy in Mathematics University of California, Los Angeles, 2017 Professor Chandrashekhar Khare, Chair This dissertation focus on automorphy lifting theorems and related questions. There are two primary components. The first deals with residually dihedral Galois representations. Namely, fix an odd prime p, and consider a continuous geometric representation ρ : GF ! GLn(O), where F is either a totally real field if n = 2, or a CM field if n > 2, and O is the integer ring of a finite extension of Qp. The goal is to prove the automorphy of representations whose residual representation ρ¯ has the property that the restriction to GF (ζp) is reducible, where ζp denotes a primitive p- th root of unity. This means the classical Taylor-Wiles hypothesis fails and classical patching techniques do not suffice to prove the automorphy of ρ. Building off the work of Thorne, we prove an automorphy theorem in the n = 2 case and apply the result to elliptic curves. The case n > 2 is examined briefly as well. The second component deals with the generic unobstructedness of compatible systems of adjoint representations. -
Program of the Sessions San Diego, California, January 9–12, 2013
Program of the Sessions San Diego, California, January 9–12, 2013 AMS Short Course on Random Matrices, Part Monday, January 7 I MAA Short Course on Conceptual Climate Models, Part I 9:00 AM –3:45PM Room 4, Upper Level, San Diego Convention Center 8:30 AM –5:30PM Room 5B, Upper Level, San Diego Convention Center Organizer: Van Vu,YaleUniversity Organizers: Esther Widiasih,University of Arizona 8:00AM Registration outside Room 5A, SDCC Mary Lou Zeeman,Bowdoin upper level. College 9:00AM Random Matrices: The Universality James Walsh, Oberlin (5) phenomenon for Wigner ensemble. College Preliminary report. 7:30AM Registration outside Room 5A, SDCC Terence Tao, University of California Los upper level. Angles 8:30AM Zero-dimensional energy balance models. 10:45AM Universality of random matrices and (1) Hans Kaper, Georgetown University (6) Dyson Brownian Motion. Preliminary 10:30AM Hands-on Session: Dynamics of energy report. (2) balance models, I. Laszlo Erdos, LMU, Munich Anna Barry*, Institute for Math and Its Applications, and Samantha 2:30PM Free probability and Random matrices. Oestreicher*, University of Minnesota (7) Preliminary report. Alice Guionnet, Massachusetts Institute 2:00PM One-dimensional energy balance models. of Technology (3) Hans Kaper, Georgetown University 4:00PM Hands-on Session: Dynamics of energy NSF-EHR Grant Proposal Writing Workshop (4) balance models, II. Anna Barry*, Institute for Math and Its Applications, and Samantha 3:00 PM –6:00PM Marina Ballroom Oestreicher*, University of Minnesota F, 3rd Floor, Marriott The time limit for each AMS contributed paper in the sessions meeting will be found in Volume 34, Issue 1 of Abstracts is ten minutes.