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A Historical Perspective of Spectrum Estimation
PROCEEDINGSIEEE, OF THE VOL. 70, NO. 9, SEPTEMBER885 1982 A Historical Perspective of Spectrum Estimation ENDERS A. ROBINSON Invited Paper Alwhrct-The prehistory of spectral estimation has its mots in an- times, credit for the empirical discovery of spectra goes to the cient times with the development of the calendar and the clock The diversified genius of Sir Isaac Newton [ 11. But the great in- work of F’ythagom in 600 B.C. on the laws of musical harmony found mathematical expression in the eighteenthcentury in terms of the wave terest in spectral analysis made its appearanceonly a little equation. The strueto understand the solution of the wave equation more than a century ago. The prominent German chemist was fhlly resolved by Jean Baptiste Joseph de Fourier in 1807 with Robert Wilhelm Bunsen (18 1 1-1899) repeated Newton’s his introduction of the Fourier series TheFourier theory was ex- experiment of the glass prism. Only Bunsen did not use the tended to the case of arbitrary orthogollpl functions by Stmn and sun’s rays Newton did. Newtonhad found that aray of Liowillein 1836. The Stum+Liouville theory led to the greatest as empirical sum of spectral analysis yet obbhed, namely the formulo sunlight is expanded into a band of many colors, the spectrum tion of quantum mechnnics as given by Heisenberg and SchrMngm in of the rainbow. In Bunsen’s experiment, the role of pure sun- 1925 and 1926. In 1929 John von Neumann put the spectral theory of light was replaced by the burning of an old rag that had been the atom on a Turn mathematical foundation in his spectral represent, soaked in a salt solution (sodium chloride). -
A MATHEMATICIAN's SURVIVAL GUIDE 1. an Algebra Teacher I
A MATHEMATICIAN’S SURVIVAL GUIDE PETER G. CASAZZA 1. An Algebra Teacher I could Understand Emmy award-winning journalist and bestselling author Cokie Roberts once said: As long as algebra is taught in school, there will be prayer in school. 1.1. An Object of Pride. Mathematician’s relationship with the general public most closely resembles “bipolar” disorder - at the same time they admire us and hate us. Almost everyone has had at least one bad experience with mathematics during some part of their education. Get into any taxi and tell the driver you are a mathematician and the response is predictable. First, there is silence while the driver relives his greatest nightmare - taking algebra. Next, you will hear the immortal words: “I was never any good at mathematics.” My response is: “I was never any good at being a taxi driver so I went into mathematics.” You can learn a lot from taxi drivers if you just don’t tell them you are a mathematician. Why get started on the wrong foot? The mathematician David Mumford put it: “I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.” 1.2. A Balancing Act. The other most common response we get from the public is: “I can’t even balance my checkbook.” This reflects the fact that the public thinks that mathematics is basically just adding numbers. They have no idea what we really do. Because of the textbooks they studied, they think that all needed mathematics has already been discovered. -
2012-13 Annual Report of Private Giving
MAKING THE EXTRAORDINARY POSSIBLE 2012–13 ANNUAL REPORT OF PRIVATE GIVING 2 0 1 2–13 ANNUAL REPORT OF PRIVATE GIVING “Whether you’ve been a donor to UMaine for years or CONTENTS have just made your first gift, I thank you for your Letter from President Paul Ferguson 2 Fundraising Partners 4 thoughtfulness and invite you to join us in a journey Letter from Jeffery Mills and Eric Rolfson 4 that promises ‘Blue Skies ahead.’ ” President Paul W. Ferguson M A K I N G T H E Campaign Maine at a Glance 6 EXTRAORDINARY 2013 Endowments/Holdings 8 Ways of Giving 38 POSSIBLE Giving Societies 40 2013 Donors 42 BLUE SKIES AHEAD SINCE GRACE, JENNY AND I a common theme: making life better student access, it is donors like you arrived at UMaine just over two years for others — specifically for our who hold the real keys to the ago, we have truly enjoyed our students and the state we serve. While University of Maine’s future level interactions with many alumni and I’ve enjoyed many high points in my of excellence. friends who genuinely care about this personal and professional life, nothing remarkable university. Events like the surpasses the sense of reward and Unrestricted gifts that provide us the Stillwater Society dinner and the accomplishment that accompanies maximum flexibility to move forward Charles F. Allen Legacy Society assisting others to fulfill their are one of these keys. We also are luncheon have allowed us to meet and potential. counting on benefactors to champion thank hundreds of donors. -
Martin Gardner Receives JPBM Communications Award
THE NEWSLETTER OF THE MATHEMATICAL ASSOCIAnON OF AMERICA Martin Gardner Receives JPBM voIome 14, Number 4 Communications Award Martin Gardner has been named the 1994 the United States Navy recipient of the Joint Policy Board for Math and served until the end ematics Communications Award. Author of of the Second World In this Issue numerous books and articles about mathemat War. He began his Sci ics' Gardner isbest known for thelong-running entific Americancolumn "Mathematical Games" column in Scientific in December 1956. 4 CD-ROM American. For nearly forty years, Gardner, The MAA is proud to count Gardneras one of its Textbooks and through his column and books, has exertedan authors. He has published four books with the enormous influence on mathematicians and Calculus Association, with three more in thepipeline. This students of mathematics. September, he begins "Gardner's Gatherings," 6 Open Secrets When asked about the appeal of mathemat a new column in Math Horizons. ics, Gardner said, "It's just the patterns, and Previous JPBM Communications Awards have their order-and their beauty: the way it all gone to James Gleick, author of Chaos; Hugh 8 Section Awards fits together so it all comes out right in the Whitemore for the play Breaking the Code; Ivars end." for Distinguished Peterson, author of several books and associate Teaching Gardner graduated Phi Beta Kappa in phi editor of Science News; and Joel Schneider, losophy from the University of Chicago in content director for the Children's Television 10 Personal Opinion 1936, and then pursued graduate work in the Workshop's Square One TV. -
Publications of Members, 1930-1954
THE INSTITUTE FOR ADVANCED STUDY PUBLICATIONS OF MEMBERS 1930 • 1954 PRINCETON, NEW JERSEY . 1955 COPYRIGHT 1955, BY THE INSTITUTE FOR ADVANCED STUDY MANUFACTURED IN THE UNITED STATES OF AMERICA BY PRINCETON UNIVERSITY PRESS, PRINCETON, N.J. CONTENTS FOREWORD 3 BIBLIOGRAPHY 9 DIRECTORY OF INSTITUTE MEMBERS, 1930-1954 205 MEMBERS WITH APPOINTMENTS OF LONG TERM 265 TRUSTEES 269 buH FOREWORD FOREWORD Publication of this bibliography marks the 25th Anniversary of the foundation of the Institute for Advanced Study. The certificate of incorporation of the Institute was signed on the 20th day of May, 1930. The first academic appointments, naming Albert Einstein and Oswald Veblen as Professors at the Institute, were approved two and one- half years later, in initiation of academic work. The Institute for Advanced Study is devoted to the encouragement, support and patronage of learning—of science, in the old, broad, undifferentiated sense of the word. The Institute partakes of the character both of a university and of a research institute j but it also differs in significant ways from both. It is unlike a university, for instance, in its small size—its academic membership at any one time numbers only a little over a hundred. It is unlike a university in that it has no formal curriculum, no scheduled courses of instruction, no commitment that all branches of learning be rep- resented in its faculty and members. It is unlike a research institute in that its purposes are broader, that it supports many separate fields of study, that, with one exception, it maintains no laboratories; and above all in that it welcomes temporary members, whose intellectual development and growth are one of its principal purposes. -
Sir Andrew J. Wiles
ISSN 0002-9920 (print) ISSN 1088-9477 (online) of the American Mathematical Society March 2017 Volume 64, Number 3 Women's History Month Ad Honorem Sir Andrew J. Wiles page 197 2018 Leroy P. Steele Prize: Call for Nominations page 195 Interview with New AMS President Kenneth A. Ribet page 229 New York Meeting page 291 Sir Andrew J. Wiles, 2016 Abel Laureate. “The definition of a good mathematical problem is the mathematics it generates rather Notices than the problem itself.” of the American Mathematical Society March 2017 FEATURES 197 239229 26239 Ad Honorem Sir Andrew J. Interview with New The Graduate Student Wiles AMS President Kenneth Section Interview with Abel Laureate Sir A. Ribet Interview with Ryan Haskett Andrew J. Wiles by Martin Raussen and by Alexander Diaz-Lopez Allyn Jackson Christian Skau WHAT IS...an Elliptic Curve? Andrew Wiles's Marvelous Proof by by Harris B. Daniels and Álvaro Henri Darmon Lozano-Robledo The Mathematical Works of Andrew Wiles by Christopher Skinner In this issue we honor Sir Andrew J. Wiles, prover of Fermat's Last Theorem, recipient of the 2016 Abel Prize, and star of the NOVA video The Proof. We've got the official interview, reprinted from the newsletter of our friends in the European Mathematical Society; "Andrew Wiles's Marvelous Proof" by Henri Darmon; and a collection of articles on "The Mathematical Works of Andrew Wiles" assembled by guest editor Christopher Skinner. We welcome the new AMS president, Ken Ribet (another star of The Proof). Marcelo Viana, Director of IMPA in Rio, describes "Math in Brazil" on the eve of the upcoming IMO and ICM. -
PRESENTAZIONE E LAUDATIO DI DAVID MUMFOD by ALBERTO
PRESENTAZIONE E LAUDATIO DI DAVID MUMFOD by ALBERTO CONTE David Mumford was born in 1937 in Worth (West Sussex, UK) in an old English farm house. His father, William Mumford, was British, ... a visionary with an international perspective, who started an experimental school in Tanzania based on the idea of appropriate technology... Mumford's father worked for the United Nations from its foundations in 1945 and this was his job while Mumford was growing up. Mumford's mother was American and the family lived on Long Island Sound in the United States, a semi-enclosed arm of the North Atlantic Ocean with the New York- Connecticut shore on the north and Long Island to the south. After attending Exeter School, Mumford entered Harvard University. After graduating from Harvard, Mumford was appointed to the staff there. He was appointed professor of mathematics in 1967 and, ten years later, he became Higgins Professor. He was chairman of the Mathematics Department at Harvard from 1981 to 1984 and MacArthur Fellow from 1987 to 1992. In 1996 Mumford moved to the Division of Applied Mathematics of Brown University where he is now Professor Emeritus. Mumford has received many honours for his scientific work. First of all, the Fields Medal (1974), the highest distinction for a mathematician. He was awarded the Shaw Prize in 2006, the Steele Prize for Mathematical Exposition by the American Mathematical Society in 2007, and the Wolf Prize in 2008. Upon receiving this award from the hands of Israeli President Shimon Peres he announced that he will donate the money to Bir Zeit University, near Ramallah, and to Gisha, an Israeli organization that advocates for Palestinian freedom of movement, by saying: I decided to donate my share of the Wolf Prize to enable the academic community in occupied Palestine to survive and thrive. -
Density of Algebraic Points on Noetherian Varieties 3
DENSITY OF ALGEBRAIC POINTS ON NOETHERIAN VARIETIES GAL BINYAMINI Abstract. Let Ω ⊂ Rn be a relatively compact domain. A finite collection of real-valued functions on Ω is called a Noetherian chain if the partial derivatives of each function are expressible as polynomials in the functions. A Noether- ian function is a polynomial combination of elements of a Noetherian chain. We introduce Noetherian parameters (degrees, size of the coefficients) which measure the complexity of a Noetherian chain. Our main result is an explicit form of the Pila-Wilkie theorem for sets defined using Noetherian equalities and inequalities: for any ε> 0, the number of points of height H in the tran- scendental part of the set is at most C ·Hε where C can be explicitly estimated from the Noetherian parameters and ε. We show that many functions of interest in arithmetic geometry fall within the Noetherian class, including elliptic and abelian functions, modular func- tions and universal covers of compact Riemann surfaces, Jacobi theta func- tions, periods of algebraic integrals, and the uniformizing map of the Siegel modular variety Ag . We thus effectivize the (geometric side of) Pila-Zannier strategy for unlikely intersections in those instances that involve only compact domains. 1. Introduction 1.1. The (real) Noetherian class. Let ΩR ⊂ Rn be a bounded domain, and n denote by x := (x1,...,xn) a system of coordinates on R . A collection of analytic ℓ functions φ := (φ1,...,φℓ): Ω¯ R → R is called a (complex) real Noetherian chain if it satisfies an overdetermined system of algebraic partial differential equations, i =1,...,ℓ ∂φi = Pi,j (x, φ), (1) ∂xj j =1,...,n where P are polynomials. -
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. -
Download PDF of Summer 2016 Colloquy
Nonprofit Organization summer 2016 US Postage HONORING EXCELLENCE p.20 ONE DAY IN MAY p.24 PAID North Reading, MA Permit No.8 What’s the BUZZ? Bees, behavior & pollination p.12 What’s the Buzz? 12 Bees, Behavior, and Pollination ONE GRADUATE STUDENT’S INVESTIGATION INTO BUMBLEBEE BEHAVIOR The 2016 Centennial Medalists 20 HONORING FRANCIS FUKUYAMA, DAVID MUMFORD, JOHN O’MALLEY, AND CECILIA ROUSE Intellectual Assembly 22 ALUMNI DAY 2016 One Day in May 24 COMMENCEMENT 2016 summer/16 An alumni publication of Harvard University’s Graduate School of Arts and Sciences 3 FROM UNIVERSITY HALL 4 NEWS & NOTES Harvard Horizons, Health Policy turns 25, new Alumni Council leadership. 8 Q&A WITH COLLEEN CAVANAUGH A path-breaking biologist provides new evolutionary insights. 10 SHELF LIFE Elephants, Manchuria, the Uyghur nation and more. 26 NOTED News from our alumni. 28 ALUMNI CONNECTIONS Dudley 25th, Life Lab launches, and recent graduates gathering. summer Cover Image: Patrick Hruby Facing Image: Commencement Begins /16 Photograph by Tony Rinaldo CONTRIBUTORS Xiao-Li Meng dean, PhD ’90 Jon Petitt director of alumni relations and publications Patrick Hruby is a Los Angeles–based Ann Hall editor freelance illustrator and designer with Visual Dialogue design an insatiable appetite for color. His work Colloquy is published three times a year by the Graduate School Alumni has appeared in The New York Times, Association (GSAA). Governed by its Alumni Council, the GSAA represents Fortune Magazine, and WIRED, among and advances the interests of alumni of the Graduate School of Arts and Sciences through alumni events and publications. others. -
Mathematicians Fleeing from Nazi Germany
Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D. -
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.