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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. -
Robert F. Coleman 1954–2014
Baker et al. Mathematical Sciences (2015) 2:21 DOI 10.1186/s40687-015-0036-7 REVIEW Open Access Robert F. Coleman 1954–2014 Matthew Baker*, Barry Mazur and Ken Ribet *Correspondence: In Memoriam: Robert Coleman, Professor of Mathematics, UC Berkeley [email protected] Georgia Institute of Technology, Atlanta, GA, USA 1 Biography Robert F. Coleman, an extraordinarily original and creative mathematician who has had a profound influence on modern number theory and arithmetic geometry, died of a sud- den heart attack in El Cerrito, CA, on the morning of March 24, 2014. He is survived by his wife Tessa, his sister Rosalind, and brother Mark, his nephew Jeffrey, and niece Elise, and his service dog Julep. The depth and importance of his mathematical ideas, his congeniality, the joy radiating from his playful disposition, and his sheer inexhaust- ible energy—all this in the face of Multiple Sclerosis, a condition that did not deter him from full engagement with life—made Robert an inspiration to his friends, family, stu- dents, and colleagues. Robert also worked toward making civic structures and laws more appropriate for people with disabilities. His activism is yet another reason that Robert was so widely admired. Robert was born on November 22, 1954 in Glen Cove, NY, USA. He displayed an early talent for mathematics, winning an Intel Science Talent Search Award in 1972 as a high school student. He earned a mathematics degree from Harvard University and subsequently completed Part III of the mathematical tripos at Cambridge, where he did research under the supervision of John Coates. -
Overview of Some Iwasawa Theory
Overview of some Iwasawa theory Christian Wuthrich 23rd | 27th of July 2012 Contents 0 Introduction 1 1 Iwasawa theory of the class group 1 2 Iwasawa theory for elliptic curves 8 3 The leading term formula 14 4 Selmer groups for general Galois representations 21 5 Kato's Euler system 22 0 Introduction This is the draft version of the notes to my lectures at Heidelberg in July 2012. The intention is to give an overview of some topics in Iwasawa theory. These lectures will contain a lot of definitions and results, but hardly any proofs and details. Especially I would like to emphasise that the word \proof" should actually be replaced by \sketch of proof" in all cases below. Also I have no claim at making this a complete introduction to the subject, nor is the list of references at the end. For this the reader might find [14] a better source. All computations were done in [46]. Any comments and corrections are very welcome. It is my pleasure to thank Thanasis Bouganis, Sylvia Guibert, Chern-Yang Lee, Birgit Schmoetten-Jonas and Otmar Venjakob. 1 Iwasawa theory of the class group Let F be a number field and let p be an odd prime. Suppose we are given a tower of Galois extensions F = 0F ⊂ 1F ⊂ 2F ⊂ · · · such that the Galois group of nF=F is cyclic n n n of order p for all n > 1. Write C for the p-primary part of the class group of F and write pen for its order. Theorem 1 (Iwasawa 56 [15]). -
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. -
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. -
Algebraic Geometry TATA INSTITUTE of FUNDAMENTAL RESEARCH STUDIES in MATHEMATICS
Algebraic Geometry TATA INSTITUTE OF FUNDAMENTAL RESEARCH STUDIES IN MATHEMATICS General Editor : M. S. Narasimhan 1. M. Herve´ : S everal C omplex V ariables 2. M. F. Atiyah and others : D ifferential A nalysis 3. B. Malgrange : I deals of D ifferentiable F unctions 4. S. S. Abhyankar and others : A l g e b r a i c G eometry ALGEBRAIC GEOMETRY Papers presented at the Bombay Colloquium 1968, by ABHYANKAR ARTIN BIRCH BOREL CASSELS DWORK GRIFFITHS GROTHENDIECK HIRONAKA HIRZEBRUCH IGUSA JANICH¨ MANIN MATSUSAKA MUMFORD NAGATA NARASIMHAN RAMANAN SESHADRI SPRINGER TITS VERDIER WEIL Published for the tata institute of fundamental research, bombay OXFORD UNIVERSITY PRESS 1969 Oxford University Press, Ely House, London W. 1 glasgow new york toronto melbourne wellington cape town salisbury ibadan nairobi lusaka addis ababa bombay calcutta madras karachi lahore dacca kuala lumpur singapore hong kong tokyo Oxford House, Apollo Bunder, Bombay 1 BR © Tata Institute of Fundamental Research, 1969 printed in india INTERNATIONAL COLLOQUIUM ON ALGEBRAIC GEOMETRY Bombay, 16-23 January 1968 REPORT An International Colloquium on Algebraic Geometry was held at the Tata Institute of Fundamental Research, Bombay on 16-23 January, 1968. The Colloquium was a closed meeting of experts and others seri- ously interested in Algebraic Geometry. It was attended by twenty-six members and thirty-two other participants, from France, West Germany, India, Japan, the Netherlands, the Soviet Union, the United Kingdom and the United States. The Colloquium was jointly sponsored, and financially supported, by the International Mathematical Union, the Sir Dorabji Tata Trust and the Tata Institute of Fundamental Research. -
IWASAWA 2017 Main Conference (July 24–July 28) Lecture Hall, Graduate School of Mathematical Sciences the University of Tokyo
IWASAWA 2017 To commemorate the 100th anniversary of Kenkichi Iwasawa's birth. Main Conference (July 24{July 28) Lecture Hall, Graduate School of Mathematical Sciences the University of Tokyo July 24 (Mon) 10:00{11:00 Christopher Skinner Iwasawa theory and modular forms 11:20{12:20 Xin Wan Iwasawa main conjecture for non-ordinary modular forms 14:00{15:00 Kazuya Kato Adelic period domains, heights of motives, and Iwasawa the- ory 15:20{16:20 Otmar Venjakob Towards regulator maps for Lubin-Tate extensions 16:40{17:40 John Coates, Ehud de Shalit, and Ralph Greenberg Memories of Kenkichi Iwasawa 18:00{ Reception party July 25 (Tues) 10:00{11:00 Samit Dasgupta On the Gross-Stark conjecture and refinements I 11:20{12:20 Mahesh Kakde On the Gross-Stark conjecture and refinements II 14:00{15:00 Henri Darmon Singular moduli for real quadratic fields: a rigid analytic ap- proach 15:20{16:20 David Burns On higher rank Euler and Kolyvagin systems 16:40{17:40 Poster session 1 IWASAWA 2017 2 July 26 (Wed) 10:00{11:00 Sarah Zerbes An Euler system for GSp(4) 11:20{12:20 Kazim B¨uy¨ukboduk Non-ordinary symmetric squares and Euler systems of rank 2 Evening Yakata-bune (boat trip) dinner July 27 (Thu) 10:00{11:00 Haruzo Hida Cyclicity of adjoint Selmer groups and fundamental units 11:20{12:20 Preston Wake Massey products, pseudo-representations, and the Eisenstein ideal 14:00{15:00 Yasushi Mizusawa Pro-p link groups in Iwasawa theory 15:20{16:20 Werner Bley Solomon's construction in the elliptic rank 2 case 16:40{17:40 Takenori Kataoka Fitting ideals in equivariant -
Interview with Mikio Sato
Interview with Mikio Sato Mikio Sato is a mathematician of great depth and originality. He was born in Japan in 1928 and re- ceived his Ph.D. from the University of Tokyo in 1963. He was a professor at Osaka University and the University of Tokyo before moving to the Research Institute for Mathematical Sciences (RIMS) at Ky- oto University in 1970. He served as the director of RIMS from 1987 to 1991. He is now a professor emeritus at Kyoto University. Among Sato’s many honors are the Asahi Prize of Science (1969), the Japan Academy Prize (1976), the Person of Cultural Merit Award of the Japanese Education Ministry (1984), the Fujiwara Prize (1987), the Schock Prize of the Royal Swedish Academy of Sciences (1997), and the Wolf Prize (2003). This interview was conducted in August 1990 by the late Emmanuel Andronikof; a brief account of his life appears in the sidebar. Sato’s contributions to mathematics are described in the article “Mikio Sato, a visionary of mathematics” by Pierre Schapira, in this issue of the Notices. Andronikof prepared the interview transcript, which was edited by Andrea D’Agnolo of the Univer- sità degli Studi di Padova. Masaki Kashiwara of RIMS and Tetsuji Miwa of Kyoto University helped in various ways, including checking the interview text and assembling the list of papers by Sato. The Notices gratefully acknowledges all of these contributions. —Allyn Jackson Learning Mathematics in Post-War Japan When I entered the middle school in Tokyo in Andronikof: What was it like, learning mathemat- 1941, I was already lagging behind: in Japan, the ics in post-war Japan? school year starts in early April, and I was born in Sato: You know, there is a saying that goes like late April 1928. -
Tate Receives 2010 Abel Prize
Tate Receives 2010 Abel Prize The Norwegian Academy of Science and Letters John Tate is a prime architect of this has awarded the Abel Prize for 2010 to John development. Torrence Tate, University of Texas at Austin, Tate’s 1950 thesis on Fourier analy- for “his vast and lasting impact on the theory of sis in number fields paved the way numbers.” The Abel Prize recognizes contributions for the modern theory of automor- of extraordinary depth and influence to the math- phic forms and their L-functions. ematical sciences and has been awarded annually He revolutionized global class field since 2003. It carries a cash award of 6,000,000 theory with Emil Artin, using novel Norwegian kroner (approximately US$1 million). techniques of group cohomology. John Tate received the Abel Prize from His Majesty With Jonathan Lubin, he recast local King Harald at an award ceremony in Oslo, Norway, class field theory by the ingenious on May 25, 2010. use of formal groups. Tate’s invention of rigid analytic spaces spawned the John Tate Biographical Sketch whole field of rigid analytic geometry. John Torrence Tate was born on March 13, 1925, He found a p-adic analogue of Hodge theory, now in Minneapolis, Minnesota. He received his B.A. in called Hodge-Tate theory, which has blossomed mathematics from Harvard University in 1946 and into another central technique of modern algebraic his Ph.D. in 1950 from Princeton University under number theory. the direction of Emil Artin. He was affiliated with A wealth of further essential mathematical ideas Princeton University from 1950 to 1953 and with and constructions were initiated by Tate, includ- Columbia University from 1953 to 1954. -
Mathematics People
Mathematics People Akshay Venkatesh was born in New Delhi in 1981 but Venkatesh Awarded 2008 was raised in Perth, Australia. He showed his brillance in SASTRA Ramanujan Prize mathematics very early and was awarded the Woods Me- morial Prize in 1997, when he finished his undergraduate Akshay Venkatesh of Stanford University has been studies at the University of Western Australia. He did his awarded the 2008 SASTRA Ramanujan Prize. This annual doctoral studies at Princeton under Peter Sarnak, complet- prize is given for outstanding contributions to areas of ing his Ph.D. in 2002. He was C.L.E. Moore Instructor at the mathematics influenced by the Indian genius Srinivasa Massachusetts Institute of Technology for two years and Ramanujan. The age limit for the prize has been set at was selected as a Clay Research Fellow in 2004. He served thirty-two, because Ramanujan achieved so much in his as associate professor at the Courant Institute of Math- brief life of thirty-two years. The prize carries a cash award ematical Sciences at New York University and received the of US$10,000. Salem Prize and a Packard Fellowship in 2007. He is now professor of mathematics at Stanford University. The 2008 SASTRA Prize Citation reads as follows: “Ak- The 2008 SASTRA Ramanujan Prize Committee con- shay Venkatesh is awarded the 2008 SASTRA Ramanujan sisted of Krishnaswami Alladi (chair), Manjul Bhargava, Prize for his phenomenal contributions to a wide variety Bruce Berndt, Jonathan Borwein, Stephen Milne, Kannan of areas in mathematics, including number theory, auto- Soundararajan, and Michel Waldschmidt. Previous winners morphic forms, representation theory, locally symmetric of the SASTRA Ramanujan Prize are Manjul Bhargava and spaces, and ergodic theory, by himself and in collabora- Kannan Soundararajan (2005), Terence Tao (2006), and tion with several mathematicians. -
An Incomplete Bibliography of Publications in Historia Scientiarum (International Journal of the History of Science Society of Japan)
An Incomplete Bibliography of Publications in Historia Scientiarum (International Journal of the History of Science Society of Japan) 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/ 27 December 2018 Version 1.03 Title word cross-reference $124.00 [Hij90]. $29.00 [Bur93a]. 3[+]1=8 [Hol03]. $49.95 [Yaj07]. 7 × 7 e `eme ieme th [Yam10]. 9 [Mur94]. [Gui86, Pen04, Yos81a]. [DP88].P [Ano94b]. ≈ n 2 2 [Pen04]. π [HKY89, Nak94a, Vol94]. π 3(1=8) [Mur92b]. i=1 xi = x [Ras94a]. × [Har87b]. 0 [Hig01a, Izu05, Miu03, Mor04b, Sat05, She06a, She06b]. 0-19-860665-6 [Sat05]. 0-19-927016-3 [Izu05]. 0-520-24607-1 [Yaj07]. 0-691-11445-5 [She06b]. 0-8018-8235-4 [She06a]. 0-86078-668-4 [Hig01a]. 000 [Sas81b]. 00FF [Yos82]. 02/06/2000 [Has01]. 1 [Kaw93a, Oka98, Yos98]. 10 [Høy03, Yos81c]. 10th [Suz81]. 11 [Hay94]. 12/02/1906 [Has01]. 1475/76 [Hig01b]. 1500 [Ito83]. 15073 [Mur05b]. 1 2 16th [Maa91]. 17 [Sat86, Sat87]. 1700 [Nak83]. 17th [Maa91, Oh14, Yin13]. 18.5cm [Har87b]. 1843 [Ito16]. 1847 [Nak00a]. 1847/48 [Nak00a]. 1880s [Kim08a]. 18th [Ano94b, Kaw11, Kob02, Lor86, Nag80, Oh14, Nak98, THI17]. 18th-century [Kob02]. 19 [Nis92]. 190F [Yos98]. 1920s [Bro07, Kan13, Kim08b]. 1930 [Yaj07]. 1930s [Bro89, Kan13]. 1940 [Fur97]. 1940s [Mat98, YW05]. 1950s [HR15, Yam09]. 1955 [Nis92]. 1960s [FH12]. -
On the Chain Problem of Prime Ideals
ON THE CHAIN PROBLEM OF PRIME IDEALS MASAYOSHI NAGATA There is a problem called the chain problem of prime ideals, which asks, when o is a Noetherian local integral domain, whether the length of an arbi- trary maximal chain of prime ideals in o is equal to rank o or not. In the present paper, we want to show that the answer is not affirmative in the general case. On the other hand, we shall show that if the ring o is quasi-unmixed (the quasi-unmixedness is a generalized notion of the unmixedness ( - equi-dimensionality)), then the answer of the above question is affirmative. In order to discuss the problem, we first introduce some conditions on chains of prime ideals in a ring in § 1. Then, in § 2, we introduce the notion of quasi- unmixedness of semi-local rings and we shall show that in every quasi-unmixed semi-local ring the chain conditions which will be introduced in §1 hold (and in particular wτe see that in every quasi-unmixed semi-local ring, the length of an arbitrary maximal chain of prime ideals is equal to the rank of the ring). In § 3, we shall construct a counter example against the chain problem. In § 4, we shall state some sufficient conditions for a Noetherian local ring to be un- mixed. Terminology. Terms which were used in Nagata [3] and [5] are used in the same sense, except for local or semi-local rings local or semi-local rings may be non-Noetherian (see [4]). Results assumed to be known.