Overview

This authoritative volume covers aspects of the life and enduring mathematical research of Srinivasa Ramanujan. Born in the late 19th century, Ramanujan had little formal training in pure mathematics. This iconic figure made extraordinary contributions to many facets of mathematical analysis and number theory. During his short life, Ramanujan published 37 papers and curated in notebooks more than 3900 identities which he recorded without proof. Nearly all of his claims that were new have now been proven correct. He stated numerous results that were both original and highly unconventional. Many of these identities have led to major achievements in a wide range of areas of mathematics and theoretical physics. The eight editors of this Handbook have assembled articles on many aspects of Ramanujan’s life and mathematical legacy with a focus on the evolution of his discoveries into many important sub-disciplines of current mathematical research. Included are 234 articles supplied by 88 authors. The book will be of interest to students, teachers, researchers and anyone who is intrigued by the legacy of one of the most striking figures in the history of mathematics.

Full Product Details

9783031501463

Table of Contents

Reviews

Author Information

KRISHNASWAMI ALLADI is professor of mathematics at the University of Florida where he was department chairman during 1998–2008. He received his PhD from the University of California, Los Angeles, in 1978. His research covers many areas of number theory such as analytic number theory, diophantine approximations, sieve methods, probabilistic number theory, and the theory of partitions and q-hypergeometric series. He is the Founder and Editor-in-Chief of The Ramanujan Journal (Springer), Founder and Editor of the book series Developments in Mathematics (Springer) and Chair of the SASTRA Ramanujan Prize Committee. He was an Associate Editor of the Notices of the American Mathematical Society. In 2012 he was inducted as an Inaugural Fellow of the American Mathematical Society for his distinguished contributions. In recognition of his research accomplishments and service to the profession, he was awarded an Honorary Doctorate (Honoris Causa) by SASTRA University in September 2022. GEORGE ANDREWS received his PhD from the University of Pennsylvania in 1964. He was Hans Rademacher’s last student. He is the Atherton Professor of Mathematics at the Pennsylvania State University. He is a member of the National Academy of Sciences (USA), a fellow of the American Academy of Arts and Sciences, a fellow of the American Mathematical Society and a fellow of the Society of Industrial and Applied Mathematics. He holds honorary doctorates from the University of Parma (Italy), the University of Florida, the University of Waterloo (Canada), SASTRA University (India), and the University of Illinois. He was awarded an honorary professorship at Nankai University (China). He was a Guggenheim Fellow in 1983. In 2022, the Institute of Combinatorics and its Applications presented him with the Euler Medal. He was President of the American Mathematical Society from 2009–2011. In 1976, while visiting the Wren Library of Trinity College, Cambridge, he had the good fortune to find the manuscript now called Ramanujan’s Lost Notebook. He and Bruce Berndt collaborated on a five volume explication of the unproven identities in this masterpiece. BRUCE BERNDT received an A.B. degree in 1961 from Albion College, and a PhD in 1966 at the University of Wisconsin, where his primary mentors were Rod Smart (thesis advisor), Marvin Knopp, and Richard Askey. He held a one-year postdoctoral position at the University of Glasgow, where his mentor was Robert Rankin. In 1967, Berndt joined the faculty at the University of Illinois, where he taught for 52 years before retiring in 2019. While at Illinois, he served as the thesis advisor for 37 students; he also mentored about ten postdocs. Since 1974, Berndt has devoted the bulk of his research to explicating and proving claims from Ramanujan’s notebooks and his lost notebook. He published five books on Ramanujan’s Notebooks (Springer), for which he received the Steele Prize for Mathematical Exposition from the American Mathematical Society. Furthermore, he and George Andrews published five books on Ramanujan’s Lost Notebook (Springer). Altogether, Berndt has authored, co-authored, and co-edited 30 books. He received the Ford Award (twice) and the Allendorfer Award for papers published with the Mathematical Association of America. Berndt is the founding editor of International Journal of Number Theory. He was a Guggenheim Fellow in 1998–1999. FRANK GARVAN received his B.Sc.(Hons) and DipEd. from the University of New South Wales (UNSW), Australia. After he taught high school in inner city Sydney and Outback NSW he completed a M.Sc.(research) degree at UNSW under the supervision of Mike Hirschhorn. From 1983–1986 he did a PhD under the supervision of George Andrews at the Pennsylvania State University. He then was a post-doc at the University of Wisconsin (mentor Richard Askey), the Institute for Mathematics and Its Applications (mentor Dennis Stanton), Macquarie University (mentor John Loxton), and Dalhousie University (mentors Jon and Peter Borwein). Since 2000 he has been a full professor at the University of Florida. His interests include q-series, partitions, mock theta functions, and symbolic computation. He has written books on the symbolic software MAPLE and written numerous public packages to aid q-series research. He is Managing Editor of The Ramanujan Journal. He has been privileged to organize several number theory conferences in Florida together with their conference proceedings. In 2022, he was honored to be the principal lecturer for the CBMS Conference, Ramanujan’s Partition Congruences, Mock Theta Functions, and Beyond, at the University of Texas Rio Grande Valley. KEN ONO is the STEM Advisor to the Provost and the Marvin Rosenblum Professor of Mathematics at the University of Virginia. He is a Fellow of the Shannon Center for Advanced Studies. He earned his PhD in mathematics from UCLA in 1993, and he earned a BA in mathematics from the University of Chicago in 1989. He is a recipient of a Guggenheim Fellowship, David and Lucile Packard Fellowship, Alfred P. Sloan Foundation Fellowship, and an NSF CAREER Award. In 2000 he received a Presidential Early Career Award from Bill Clinton at a ceremony at the White House. In 2005 he was named the National Science Foundation Director’s Distinguished Teaching Scholar, the highest honor awarded by NSF for excellence in research and teaching. He is a Fellow of the American Mathematical Society, and he is the recipient of the 2023 University of Chicago Alumni Medal for Professional Achievement. Heis the Founding Director of the Spirit of Ramanujan Global STEM Talent Search, which supports emerging engineers, mathematicians, and scientists who lack traditional institutional support through financial grants and mentorship opportunities. He was an Associate Producer of the film The Man Who Knew Infinity, which starred Dev Patel and Jeremy Irons. PETER PAULE earned his doctorate from the University of Vienna in 1983 (advisor: Johann Cigler). He was awarded a Humboldt Research Fellowship (1984–86, University of Bayreuth, host: Adalbert Kerber). In 2005 he was appointed full professor as successor to Bruno Buchberger; from 2009 to 2023 he was director of the Research Institute for Symbolic Computation (RISC) of the Johannes Kepler University Linz (JKU). From 2003 to 2008 he was Speaker of the Special Research Program Numerical and Symbolic Scientific Computing, from 2008 to 2017 director of the Doctoral Program Computational Mathematics, both excellence programs at JKU sponsored by the Austrian Science Fund (FWF). Paule was a member of the original editorial committee for the Digital Library of Mathematical Functions (DLMF) project, in existence from the mid-1990’s to the mid-2010’s. He is adjunct professor at the Center for Applied Mathematics, Tianjin University. He is a member of the Academia Europaea, and a Fellow of the American Mathematical Society. OLE WARNAAR completed his PhD at the University of Amsterdam in 1993 under the guidance of Bernard Nienhuis, and currently holds the position of Chair and Professor of Pure Mathematics at The University of Queensland, Australia. His research interests include algebraic combinatorics, basic and elliptic hypergeometric series, q-series and partition theory, representation theory, and special functions. Warnaar has held a Research Fellowship of the Royal Netherlands Academy of Arts and Sciences (KNAW) from 1997 to 2000, was elected Fellow of the Australian Academy of Science in 2008, and was awarded the George Szekeres Medal of the Australian Mathematical Society (AustMS) in 2020. He served as President of AustMS in 2021–2022. Warnaar has a long-standing involvement with Australian as well as international mathematics competitions, and chaired the organizing committee of the Simon Marais Mathematics Competition (SMMC) from 2019 till 2022. AE JA YEE is professor of mathematics at the Pennsylvania State University. She received her PhD from Korea Advanced Institute of Science and Technology in 2000. Her research covers areas of combinatorics and number theory, in particular the theory of partitions and q-hypergeometric series. She is a managing editor of International Journal of Number Theory and an associate editor of Discrete Mathematics. She also serveson the editorial boards of The Ramanujan Journal and Combinatory Theory.

Tab Content 6

Customer Reviews

Recent Reviews

Countries Available