Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative Study

ISBN-13: 9789811562402 / Angielski / Twarda / 2021 / 264 str.

Krishnaswami Alladi

Opis

This book introduces Ramanujan's mathematics and compares his work with other great mathematicians. It examines such contributions as his formulae for pi, his groundbreaking work in the theory of partitions, and his fundamental observations on quadratic forms.

Spis treści

-Foreword (by George Andrews).- Preface.- Part I - Ramanujan and other mathematical luminaries.- Chapter 1: Ramanujan: An Estimation.- Chapter 2: Ramanujan: The Second Century.- Chapter 3: L. J. Rogers: A Contemporary of Ramanujan.- Chapter 4: P. A. MacMahon: Ramanujan's Distinguished Contemporary.- Chapter 5: Fermat and Ramanujan: A Comparison.- Chapter 6: J. J. Sylvester: Ramanujan's Illustrious Predecessor.- Chapter 7: Erdos and Ramanujan: Legends of Twentieth Century Mathematics.- Chapter 8: C. G. J. Jacobi: Algorist par-excelence.- Chapter 9: Evariste Galois: Founder of Group Theory.- Chapter 10: Leonhard Euler: Most Prolic Mathematician in History.- Chapter 11: G. H. Hardy: Ramanujan's Mentor.- Chapter 12: J. E. Littlewood: Ramanujan's Contemporary and Hardy's Collaborator.- Chapter 13: Niels Henrik Abel: Norwegian Mathematical Genius.- Chapter 14: Issai Schur: Ramanujan's German Contemporary.- Chapter 15: Robert Rankin: Scottish link with Ramanujan.- Chapter 16: G. N. Watson: First to Investigate the Mock Theta Functions.- Part II - Some Aspects of Ramanujan's Mathematics.- Chapter 17: Ramanujan and.- Chapter 18. Ramanujan and partitions.- Chapter 19: Major progress on a problem of Ramanujan.- Part III - Reviews of Books and Stage Productions.- Chapter 20. Genius Whom the Gods Loved - A Review of "Srinivasa Ramanujan: The Lost Notebook and Other Unpublished Papers".- 21. The Discovery and Rediscovery of Mahematical Genius - A Review of the book "The Man Who Knew Infinity: A Life of the Genius Ramanujan".- Chapter 22. A Review of "Ramanujan: Letters and Commentary".- Chapter 23. A Review of "Ramanujan: Essays and Surveys".- Chapter 24. Review of "Partition: A Play on Ramanujan".- Chapter 25. Review of the movie "The Man Who Knew Infinity".- Part IV - Preserving Ramanujan's Legacy.- Chapter 26: The Ramanujan Journal: Its Conception, Need and Place.- Chapter 27. A Pilgrimage to Ramanujan's Hometown.- Chapter 28. The First SASTRA Ramanujan Prizes.- Chapter 29. Ramanujan's Growing Influence.- Chapter 30. The SASTRA Ramanujan Prize - Its Origins and its Winners.- Chapter 31. Srinivasa Ramanujan - Going Strong at 125.- Chapter 32: Ramanujan in Mauritius.- Chapter 33. Royal Society Conference and Publication for Centenary of Ramanujan's Election as FRS.

O autorze

Krishnaswami Alladi is Professor at the Department of Mathematics at the University of Florida, where he has been the department chairman from 1998–2008. He received his Ph.D. from the University of California in 1978. His research area is number theory, where he has made notable contributions. In 1987, during the Ramanujan Centennial in India, he got the inspiration to launch The Ramanujan Journal (now published by Springer), devoted to all areas of research influenced by Ramanujan. He annually writes articles about Ramanujan and his place in the world of mathematics in several national dailies and scientific magazines. He is presently editor-in-chief of The Ramanujan Journal, editor of the book series Developments in Mathematics (Springer), and Chair of the SASTRA Ramanujan Prize Committee. He was associate editor of Notices of the American Mathematical Society.

Blurb

The First Edition of the book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians in history whose life and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan’s spectacular discoveries and remarkable life with the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. Also, among the articles are reviews of three important books on Ramanujan’s mathematics and life. In addition, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number pi, his path-breaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future.

This Second Edition is an expanded version of the first with six more articles by the author. Of note is the inclusion of a detailed review of the movie The Man Who Knew Infinity, a description of the fundamental work of the SASTRA Ramanujan Prize Winners, and an account of the Royal Society Conference to honour Ramanujan’s legacy on the centenary of his election as FRS. 

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 area of research is number theory where he has made notable contributions. 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 Notices of the American Mathematical Society. 

From some Reviews of Edition 1

The book is an enlightening study of Ramanujan as a mathematician and as a human being and will appeal to mathematicians, students and the general public interested in mathematics. Themistocles M. Rassias, European Math. Soc. Newsletter, March 2013 

A great book to go swimming in; Alladi has put together a sweeping compendium of essays on Ramanujan ... a wonderful book to browse through, and before you know it, you'll have read it all. ... This book is clearly entirely irresistible. Get a copy for yourself .... You can’t miss. Michael Berg, Math. Assoc. of America Reviews, January 2013