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

  • Formāts: EPUB+DRM
  • Izdošanas datums: 17-Sep-2021
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789811562419
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  • Formāts: EPUB+DRM
  • Izdošanas datums: 17-Sep-2021
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789811562419
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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.

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.

Part I Ramanujan and Other Mathematical Luminaries
1 Ramanujan: An Estimation
3(4)
2 Ramanujan: The Second Century
7(6)
3 L.J. Rogers: A Contemporary of Ramanujan
13(6)
4 P.A. MacMahon: Ramanujan's Distinguished Contemporary
19(8)
5 Fermat and Ramanujan: A Comparison
27(4)
6 J.J. Sylvester: Ramanujan's Illustrious Predecessor
31(6)
7 Erdos and Ramanujan: Legends of Twentieth Century Mathematics
37(8)
8 C.G.J. Jacobi: Algorist par-excellence
45(6)
9 Evariste Galois: Founder of Group Theory
51(8)
10 Leonhard Euler: Most Prolific Mathematician in History
59(10)
11 G.H. Hardy: Ramanujan's Mentor
69(8)
12 J.E. Littlewood: Ramanujan's Contemporary and Hardy's Collaborator
77(6)
13 Niels Henrik Abel: Norwegian Mathematical Genius
83(8)
14 Issai Schur: Ramanujan's German Contemporary
91(6)
15 Robert Rankin: Scottish Link with Ramanujan
97(6)
16 G. N. Watson: First to Investigate the Mock Theta Functions
103(10)
Part II Some Aspects of Ramanujan's Mathematics
17 Ramanujan and it
113(8)
18 Ramanujan and Partitions
121(6)
19 Major Progress on a Problem of Ramanujan
127(4)
Part III Reviews of Books and Stage Productions
20 Genius Whom the Gods Loved--A Review of "Srinivasa Ramanujan: The Lost Notebook and Other Unpublished Papers"
131(4)
21 The Discovery and Rediscovery of Mathematical Genius--A Review of "The Man Who Knew Infinity: A Life of the Genius Ramanujan"
135(4)
22 A Review of "Ramanujan: Letters and Commentary"
139(8)
23 A Review of "Ramanujan: Essays and Surveys"
147(6)
24 A Review of "Partition: A Play on Ramanujan"
153(2)
25 Review of the Movie on the Mathematical Genius Ramanujan
155(22)
Part IV Preserving Ramanujan's Legacy
26 The Ramanujan Journal: Its Conception, Need and Place
177(6)
27 A Pilgrimage to Ramanujan's Hometown
183(8)
28 The First SASTRA Ramanujan Prizes
191(6)
29 Ramanujan's Growing Influence
197(4)
30 The Sastra Ramanujan Prize: Its Origins and Its Winners
201(24)
31 Srinivasa Ramanujan: Going Strong at 125
225(14)
32 Ramanujan in Mauritius
239(8)
33 Royal Society Conference and Publication for the Centenary of Srinivasa Ramanujan's Election as FRS
247(8)
Index 255
Krishnaswami Alladi is Professor at the Department of Mathematics at the University of Florida, where he has been the department chairman from 19982008. 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.
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