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Ramanujan's Place in the World of Mathematics

Essays Providing a Comparative Study

  • Book
  • © 2013

Overview

Authors:
  1. Krishnaswami Alladi

    1. Department of Mathematics, University of Florida, Gainesville, USA

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  • Encourages bright students to pursue mathematics and exposes them to the enchanting world of Ramanujan

  • Introduces many aspects of Ramanujan’s mathematics and compares his work with other great mathematicians throughout history

  • Appeals to the readers by presenting the life and work of not only Ramanujan but also of many other mathematical luminaries

  • Includes supplementary material: sn.pub/extras

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Table of contents (27 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Ramanujan and Other Mathematical Luminaries

    1. Front Matter

      Pages 1-1
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  3. Ramanujan and other mathematical luminaries

    1. Ramanujan: An Estimation

      • Krishnaswami Alladi
      Pages 3-5

    2. Ramanujan: The Second Century

      • Krishnaswami Alladi
      Pages 7-11

    3. L.J. Rogers: A Contemporary of Ramanujan

      • Krishnaswami Alladi
      Pages 13-18

    4. P.A. MacMahon: Ramanujan’s Distinguished Contemporary

      • Krishnaswami Alladi
      Pages 19-25

    5. Fermat and Ramanujan: A Comparison

      • Krishnaswami Alladi
      Pages 27-30

    6. J.J. Sylvester: Ramanujan’s Illustrious Predecessor

      • Krishnaswami Alladi
      Pages 31-36

    7. Erdös and Ramanujan: Legends of Twentieth Century Mathematics

      • Krishnaswami Alladi
      Pages 37-44

    8. C.G.J. Jacobi: Algorist par-excellence

      • Krishnaswami Alladi
      Pages 45-50

    9. Evariste Galois: Founder of Group Theory

      • Krishnaswami Alladi
      Pages 51-56

    10. Leonhard Euler: Most Prolific Mathematician in History

      • Krishnaswami Alladi
      Pages 57-66

    11. G.H. Hardy: Ramanujan’s Mentor

      • Krishnaswami Alladi
      Pages 67-73

    12. J.E. Littlewood: Ramanujan’s Contemporary and Hardy’s Collaborator

      • Krishnaswami Alladi
      Pages 75-79

    13. Niels Henrik Abel: Norwegian Mathematical Genius

      • Krishnaswami Alladi
      Pages 81-88

    14. Issai Schur: Ramanujan’s German Contemporary

      • Krishnaswami Alladi
      Pages 89-94

    15. Robert Rankin: Scottish Link with Ramanujan

      • Krishnaswami Alladi
      Pages 95-100

  4. Some Aspects of Ramanujan’s Mathematics

    1. Front Matter

      Pages 101-101
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  5. On Some Aspects of Ramanujan's Mathematics

    1. Ramanujan and π

      • Krishnaswami Alladi
      Pages 103-109

    2. Ramanujan and Partitions

      • Krishnaswami Alladi
      Pages 111-116
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Keywords

About this book

This 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 throughout the 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 and of the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. In the book, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number pi, his pathbreaking 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. Thus the book is an enlightening study of Ramanujan as a mathematician and a human being.

Reviews

From the reviews:

“One of the best ways to understand Ramanujan and his mathematics is to study his life and work in comparison to other outstanding mathematicians in history whose lives and works have things in common with Ramanujan. Some of them, like Ramanujan, underwent great difficulties in life but, undeterred by these obstacles, produced work of the highest quality. After providing an evaluation of Ramanujan and discussing the possible impact of his work in the years following his centenary, there is a collection of essays on 13 mathematical luminaries that provides a comparative study. These essays are really the heart of the book….As [George] Andrews writes in his Foreword: “Alladi, who has worked in several areas of number theory and analysis, and who, as the editor of The Ramanujan Journal, is uniquely qualified to write these historical sketches which provide an unusual and compelling view of Ramanujan.” 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, EMS Newsletter March 2013

“It is in fact a great book to go swimming in. Alladi has put together a sweeping compendium of essays on Ramanujan … . It is a wonderful book to browse through, and before you know it, you’ll have read it all. … All in all, this book is clearly entirely irresistible. Get a copy for yourself. … You can’t miss.” (Michael Berg, MAA Reviews, January, 2013)

“It is a unique book and can be read effortlessly even by non-mathematicians. Each article can be read separately. … strongly recommends this book to each and every one irrespective of their area of work and interest and also to school teachers and students. To sum up, it is an excellent book, highly enjoyable and easily readable.” (Girish Kumar Ramaiah, Zentralblatt MATH, Vol. 1257, 2013)

Authors and Affiliations

  • Department of Mathematics, University of Florida, Gainesville, USA

    Krishnaswami Alladi

About the author

Krishnaswami Alladi is professor of mathematics at the University of Florida, where he was the department chairman during 1998–2008. He received his PhD 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, being published in several national dailies. He is presently editor-in-chief of The Ramanujan Journal, editor of the book series Developments in Mathematics (Springer), and associated editor of Notices of the American Mathematical Society.

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