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

4.33/5 (3 ratings by Goodreads)
  • Formatas: PDF+DRM
  • Išleidimo metai: 30-Oct-2012
  • Leidėjas: Springer, India, Private Ltd
  • Kalba: eng
  • ISBN-13: 9788132207672
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Ramanujan's Place in the World of Mathematics: Essays Providing a Comparative StudyDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 30-Oct-2012
  • Leidėjas: Springer, India, Private Ltd
  • Kalba: eng
  • ISBN-13: 9788132207672
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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.

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.

Recenzijos

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, youll have read it all. All in all, this book is clearly entirely irresistible. Get a copy for yourself. You cant 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)

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-excellence.
Chapter 9: Evariste Galois - founder of
group theory.
Chapter 10: Leonhard Euler - most prolific 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:
Neils Henrik Abel - Norwegian mathematical genius.
Chapter 14: Issai Schur -
Ramanujan's German contemporary.
Chapter 15: Robert Rankin - Scottish link
with Ramanujan.- Part II: On some aspects of Ramanujan's mathematics.-
Chapter 16: Ramanujan and pi.
Chapter 17: Ramanujan and partitions.
Chapter
18: Major progress on a problem of Ramanujan.- Part III: Reviews.
Chapter
19: Review of Srinivasa Ramanujan: The Lost Notebook and other unpublished
papers.
Chapter 20: Review of The man who knew infinity - book by Robert
Kanigel.
Chapter 21: Review of Ramanujan: Letters and Commentary - book by
Bruce Berndt and Robert Rankin.
Chapter 22: Review of Ramanujan: Essays
and Surveys - book by Bruce Berndt and Robert Rankin.
Chapter 23: Review of
Partitions - a play on Ramanujan.- Part IV: Preserving Ramanujan's legacy.-
Chapter 24: The Ramanujan Journal - its conception, need and place.
Chapter
25: A pilgrimage to Ramanujan's hometown.
Chapter 26: The first SASTRA
Ramanujan prizes.
Chapter 27: Ramanujan's growing influence.- Index.
Krishnaswami Alladi is professor of mathematics at the University of Florida, where he was the department chairman during 19982008. 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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