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.
Mục lục
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. Mac Mahon – 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: Onsome 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on a problem of Ramanujan.- Part III: Reviews.- Chapter 19: Review of “Srinivasa Ramanujan: The Lost Notebook and other unpublished papers”.- Chapter 20: Review of “The man who knew infinity – book by Robert Kanigel”.- Chapter 21: Review of “Ramanujan: Letters and Commentary – book by Bruce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.
Giới thiệu về tác giả
Krishnaswami Alladi is professor of mathematics at the University of Florida, where he was the department chairman during 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, 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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