Srinivasa Ramanujan : life and works of a natural mathematical genius, Swayambhu / K. Srinivasa Rao.

Format:

Book

Author/Creator:

Srinivasa Rao, K., 1942- author.

Language:

English

Subjects (All):

Ramanujan Aiyangar, Srinivasa, 1887-1920.

Ramanujan Aiyangar, Srinivasa.

Mathematicians--India--Biography.

Mathematicians.

Mathematics--History.

Mathematics.

Physical Description:

1 online resource (299 pages)

Place of Publication:

Singapore : Springer, [2021]

Summary:

This book offers a unique account on the life and works of Srinivasa Ramanujan--often hailed as the greatest "natural" mathematical genius. Sharing valuable insights into the many stages of Ramanujan's life, this book provides glimpses into his prolific research on highly composite numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric functions which led the author to discover a new summation theorem. It also includes the list of Ramanujan's collected papers, letters and other material present at the Wren Library, Trinity College in Cambridge, UK. This book is a valuable resource for all readers interested in Ramanujan's life, work and indelible contributions to mathematics.

Contents:

Intro

Foreword

Preface

Acknowledgements

Contents

About the Author

1 Life of Srinivasa Ramanujan

1.1 Early Years

1.2 Years of Adversity

1.3 A Turning Point

1.4 Ramanujan's First Letter to Hardy

1.5 The Years of Fruition

1.6 Ramanujan's Medicography

1.7 Excerpt from Records of the Royal Society and F.R.S.

1.8 The Beginning of the End

1.9 Janaki Ramanujan (Janakiammal)

1.10 Human Qualities

2 Ramanujan at Cambridge

2.1 Research Publications

2.2 On Selected Formulae of Ramanujan

2.3 Elementary Mathematics

2.4 Highly Composite Numbers

2.5 Partitions

2.6 Ramanujan's Congruences

2.7 Rogers-Ramanujan Identities

2.8 An `Astonishing' Theorem

2.9 Ramanujan on Elliptic and Modular Functions

2.10 Mock Theta Functions

2.11 Continued Fractions

3 Ramanujan's Mathematics: Further Glimpses

3.1 Ramanujan Summation and Ramanujan Sum

3.2 Arithmetic Functions

3.3 Ramanujan's τ-Function

3.4 Ramanujan's Notebooks

3.5 Resurgence of Interest

3.6 A Page from the Second Notebook of Ramanujan

3.7 Bruce Berndt's Work on the Notebooks

3.8 Ratan P. Agarwal's Work on the Notebooks

3.9 Dyson on Ramanujan's Notebooks

3.10 CD ROMs on the Life and Work of Ramanujan

4 Hardy on Ramanujan

4.1 Ramanujan Discovers Hardy

4.2 Hardy: A Brief Biography

4.3 Hardy's Collaborations

4.4 The Hardy-Ramanujan Collaboration: Pros and Cons

4.5 Hardy's Lectures on Ramanujan's Work

4.6 Ramanujan's Work on Hypergeometric Series

5 Ramanujan and Hypergeometric Series

5.1 A Few Illustrative Examples

5.2 In the Notebooks of Ramanujan

5.3 An Entry in Ramanujan's Notebook

5.4 A New Summation Theorem and its Proof

6 Chandrasekhar (Chandra) and Ramanujan

6.1 S. Chandrasekhar: Nobel Laureate

6.2 Chandrasekhar on Ramanujan.

6.3 The Passport Photograph of Ramanujan

6.4 A Remarkable Story

6.5 Sources for the Books on Ramanujan

6.6 The Centenary Year, 1987: Ramanujan Revisited

7 Books on Ramanujan and Busts of Ramanujan

7.1 S.R. Ranganathan's Biography (1967)

7.2 Robert Kanigel's The Man Who Knew Infinity

7.3 Review of Ramanujan: Letters and Commentary by Berndt and Rankin

7.4 Busts of Ramanujan

7.4.1 On the Temple Tower of BITS, Pilani

7.4.2 Bust Made by Paul Granlund

7.4.3 Bust Made by N. Masilamani

7.4.4 Bronze Statue in Ramanujan IT City by K. G. Ravi

7.5 The Notebooks of Ramanujan

7.6 The Wren Library

8 Ramanujan Birth Anniversaries and Documentarieson Ramanujan

8.1 The 75th Birth Anniversary of Ramanujan

8.2 Notebooks of Ramanujan and Their Accessibility

8.3 Awareness Today

8.4 Promising Prospects

8.5 Video Programmes

8.6 Ira Hauptman's Partition

8.7 Web Sites

8.8 The ISC, πie Pavilion and Ramanujan Exhibitions

9 Relevance of Ramanujan Today

9.1 Contents of the CD ROMs

9.2 Birth Centenary of Ramanujan (1987)

9.3 ICM 2010

9.4 The Author's Contributions

9.5 A Plea for a National Science Museum

A Research Publications of Ramanujan

Papers Written by S. Ramanujan

Papers Written by S. Ramanujan with G.H. Hardy

B Wren Library Card Catalogue and Papers of Ramanujan

C Personal File of S. Ramanujan at the National Archives and Papers at the Tamilnadu Archives

Files in the Tamilnadu Archives

References

Notes

Index.

Notes:

Description based on print version record.

ISBN:

9789811604478

981-16-0447-9

OCLC:

1253476333