Ramanujan: Essays and Surveys
About this Title
Bruce C. Berndt, University of Illinois, Urbana-Champaign, IL and Robert A. Rankin, University of Glasgow, Glasgow, Scotland, Editors
Publication: History of Mathematics
Publication Year: 2001; Volume 22
ISBNs: 978-0-8218-2624-9 (print); 978-1-4704-3890-6 (online)
MathSciNet review: MR1862732
MSC: Primary 01A70; Secondary 00B60, 11-03, 33-03, 33C05, 33C20, 33D15
This book contains essays on Ramanujan and his work that were written especially for this volume. It also includes important survey articles in areas influenced by Ramanujan's mathematics. Most of the articles in the book are nontechnical, but even those that are more technical contain substantial sections that will engage the general reader.
The book opens with the only four existing photographs of Ramanujan, presenting historical accounts of them and information about other people in the photos. This section includes an account of a cryptic family history written by his younger brother, S. Lakshmi Narasimhan. Following are articles on Ramanujan's illness by R. A. Rankin, the British physician D. A. B. Young, and Nobel laureate S. Chandrasekhar. They present a study of his symptoms, a convincing diagnosis of the cause of his death, and a thorough exposition of Ramanujan's life as a patient in English sanitariums and nursing homes.
Following this are biographies of S. Janaki (Mrs. Ramanujan) and S. Narayana Iyer, Chief Accountant of the Madras Port Trust Office, who first communicated Ramanujan's work to the Journal of the Indian Mathematical Society. The last half of the book begins with a section on “Ramanujan's Manuscripts and Notebooks”. Included is an important article by G. E. Andrews on Ramanujan's lost notebook.
The final two sections feature both nontechnical articles, such as Jonathan and Peter Borwein's “Ramanujan and pi”, and more technical articles by Freeman Dyson, Atle Selberg, Richard Askey, and G. N. Watson.
This volume complements the book Ramanujan: Letters and Commentary, Volume 9, in the AMS series, History of Mathematics. For more on Ramanujan, see these AMS publications, Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Volume 136.H, and Collected Papers of Srinivasa Ramanujan, Volume 159.H, in the AMS Chelsea Publishing series.
General mathematical audience.
Table of Contents
- Bruce C. Berndt – The four photographs of Ramanujan
- Bruce C. Berndt and Robert A. Rankin – The books studied by Ramanujan in India
- Bruce C. Berndt – The influence of Carr’s synopsis on Ramanujan
- Bruce C. Berndt – The notebooks of Srinivasa Ramanujan
- A recently discovered letter giving Ramanujan’s examination scores
- S. Chandrasekhar – On Ramanujan
- Robert A. Rankin – The Ramanujan family record
- Robert A. Rankin – Ramanujan as a patient
- D. A. B. Young – Ramanujan’s illness
- S. Chandrasekhar – An incident in the life of S. Ramanujan, F.R.S.: Conversations with G. H. Hardy, F.R.S. and J. E. Littlewood, F.R.S. and their sequel
- Bruce C. Berndt – S. Janaki Ammal (Mrs. Ramanujan)
- Conversation “I didn’t understand his work, but I knew his worth”
- Bruce C. Berndt – A short biography of S. Narayana Iyer
- S. Narayana Aiyar – The distribution of primes
- S. Narayana Aiyar – Some theorems in summation
- Robert A. Rankin – Ramanujan’s manuscripts and notebooks
- Robert A. Rankin – Ramanujan’s manuscripts and notebooks, II
- Bruce C. Berndt – An overview of Ramanujan’s notebooks [redacted]
- George E. Andrews – An introduction to Ramanujan’s “lost” notebook
- Jonathan M. Borwein and Peter B. Borwein – Ramanujan and pi [redacted]
- Bruce C. Berndt – $\pi $ related developments since 1988
- Atle Selberg – Reflections around the Ramanujan centenary
- Bruce C. Berndt, Youn-Seo Choi and Soon-Yi Kang – The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society
- Freeman J. Dyson – A walk through Ramanujan’s garden
- R. Askey – Ramanujan and hypergeometric and basic hypergeometric series
- G. N. Watson – The final problem: An account of the mock theta functions