Download or read book Ramanujan s Lost Notebook written by George E. Andrews and published by Springer Science & Business Media. This book was released on 2005-05-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated as "Ramanujan’s Lost Notebook," it contains considerable material on mock theta functions and undoubtedly dates from the last year of Ramanujan’s life. In this book, the notebook is presented with additional material and expert commentary.
Download or read book The Lost Notebook and Other Unpublished Papers written by Srinivasa Ramanujan Aiyangar and published by Springer. This book was released on 1988 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The so-called Lost Notebook of S.R. Ramanujan was brought to light in 1976 as part of the Watson bequest, by G.E. Andrews with whose introduction this collection of unpublished manuscripts opens. A major portion of the Lost Notebook - really just 90 unpaginated sheets of work on q-series and other topics - is reproduced here in facsimile. Letters from Ramanujan to Hardy as well as various other sheets of seemingly related notes are then included, on topics including coefficients in the 1/q3 and 1/q2 problems and the mock theta functions. The next 180 pages consist of unpublished manuscripts of Ramanujan, including 28 pages from the 'Loose Papers` held in the Trinity College Library. Finally a number of interesting letters that were exchanged between Ramanujan, Littlewood, Hardy and Watson, with a bearing on Ramanujan's work are collected together here with other extracts and fragments.
Download or read book Number Theory in the Spirit of Ramanujan written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 2006 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.
Download or read book Lost Notebook and Other Unpublished Papers written by Srinivasa Ramanujan and published by . This book was released on 1993-12 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Srinivasa Ramanujan's achievements in research made him perhaps the greatest Indian mathematician of modern times. By the time he was 12 years old he had worked through a copy of Loney's Trigonometry. At the age of 16 he verified over 6,000 formulae in Carr's Synopsis of Pure Mathematics. By the time he was married at 21 he had already obtained several results in the areas of elliptic integrals, hypergeometric series and divergent series. In 1918 he was elected a Fellow of the Royal Society and a Fellow of Trinity College, but died shortly thereafter.
Download or read book Ramanujan s Lost Notebook written by George E. Andrews and published by Springer Science & Business Media. This book was released on 2009-04-05 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated "Ramanujan's lost notebook." The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work.
Download or read book Ramanujan s Notebooks written by Srinivasa Ramanujan Aiyangar and published by . This book was released on 1985 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ramanujan written by Srinivasa Ramanujan Aiyangar and published by American Mathematical Soc.. This book was released on 1995-09-07 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The letters that Ramanujan wrote to G. H. Hardy on January 16 and February 27, 1913, are two of the most famous letters in the history of mathematics. These and other letters introduced Ramanujan and his remarkable theorems to the world and stimulated much research, especially in the 1920s and 1930s. This book brings together many letters to, from, and about Ramanujan. The letters came from the National Archives in Delhi, the Archives in the State of Tamil Nadu, and a variety of other sources. Helping to orient the reader is the extensive commentary, both mathematical and cultural, by Berndt and Rankin; in particular, they discuss in detail the history, up to the present day, of each mathematical result in the letters. Containing many letters that have never been published before, this book will appeal to those interested in Ramanujan's mathematics as well as those wanting to learn more about the personal side of his life. Ramanujan: Letters and Commentary was selected for the CHOICE list of Outstanding Academic Books for 1996.
Download or read book Notebooks of Srinivasa Ramanujan written by Srinivasa Ramanujan Aiyangar and published by . This book was released on 1957 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory and Discrete Mathematics written by A. K. Agarwal and published by Springer. This book was released on 2002-01-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ramanujan s Place in the World of Mathematics written by Krishnaswami Alladi and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Collected Papers of Srinivasa Ramanujan written by Srinivasa Ramanujan and published by Cambridge University Press. This book was released on 2015-12-03 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887-1920), with editorial contributions from G. H. Hardy (1877-1947). Detailed notes are incorporated throughout and appendices are also included. This book will be of value to anyone with an interest in the works of Ramanujan and the history of mathematics.
Download or read book Heidegger s Black Notebooks written by Andrew J. Mitchell and published by Columbia University Press. This book was released on 2017-09-05 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the 1930s through the 1970s, the philosopher Martin Heidegger kept a running series of private writings, the so-called Black Notebooks. The recent publication of the Black Notebooks volumes from the war years have sparked international controversy. While Heidegger’s engagement with National Socialism was well known, the Black Notebooks showed for the first time that this anti-Semitism was not merely a personal resentment. They contain not just anti-Semitic remarks, they show Heidegger incorporating basic tropes of anti-Semitism into his philosophical thinking. In them, Heidegger tried to assign a philosophical significance to anti-Semitism, with “the Jew” or “world Judaism” cast as antagonist in his project. How, then, are we to engage with a philosophy that, no matter how significant, seems contaminated by anti-Semitism? This book brings together an international group of scholars from a variety of disciplines to discuss the ramifications of the Black Notebooks for philosophy and the humanities at large. Bettina Bergo, Robert Bernasconi, Martin Gessmann, Sander Gilman, Peter E. Gordon, Hans Ulrich Gumbrecht, Michael Marder, Eduardo Mendieta, Richard Polt, Tom Rockmore, Peter Trawny, and Slavoj Žižek discuss issues including anti-Semitism in the Black Notebooks and Heidegger’s thought more broadly, such as German conceptions of Jews and Judaism, Heidegger’s notions of metaphysics, and anti-Semitism’s entanglement with Heidegger’s views on modernity and technology, grappling with material as provocative as it is deplorable. In contrast to both those who seek to exonerate Heidegger and those who simply condemn him, and rather than an all-or-nothing view of Heidegger’s anti-Semitism, they urge careful reading and rereading of his work to turn Heideggerian thought against itself. These measured and thoughtful responses to one of the major scandals in the history of philosophy unflinchingly take up the tangled and contested legacy of Heideggerian thought.
Download or read book Eric Hoffer written by Tom Bethell and published by Hoover Press. This book was released on 2013-09-01 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawn from Eric Hoffer's private papers as well as interviews with those who knew him, this detailed biography paints a picture of a truly original American thinker and writer. Author Tom Bethell interviewed Hoffer in the years just before his death, and his meticulous accounts of those meetings offer new insights into the man known as the "Longshoreman Philosopher."
Download or read book Development of Elliptic Functions According to Ramanujan written by K. Venkatachaliengar and published by World Scientific. This book was released on 2012 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.
Download or read book Lost Laysen written by Margaret Mitchell and published by Simon and Schuster. This book was released on 1997-05-06 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently, the odd thought Margaret Mitchell had only one story to tell: Gone With the Wind. Now meet a heroine to match Scarlett: Courtenay Ross, a feisty, independent-minded woman, and the two men -- one a cool-headed, well-heeled gentleman, the other a hot-blooded, pugnacious sailor -- who adore her. A tale of yearning, valor, and devotion, Lost Laysen enthralls from its delightful beginning to its unforgettable end. Equally intriguing is the story behind the story -- the real-life romance that inspired Mitchell: how she gave the original manuscript as a gift to her beau. Henry Love Angel, and how the manuscript, along with Mitchell's intimate letters and treasured photographs, were lovingly safeguarded only to be discovered decades later in a shoebox Lost Laysen is pure magic, a gift for us to cherish from America's most beloved storyteller.
Download or read book The Lost Notebook and Other Unpublished Papers written by Srinivasa Ramanujan Aiyangar and published by Springer. This book was released on 1988-01-01 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: The so-called "Lost Notebook" of S.R. Ramanujan was brought to light in 1976 as part of the Watson bequest, by G.E. Andrews with whose introduction this collection of unpublished manuscripts opens. A major portion of the "Lost Notebook" - really just 90 unpaginated sheets of work on "q"-series and other topics - is reproduced here in facsimile. Letters from Ramanujan to Hardy as well as various other sheets of seemingly related notes are then included, on topics including coefficients in the 1/q3 and 1/q2 problems and the mock theta functions. The next 180 pages consist of unpublished manuscripts of Ramanujan, including 28 pages from the 'Loose Papers held in the Trinity College Library. Finally a number of interesting letters that were exchanged between Ramanujan, Littlewood, Hardy and Watson, with a bearing on Ramanujan's work are collected together here with other extracts and fragments.
Download or read book Harmonic Maass Forms and Mock Modular Forms Theory and Applications written by Kathrin Bringmann and published by American Mathematical Soc.. This book was released on 2017-12-15 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.
