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Author : partitions Conference on elliptic functions
Publisher :
ISBN 13 : 9781571462459
Total Pages : 199 pages
Book Rating : 4.4/5 (624 download)
Download or read book Ramanujan Rediscovered written by partitions Conference on elliptic functions and published by . This book was released on 2012 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
ISBN 13 : 9780821826249
Total Pages : 388 pages
Book Rating : 4.8/5 (262 download)
Download or read book Ramanujan: Essays and Surveys written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 2001 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Bruce C. Berndt
Publisher : Springer Science & Business Media
ISBN 13 : 146120965X
Total Pages : 521 pages
Book Rating : 4.4/5 (612 download)
Download or read book Ramanujan’s Notebooks written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon Ramanujans death in 1920, G. H. Hardy strongly urged that Ramanujans notebooks be published and edited. In 1957, the Tata Institute of Fundamental Research in Bombay finally published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the task of editing Ramanujans notebooks: proofs are provided to theorems not yet proven in previous literature, and many results are so startling as to be unique.
Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
ISBN 13 : 0821841785
Total Pages : 210 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Godfrey Harold Hardy
Publisher : American Mathematical Soc.
ISBN 13 : 0821820230
Total Pages : 266 pages
Book Rating : 4.8/5 (218 download)
Download or read book Ramanujan written by Godfrey Harold Hardy and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Another excellent book long out of print but much in demand. This book is pulled together by Ramanujan's primary mentor, G. H. Hardy, who was the first to recognize the amazing nature of Ramanujan's ideas. Another exceptional classic from the Chelsea list.
Author : George Shoobridge Carr
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.R/5 (6 download)
Download or read book A Synopsis of Elementary Results in Pure and Applied Mathematics written by George Shoobridge Carr and published by . This book was released on 1880 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chandrashekar Adiga
Publisher : American Mathematical Soc.
ISBN 13 : 0821823167
Total Pages : 99 pages
Book Rating : 4.8/5 (218 download)
Download or read book Chapter 16 of Ramanujan's Second Notebook: Theta-Functions and $q$-Series written by Chandrashekar Adiga and published by American Mathematical Soc.. This book was released on 1985 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of Chapter 16 in Ramanujan's second notebook is devoted to q-series. Several of the results obtained by Ramanujan are classical, but many are new. In particular, certain elegant q-continued fraction expansions have not appeared heretofore in print. In the remainder of this chapter, Ramanujan develops the theory of the classical theta-functions in a manner different from his nineteenth century predecessors such as Jacobi. Although many of Ramanujan's discoveries about theta-functions are well-known, several new results are also to be found.
Author : Andrew V. Sills
Publisher : CRC Press
ISBN 13 : 1351647962
Total Pages : 263 pages
Book Rating : 4.3/5 (516 download)
Download or read book An Invitation to the Rogers-Ramanujan Identities written by Andrew V. Sills and published by CRC Press. This book was released on 2017-10-16 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.
Author : Subrahmanyan Chandrasekhar
Publisher : University of Chicago Press
ISBN 13 : 9780226101033
Total Pages : 308 pages
Book Rating : 4.1/5 (1 download)
Download or read book Selected Papers, Volume 7 written by Subrahmanyan Chandrasekhar and published by University of Chicago Press. This book was released on 1997-06-09 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these selections readers are treated to a rare opportunity to see the world through the eyes of one of the twentieth century's most brilliant and sensitive scientists. Conceived by Chandrasekhar as a supplement to his Selected Papers, this volume begins with eight papers he wrote with Valeria Ferrari on the non-radial oscillations of stars. It then explores some of the themes addressed in Truth and Beauty, with meditations on the aesthetics of science and the world it examines. Highlights include: "The Series Paintings of Claude Monet and the Landscape of General Relativity," "The Perception of Beauty and the Pursuit of Science," "On Reading Newton's Principia at Age Past Eighty," and personal recollections of Indira Gandhi, Jawaharlal Nehru, and others. Selected Papers, Volume 7 paints a picture of Chandra's universe, filled with stars and galaxies, but with space for poetics, paintings, and politics. The late S. Chandrasekhar was best known for his discovery of the upper limit to the mass of a white dwarf star, for which he received the Nobel Prize in Physics in 1983. He was the author of many books, including The Mathematical Theory of Black Holes and, most recently, Newton's Principia for the Common Reader.
Author : Pradip Debnath
Publisher : World Scientific
ISBN 13 : 9811272611
Total Pages : 463 pages
Book Rating : 4.8/5 (112 download)
Download or read book Advances In Number Theory And Applied Analysis written by Pradip Debnath and published by World Scientific. This book was released on 2023-05-08 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presently, the exploration of the applications of different techniques and tools of number theory and mathematical analysis are extensively prevalent in various areas of engineering, mathematical, physical, biological and statistical sciences. This book will present the most recent developments in these two fields through contributions from eminent scientists and mathematicians worldwide.The book will present the current state of the art development in these two areas through original new contributions and surveys. As such, readers will find several useful tools and techniques to develop their skills and expertise in number theory and applied analysis. New research directions are also indicated in each of the chapters. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in number theory and mathematical analysis. The readers of this book will require minimum prerequisites of analysis, topology, number theory and functional analysis.
Author : George E. Andrews
Publisher : Springer Science & Business Media
ISBN 13 : 0387777660
Total Pages : 423 pages
Book Rating : 4.3/5 (877 download)
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.
Author : Krishnaswami Alladi
Publisher : Springer Nature
ISBN 13 : 9811562415
Total Pages : 265 pages
Book Rating : 4.8/5 (115 download)
Download or read book Ramanujan's Place in the World of Mathematics written by Krishnaswami Alladi and published by Springer Nature. This book was released on 2021-09-17 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First Edition of the 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 in 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 with the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. Also, among the articles are reviews of three important books on Ramanujan’s mathematics and life. In addition, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number pi, his path-breaking 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. This Second Edition is an expanded version of the first with six more articles by the author. Of note is the inclusion of a detailed review of the movie The Man Who Knew Infinity, a description of the fundamental work of the SASTRA Ramanujan Prize Winners, and an account of the Royal Society Conference to honour Ramanujan’s legacy on the centenary of his election as FRS.
Author : K. Srinivasa Rao
Publisher : Springer Nature
ISBN 13 : 9811604479
Total Pages : 299 pages
Book Rating : 4.8/5 (116 download)
Download or read book Srinivasa Ramanujan written by K. Srinivasa Rao and published by Springer Nature. This book was released on 2021-05-30 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Shaun Cooper
Publisher : Springer
ISBN 13 : 3319561723
Total Pages : 696 pages
Book Rating : 4.3/5 (195 download)
Download or read book Ramanujan's Theta Functions written by Shaun Cooper and published by Springer. This book was released on 2017-06-12 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.
Author : Claude Brezinski
Publisher : Springer Science & Business Media
ISBN 13 : 3642581692
Total Pages : 556 pages
Book Rating : 4.6/5 (425 download)
Download or read book History of Continued Fractions and Padé Approximants written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...
Author : Srinivasa Ramanujan Aiyangar
Publisher : American Mathematical Soc.
ISBN 13 : 0821804707
Total Pages : 362 pages
Book Rating : 4.8/5 (218 download)
Download or read book Ramanujan: Letters and Commentary written by Srinivasa Ramanujan Aiyangar and published by American Mathematical Soc.. This book was released on 1995 with total page 362 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.
Author : Stephen Wolfram
Publisher :
ISBN 13 : 9780713991161
Total Pages : 1197 pages
Book Rating : 4.9/5 (911 download)
Download or read book A New Kind of Science written by Stephen Wolfram and published by . This book was released on 2002 with total page 1197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.
