Twelve Lectures on Subjects Suggested by His Life and Work

Author: Godfrey Harold Hardy

Publisher: Taylor & Francis US

ISBN: 9780821820230

Category: Mathematics

Page: 254

View: 5327

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.
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twelve lectures on subjects suggested by his life and work

Author: Godfrey Harold Hardy

Publisher: Chelsea Pub Co

ISBN: N.A

Category: Mathematics

Page: 236

View: 1080

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Author: Srinivasa Ramanujan Aiyangar,Godfrey Harold Hardy,P. Veṅkatesvara Seshu Aiyar,Bertram Martin Wilson

Publisher: American Mathematical Soc.

ISBN: 0821820761

Category: Mathematics

Page: 426

View: 7785

The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do.
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Letters and Commentary

Author: Srinivasa Ramanujan Aiyangar,Bruce C. Berndt,Robert Alexander Rankin

Publisher: American Mathematical Soc.

ISBN: 0821804707

Category: Mathematics

Page: 347

View: 2077

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.
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Author: Godfrey Harold Hardy

Publisher: American Mathematical Soc.

ISBN: 0821826492

Category: Mathematics

Page: 396

View: 2104

Review of the original edition: This is an inspiring textbook for students who know the theory of functions of real and complex variables and wish further knowledge of mathematical analysis. There are no problems displayed and labelled ``problems,'' but one who follows all of the arguments and calculations of the text will find use for his ingenuity and pencil. The book deals with interesting and important problems and topics in many fields of mathematical analysis, to an extent very much greater than that indicated by the titles of the chapters. It is, of course, an indispensable handbook for those interested in divergent series. It assembles a considerable part of the theory of divergent series, which has previously existed only in periodical literature. Hardy has greatly simplified and improved many theories, theorems and proofs. In addition, numerous acknowledgements show that the book incorporates many previously unpublished results and improvements of old results, communicated to Hardy by his colleagues and by others interested in the book. --Mathematical Reviews
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Essays and Surveys

Author: Srinivasa Ramanujan Aiyangar,Bruce C. Berndt,Robert Alexander Rankin

Publisher: American Mathematical Soc.

ISBN: 9780821826249

Category: Mathematics

Page: 347

View: 8631

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.
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The Man and the Mathematician

Author: S. R. Ranganathan

Publisher: Ess Ess Publication

ISBN: 9788170005575

Category: Biography & Autobiography

Page: 138

View: 1873

This is the moving story of the life of Ramanujan the great Indian mathematical genius who appeared suddenly as a meteor in 1887, rushed through a short span of thirty-two years, consumed himself and disappeared with equal suddenness. At the age of thirteen, he had mastered Loney's Trigonometry and even calculated the length of the earth. Son of a clerk in a cloth merchant's shop in Kumbakonam, before the was 23, had filled a whole notebook with hundreds of mathematical theorems and results, in spite of poverty, unemployment and absence of anyone who could understand his work. Many of the theorems were new to the mathematical world and some have not yet been proved. The book unfolds in quick succession, the chief events of his life beginning with his search in 1911 for a clerical post, always carrying his notebook under his arm, to his sailing to England in 1914 and his return home in 1919. In Cambridge he was soon acknowledged to be the most remarkable mathematician of our times and was elected a Fellow of the Trinity College of Cambridge and a Fellow to The Royal Society at the early age of thirty. The book contains the reminiscences of several surviving contemporaries of Ramanujan. It highlights his penetrating intuition and childlike simplicity. He was a 'Seer' in mathematics. Though agnostic in arguments, he was ever conscious of the immanence of God.
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Author: Bruce C. Berndt

Publisher: Springer Science & Business Media

ISBN: 1461208793

Category: Mathematics

Page: 451

View: 366

During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.
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How I Learned to Count

Author: Ken Ono,Amir D. Aczel

Publisher: Springer

ISBN: 3319255681

Category: Mathematics

Page: 238

View: 9508

"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."
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Containing Propositions, Formulae, and Methods of Analysis, with Abridged Demonstrations

Author: George Shoobridge Carr

Publisher: Cambridge University Press

ISBN: 1108050689

Category: Mathematics

Page: 718

View: 8136

When George Shoobridge Carr (1837-1914) wrote his Synopsis of Elementary Results he intended it as an aid to students preparing for degree-level examinations such as the Cambridge Mathematical Tripos, for which he provided private tuition. He would have been startled to see the two volumes, first published in 1880 and 1886 respectively, reissued more than a century later. Notably, in 1903 the work fell into the hands of the Indian prodigy Srinivasa Ramanujan (1887-1920) and greatly influenced his mathematical education. It is the interaction between a methodical teaching aid and the soaring spirit of a self-taught genius which gives this reissue its interest. Volume 2 contains sections on differential calculus, integral calculus, calculus of variations, differential equations, calculus of finite differences, plane coordinate geometry and solid coordinate geometry. Also included is a historically valuable index insofar as it provides references to 890 volumes of 32 periodicals dating back to 1800.
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Essays and Surveys

Author: Srinivasa Ramanujan Aiyangar,Bruce C. Berndt,Robert Alexander Rankin

Publisher: American Mathematical Soc.

ISBN: 9780821826249

Category: Mathematics

Page: 347

View: 7558

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.
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Author: Gabriele Sicuro

Publisher: Springer

ISBN: 3319465775

Category: Science

Page: 136

View: 3821

This thesis discusses the random Euclidean bipartite matching problem, i.e., the matching problem between two different sets of points randomly generated on the Euclidean domain. The presence of both randomness and Euclidean constraints makes the study of the average properties of the solution highly relevant. The thesis reviews a number of known results about both matching problems and Euclidean matching problems. It then goes on to provide a complete and general solution for the one dimensional problem in the case of convex cost functionals and, moreover, discusses a potential approach to the average optimal matching cost and its finite size corrections in the quadratic case. The correlation functions of the optimal matching map in the thermodynamical limit are also analyzed. Lastly, using a functional approach, the thesis puts forward a general recipe for the computation of the correlation function of the optimal matching in any dimension and in a generic domain.
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26th International Symposium, DISC 2012, Salvador, Brazil, October 16-18, 2012, Proceedings

Author: Marcos K. Aguilera

Publisher: Springer

ISBN: 3642336515

Category: Computers

Page: 450

View: 6423

This book constitutes the refereed proceedings of the 26th International Symposium on Distributed Computing, DISC 2012, held in Salvador, Brazil, in October 2012. The 27 revised full papers presented together with 24 brief announcements were carefully reviewed and selected from 119 submissions. The papers are organized in topical sections on shared memory, mobile agents and overlay networks, wireless and multiple access channel networks, dynamic networks, distributed graph algorithms, wireless and loosely connected networks, robots, and lower bounds and separation.
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L-Functions

Author: Carlos J. Moreno

Publisher: American Mathematical Soc.

ISBN: 0821842668

Category: Mathematics

Page: 291

View: 8447

Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. The present book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.
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including joint papers with J.E. Littlewood and others

Author: Godfrey Harold Hardy,John Edensor Littlewood,London Mathematical Society

Publisher: Clarendon Press

ISBN: N.A

Category: Mathematics

Page: 694

View: 7016

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Author: Bruce C. Berndt

Publisher: American Mathematical Soc.

ISBN: 0821841785

Category: Mathematics

Page: 187

View: 3099

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.
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Author: Shaun Cooper

Publisher: World Scientific

ISBN: 9814366463

Category: Electronic books

Page: 184

View: 9565

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.
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Author: Wolfgang Arendt,Wolfgang P. Schleich

Publisher: John Wiley & Sons

ISBN: 3527628037

Category: Science

Page: 502

View: 1911

Mathematical Analysis of Evolution, Information, and Complexity deals with the analysis of evolution, information and complexity. The time evolution of systems or processes is a central question in science, this text covers a broad range of problems including diffusion processes, neuronal networks, quantum theory and cosmology. Bringing together a wide collection of research in mathematics, information theory, physics and other scientific and technical areas, this new title offers elementary and thus easily accessible introductions to the various fields of research addressed in the book.
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Author: W. Sierpinski,Waclaw Sierpin ́ski,Felix Klein,Carl Runge,Leonard E. Dickson

Publisher: American Mathematical Soc.

ISBN: 0821875671

Category: Congruences (Geometry)

Page: 441

View: 2565

Four volumes in one: On the Congruence of Sets and Their Equivalence by Finite Decomposition, by W. Sierpinski; The Mathematical Theory of the Top, by F. Klein--well-known lectures on the analytical formulas relating to the motion of the top; Graphical Methods, by C. Runge; Introduction to the Theory of Algebraic Equations, by L. E. Dickson--Dickson's earliest account of the subject, presented with a historical, elementary perspective.
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