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"Ramanujan's Lost Notebook"

♥ Book Title : Ramanujan's Lost Notebook
♣ Name Author : George E. Andrews
∞ Launching : 2018-09-05
◊ Info ISBN Link : 9783319778341
⊗ Detail ISBN code : 331977834X
⊕ Number Pages : Total 430 sheet
♮ News id : cDBtDwAAQBAJ

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☯ Full Synopsis : "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." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. Review from the second volume:"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."- MathSciNet Review from the first volume:"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."- Gazette of the Australian Mathematical Society"Article| George E. Andrews| Statement ..."

"Ramanujan’s Notebooks"

♥ Book Title : Ramanujan’s Notebooks
♣ Name Author : Bruce C. Berndt
∞ Launching : 1997-12-12
◊ Info ISBN Link : 0387949410
⊗ Detail ISBN code : 9780387949413
⊕ Number Pages : Total 624 sheet
♮ News id : Z__xZ9pNkZMC

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☯ Full Synopsis : "The fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, the average depth in this volume is possibly greater than in the first four. There are several results on continued fractions - a subject that Ramanujan loved very much. It is the authors wish that this and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujans remarkable ideas."Article| Bruce C. Berndt| Statement ..."

"Lost Notebook and Other Unpublished Papers"

♥ Book Title : Lost Notebook and Other Unpublished Papers
♣ Name Author : Srinivasa Ramanujan
∞ Launching : 1993-12
◊ Info ISBN Link : 8185198357
⊗ Detail ISBN code : 9788185198354
⊕ Number Pages : Total 419 sheet
♮ News id : 4Ej2AAAACAAJ

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☯ Full Synopsis : "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."Article| Srinivasa Ramanujan| Statement ..."

"Ramanujan’s Notebooks"

♥ Book Title : Ramanujan’s Notebooks
♣ Name Author : Bruce C. Berndt
∞ Launching : 2012-12-06
◊ Info ISBN Link : 9781461208792
⊗ Detail ISBN code : 1461208793
⊕ Number Pages : Total 451 sheet
♮ News id : QoMHCAAAQBAJ

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☯ Full Synopsis : "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."Article| Bruce C. Berndt| Statement ..."

"The Lost Notebook and Other Unpublished Papers"

♥ Book Title : The Lost Notebook and Other Unpublished Papers
♣ Name Author : Srinivasa Ramanujan Aiyangar
∞ Launching : 1988
◊ Info ISBN Link : 038718726X
⊗ Detail ISBN code : 9780387187266
⊕ Number Pages : Total 419 sheet
♮ News id : 0PRfQgAACAAJ

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☯ Full Synopsis : "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."Article| Srinivasa Ramanujan Aiyangar| Statement ..."

"Ramanujan's Lost Notebook"

♥ Book Title : Ramanujan's Lost Notebook
♣ Name Author : George E. Andrews
∞ Launching : 2009-04-05
◊ Info ISBN Link : 9780387777665
⊗ Detail ISBN code : 0387777660
⊕ Number Pages : Total 420 sheet
♮ News id : Yr7tm35tW48C

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☯ Full Synopsis : "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."Article| George E. Andrews| Statement ..."

"Ramanujan’s Notebooks"

♥ Book Title : Ramanujan’s Notebooks
♣ Name Author : Bruce C. Berndt
∞ Launching : 1997-12-12
◊ Info ISBN Link : 0387949410
⊗ Detail ISBN code : 9780387949413
⊕ Number Pages : Total 624 sheet
♮ News id : Z__xZ9pNkZMC

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☯ Full Synopsis : "The fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, the average depth in this volume is possibly greater than in the first four. There are several results on continued fractions - a subject that Ramanujan loved very much. It is the authors wish that this and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujans remarkable ideas."Article| Bruce C. Berndt| Statement ..."

"Ramanujan"

♥ Book Title : Ramanujan
♣ Name Author : Srinivasa Ramanujan Aiyangar
∞ Launching : 1995-09-07
◊ Info ISBN Link : 0821891251
⊗ Detail ISBN code : 9780821891254
⊕ Number Pages : Total 347 sheet
♮ News id : Of5G0r6DQiEC

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☯ Full Synopsis : "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."Article| Srinivasa Ramanujan Aiyangar| Statement ..."

"Notebooks of Srinivasa Ramanujan"

♥ Book Title : Notebooks of Srinivasa Ramanujan
♣ Name Author : Srinivasa Ramanujan
∞ Launching : 2013-12-20
◊ Info ISBN Link : 9783662302248
⊗ Detail ISBN code : 3662302241
⊕ Number Pages : Total 392 sheet
♮ News id : KvDnCAAAQBAJ

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☯ Full Synopsis : ";l ~,~. . . 0 7 ~S-5' p 7; t, ,_, t l. . ~ o I . . . -"Article| Srinivasa Ramanujan| Statement ..."

"Number Theory in the Spirit of Ramanujan"

♥ Book Title : Number Theory in the Spirit of Ramanujan
♣ Name Author : Bruce C. Berndt
∞ Launching : 2006
◊ Info ISBN Link : 9780821841785
⊗ Detail ISBN code : 0821841785
⊕ Number Pages : Total 187 sheet
♮ News id : bbLxBwAAQBAJ

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☯ Full Synopsis : "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."Article| Bruce C. Berndt| Statement ..."

"Number Theory"

♥ Book Title : Number Theory
♣ Name Author : R.P. Bambah
∞ Launching : 2012-12-06
◊ Info ISBN Link : 9783034870238
⊗ Detail ISBN code : 303487023X
⊕ Number Pages : Total 527 sheet
♮ News id : aiDyBwAAQBAJ

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☯ Full Synopsis : "The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O."Article| R.P. Bambah| Statement ..."

"Gazette - Australian Mathematical Society"

♥ Book Title : Gazette - Australian Mathematical Society
♣ Name Author : Australian Mathematical Society
∞ Launching : 2006
◊ Info ISBN Link : UOM:39015068689150
⊗ Detail ISBN code :
⊕ Number Pages : Total 233 sheet
♮ News id : N1vxAAAAMAAJ

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☯ Full Synopsis : ""Article| Australian Mathematical Society| Statement ..."