Description : Srinivasa Ramanujan was a mathematician brilliant beyond comparison who inspired many great mathematicians. There is extensive literature available on the work of Ramanujan. But what is missing in the literature is an analysis that would place his mathematics in context and interpret it in terms of modern developments. The 12 lectures by Hardy, delivered in 1936, served this purpose at the time they were given. This book presents Ramanujan’s essential mathematical contributions and gives an informal account of some of the major developments that emanated from his work in the 20th and 21st centuries. It contends that his work still has an impact on many different fields of mathematical research. This book examines some of these themes in the landscape of 21st-century mathematics. These essays, based on the lectures given by the authors focus on a subset of Ramanujan’s significant papers and show how these papers shaped the course of modern mathematics.
Description : A thorough guide to elliptic functions and modular forms that demonstrates the relevance and usefulness of historical sources.
Description : "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."
Description : 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.
Description : Wilhelm Magnus was an extraordinarily creative mathematician who made fundamental contributions to diverse areas, including group theory, geometry, and special functions. This book contains the proceedings of a conference held in May 1992 at Polytechnic University to honor the memory of Magnus. The focus of the book is on active areas of current research where Magnus' influence can be seen. The papers range from expository articles to major new research, bringing together seemingly diverse topics and providing entry points to a variety of areas of mathematics.
Description : 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.
Description : The Main Issues That Figure In The Very Title Of This Volume Are Indicative Of Its Scope And Contents. First, Philosophical Studies In Consciousness Have Their Persuppositions As Well As Implications. Secondly, In Order To Understant Clearly The Said Pre-Suppositions And Implications, The Intended Reader Group Needs To Tbe Introduced At Least To Some Core Concepts Of Philosophy And Science In Their Modern Sense. Thirdly, Since This Work Is Cross-Disciplinary In Its Orientation, The Conceptual Linkages Between Science And Philosophy Have Been Explored By Distinguished Philosophers And Scientists In Several Contributions To This Publication. Finally, A Conscious Attempt Has Been Made In Many Papers Of This Work That Every Branch Of Valid Knowledge, Philosophy Or Science, However Theoretically Abstract It May Be, Has Its Practical Moorings And The Same Are Temporarily Traceable. From The Available History Of Philosophy And Science It Is Found That These Disciplines Were Integrated In The Ancient Times. Differentiation Has Been Due To Endlessly Increasing Specialization Within Each Discipline. Even Today Many Philosophers And Historians Of Science Are Studying Carefully The Relation Between Different Strata Of Disciplines. The Emphasis On The Above Issues Is Intended, Among Other Things, To Avoid The Extremes Of Reductionosm, Mistakes Of Value-Fact Dualism, And To Clarify The Connection Between Theory And Practice, Experience And Experiment, Discovery And Legitimization Of Truth-Claims. In An Anthology Like This, Difference In Pre-Suppositions And Conclusions Of The Contributors, Cannot Be Ruled Out. Respect For The Freedom Of Thought, A Hallmark Of The Project, Has Been Tempered By Commitment To Reasoning. This Book, Primary Meant For Fairly Educated Readers, Is Likely To Be Of Interest To The Researchers In The Areas Of Social And Natural Science, And The Reading Public.
Description : This Book Breaks New Ground By Explaining For The First Time Over Three Hundred Mystical Terms In Buddhist Literature And Their Literally Miraculous Sibyllime Import Within That Literature; Its Extensive Examples Trace Such Miracles And Mystical Elements From The Time Of Buddha`S Birth In The Sixth Century B.C. To The Tenth Century A.D. When Buddhism Has Shed Its Light Beyond The Borders Of Its Homeland.