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Author: Hei-Chi Chan Publisher: World Scientific ISBN: 9814343846 Category : Mathematics Languages : en Pages : 237
Book Description
The aim of this lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers–Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G H Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers–Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.
Author: Hei-Chi Chan Publisher: World Scientific ISBN: 9814343846 Category : Mathematics Languages : en Pages : 237
Book Description
The aim of this lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers–Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G H Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers–Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.
Author: Hei-chi Chan Publisher: World Scientific ISBN: 9814460583 Category : Mathematics Languages : en Pages : 237
Book Description
The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G. H. Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.
Author: Heng Huat Chan Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110540754 Category : Mathematics Languages : en Pages : 125
Book Description
This book presents several results on elliptic functions and Pi, using Jacobi's triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan's work on Pi. The included exercises make it ideal for both classroom use and self-study.
Author: Andrew V. Sills Publisher: CRC Press ISBN: 1351647962 Category : Mathematics Languages : en Pages : 263
Book Description
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: Avi Wigderson Publisher: Princeton University Press ISBN: 0691189137 Category : Computers Languages : en Pages : 434
Book Description
An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Author: Herbert S. Wilf Publisher: Elsevier ISBN: 1483276635 Category : Mathematics Languages : en Pages : 193
Book Description
Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.
Author: Jan Hendrik Bruinier Publisher: Springer Science & Business Media ISBN: 3540741194 Category : Mathematics Languages : en Pages : 273
Book Description
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.
Author: Hei-Chi Chan
Author: Hei-Chi Chan
Author: Hei-chi Chan
Author: Chan Hei-Chi
Author: Heng Huat Chan
Author: Andrew V. Sills
Author: George E. Andrews
Author: George E. Andrews
Author: Avi Wigderson
Author: Herbert S. Wilf
Author: Jan Hendrik Bruinier