An Invitation To Q Series
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| Author | : Chan Hei-Chi |
| Publisher | : World Scientific |
| Total Pages | : 237 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9814343854 |
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 RogersOCoRamanujan continued fraction OCo a result that convinced G H Hardy that Ramanujan was a OC mathematician of the highest classOCO, and (2) what G. H. Hardy called Ramanujan''s OC Most Beautiful IdentityOCO. This book covers a range of related results, such as several proofs of the famous RogersOCoRamanujan 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 |
| Total Pages | : 237 |
| Release | : 2011 |
| Genre | : Mathematics |
| ISBN | : 9814343846 |
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 | : Andrew V. Sills |
| Publisher | : CRC Press |
| Total Pages | : 263 |
| Release | : 2017-10-16 |
| Genre | : Mathematics |
| ISBN | : 1351647962 |
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 | : Heng Huat Chan |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 152 |
| Release | : 2020-07-06 |
| Genre | : Mathematics |
| ISBN | : 3110540754 |
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 | : M. Ram Murty |
| Publisher | : Springer |
| Total Pages | : 293 |
| Release | : 2016-11-25 |
| Genre | : Mathematics |
| ISBN | : 9811026513 |
This book introduces the reader to the fascinating world of modular forms through a problem-solving approach. As such, besides researchers, the book can be used by the undergraduate and graduate students for self-instruction. The topics covered include q-series, the modular group, the upper half-plane, modular forms of level one and higher level, the Ramanujan τ-function, the Petersson inner product, Hecke operators, Dirichlet series attached to modular forms and further special topics. It can be viewed as a gentle introduction for a deeper study of the subject. Thus, it is ideal for non-experts seeking an entry into the field.
| Author | : Mateusz Michałek |
| Publisher | : American Mathematical Society |
| Total Pages | : 226 |
| Release | : 2021-03-05 |
| Genre | : Mathematics |
| ISBN | : 1470453673 |
Nonlinear algebra provides modern mathematical tools to address challenges arising in the sciences and engineering. It is useful everywhere, where polynomials appear: in particular, data and computational sciences, statistics, physics, optimization. The book offers an invitation to this broad and fast-developing area. It is not an extensive encyclopedia of known results, but rather a first introduction to the subject, allowing the reader to enter into more advanced topics. It was designed as the next step after linear algebra and well before abstract algebraic geometry. The book presents both classical topics—like the Nullstellensatz and primary decomposition—and more modern ones—like tropical geometry and semidefinite programming. The focus lies on interactions and applications. Each of the thirteen chapters introduces fundamental concepts. The book may be used for a one-semester course, and the over 200 exercises will help the readers to deepen their understanding of the subject.
| Author | : Murali Rao |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 252 |
| Release | : 1991-05-17 |
| Genre | : Mathematics |
| ISBN | : 9813103612 |
This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises. Request Inspection Copy
| Author | : India. High Court (Patna, India) |
| Publisher | : |
| Total Pages | : 856 |
| Release | : 1920 |
| Genre | : Law |
| ISBN | : |
Containing cases determined by the High court at Patna, and by the Judicial committee of the Privy Council on appeal from that court.
| Author | : |
| Publisher | : |
| Total Pages | : 1058 |
| Release | : 1999 |
| Genre | : Campaign funds |
| ISBN | : |
| Author | : Stephen Melczer |
| Publisher | : Springer Nature |
| Total Pages | : 418 |
| Release | : 2020-12-22 |
| Genre | : Mathematics |
| ISBN | : 3030670805 |
This book uses new mathematical tools to examine broad computability and complexity questions in enumerative combinatorics, with applications to other areas of mathematics, theoretical computer science, and physics. A focus on effective algorithms leads to the development of computer algebra software of use to researchers in these domains. After a survey of current results and open problems on decidability in enumerative combinatorics, the text shows how the cutting edge of this research is the new domain of Analytic Combinatorics in Several Variables (ACSV). The remaining chapters of the text alternate between a pedagogical development of the theory, applications (including the resolution by this author of conjectures in lattice path enumeration which resisted several other approaches), and the development of algorithms. The final chapters in the text show, through examples and general theory, how results from stratified Morse theory can help refine some of these computability questions. Complementing the written presentation are over 50 worksheets for the SageMath and Maple computer algebra systems working through examples in the text.
