Author by: Gary Cornell Language: en Publisher by: Springer Science & Business Media Format Available: PDF, ePub, Mobi Total Read: 76 Total Download: 848 File Size: 40,8 Mb Description: This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.
Wiles's proof of Fermat's Last Theorem is a proof, by British mathematician Andrew Wiles, of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were almost universally considered. Introduction: The proof of Fermat's Last Theorem by Andrew Wiles marks the end of a mathematical era. Fermat's last theorem (FLT) was finally settled in the affirmative by Andrew Wiles [1] in the year 1995. The present paper is about stating and proving a possible generalization of FLT. This paper proposes generalized.
Author by: Paulo Ribenboim Language: en Publisher by: Springer Science & Business Media Format Available: PDF, ePub, Mobi Total Read: 30 Total Download: 323 File Size: 46,7 Mb Description: In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.
Lan Driver C Net 100 Chantilly Va on this page. Author by: Vijaya Kumar Murty Language: en Publisher by: American Mathematical Soc. Format Available: PDF, ePub, Mobi Total Read: 51 Total Download: 711 File Size: 45,8 Mb Description: The most significant recent development in number theory is the work of Andrew Wiles on modular elliptic curves. Besides implying Fermat's Last Theorem, his work establishes a new reciprocity law.
Reciprocity laws lie at the heart of number theory. Wiles' work draws on many of the tools of modern number theory and the purpose of this volume is to introduce readers to some of this background material. Based on a seminar held during 1993-1994 at the Fields Institute for Research in Mathematical Sciences, this book contains articles on elliptic curves, modular forms and modular curves, Serre's conjectures, Ribet's theorem, deformations of Galois representations, Euler systems, and annihilators of Selmer groups. All of the authors are well known in their field and have made significant contributions to the general area of elliptic curves, Galois representations, and modular forms. Features: Brings together a unique collection of number theoretic tools.
Makes accessible the tools needed to understand one of the biggest breakthroughs in mathematics. Provides numerous references for further study. Author by: A. Van Der Poorten Language: en Publisher by: Wiley-Interscience Format Available: PDF, ePub, Mobi Total Read: 72 Total Download: 947 File Size: 50,6 Mb Description: Around 1637, the French jurist Pierre de Fermat scribbled in the margin of his copy of the book Arithmetica what came to be known as Fermat's Last Theorem, the most famous question in mathematical history. Stating that it is impossible to split a cube into two cubes, or a fourth power into two fourth powers, or any higher power into two like powers, but not leaving behind the marvelous proof he claimed to have had, Fermat prompted three and a half centuries of mathematical inquiry which culminated only recently with the proof of the theorem by Andrew Wiles. This book offers the first serious treatment of Fermat's Last Theorem since Wiles's proof.
It is based on a series of lectures given by the author to celebrate Wiles's achievement, with each chapter explaining a separate area of number theory as it pertains to Fermat's Last Theorem. Together, they provide a concise history of the theorem as well as a brief discussion of Wiles's proof and its implications. Requiring little more than one year of university mathematics and some interest in formulas, this overview provides many useful tips and cites numerous references for those who desire more mathematical detail. The book's most distinctive feature is its easy-to-read, humorous style, complete with examples, anecdotes, and some of the lesser-known mathematics underlying the newly discovered proof. In the author's own words, the book deals with 'serious mathematics without being too serious about it.' Alf van der Poorten demystifies mathematical research, offers an intuitive approach to the subject-loosely suggesting various definitions and unexplained facts-and invites the reader to fill in the missing links in some of the mathematical claims.
Entertaining, controversial, even outrageous, this book not only tells us why, in all likelihood, Fermat did not have the proof for his last theorem, it also takes us through historical attempts to crack the theorem, the prizes that were offered along the way, and the consequent motivation for the development of other areas of mathematics. Notes on Fermat's Last Theorem is invaluable for students of mathematics, and of real interest to those in the physical sciences, engineering, and computer sciences-indeed for anyone who craves a glimpse at this fascinating piece of mathematical history. An exciting introduction to modern number theory as reflected by the history of Fermat's Last Theorem This book displays the unique talents of author Alf van der Poorten in mathematical exposition for mathematicians. Here, mathematics' most famous question and the ideas underlying its recent solution are presented in a way that appeals to the imagination and leads the reader through related areas of number theory.
The first book to focus on Fermat's Last Theorem since Andrew Wiles presented his celebrated proof, Notes on Fermat's Last Theorem surveys 350 years of mathematical history in an amusing and intriguing collection of tidbits, anecdotes, footnotes, exercises, references, illustrations, and more. Author by: Richard Guy Language: en Publisher by: Springer Science & Business Media Format Available: PDF, ePub, Mobi Total Read: 89 Total Download: 855 File Size: 48,6 Mb Description: Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity.
This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections. Author by: Lloyd James Peter Kilford Language: en Publisher by: Imperial College Press Format Available: PDF, ePub, Mobi Total Read: 81 Total Download: 388 File Size: 54,7 Mb Description: This book presents a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators.
It also includes applications of modular forms to such diverse subjects as the theory of quadratic forms, the proof of Fermat's last theorem and the approximation of pi. It provides a balanced overview of both the theoretical and computational sides of the subject, allowing a variety of courses to be taught from it.
Author: Paulo Ribenboim ISBN: 928 Genre: Mathematics File Size: 87. 50 MB Format: PDF, Mobi Download: 577 Read: 238 In 1995, Andrew Wiles completed a proof of Fermat's Last Theorem. Although this was certainly a great mathematical feat, one shouldn't dismiss earlier attempts made by mathematicians and clever amateurs to solve the problem. In this book, aimed at amateurs curious about the history of the subject, the author restricts his attention exclusively to elementary methods that have produced rich results.
Author: Harold M. Edwards ISBN: Genre: Mathematics File Size: 44. 77 MB Format: PDF, Docs Download: 427 Read: 502 This introduction to algebraic number theory via 'Fermat's Last Theorem' follows its historical development, beginning with the work of Fermat and ending with Kummer theory of 'ideal' factorization.
In treats elementary topics, new concepts and techniques; and it details the application of Kummer theory to quadratic integers, relating it to Gauss theory of binary quadratic forms, an interesting connection not explored in any other book. Tcw To Dxf Converter. Author: Gary Cornell ISBN: 743 Genre: Mathematics File Size: 22. 28 MB Format: PDF Download: 904 Read: 363 This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes.
Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource. Author: Alfred J. Van der Poorten ISBN: Genre: Mathematics File Size: 58. 84 MB Format: PDF Download: 201 Read: 528 Requires one year of university mathematics and some interest in formulas for basic understanding of the concepts presented Written in an easy-to-read, humorous style Includes examples, anecdotes, and explanations of some of the lesser-known mathematics underlying Wiles's proof Demystifies mathematical research and offers an intuitive approach to the subject Cites numerous references New findings are updated from the previous edition.