13 Lectures on Fermat s Last Theorem

13 Lectures on Fermat s Last Theorem


  • Author : Paulo Ribenboim
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Mathematics
  • Pages : 302
  • ISBN 10 : 9781468493429


13 Lectures on Fermat s Last Theorem Book Description :

Fermat's problem, also ealled Fermat's last theorem, has attraeted the attention of mathematieians far more than three eenturies. Many clever methods have been devised to attaek the problem, and many beautiful theories have been ereated with the aim of proving the theorem. Yet, despite all the attempts, the question remains unanswered. The topie is presented in the form of leetures, where I survey the main lines of work on the problem. In the first two leetures, there is a very brief deseription of the early history, as well as a seleetion of a few of the more representative reeent results. In the leetures whieh follow, I examine in sue eession the main theories eonneeted with the problem. The last two lee tu res are about analogues to Fermat's theorem. Some of these leetures were aetually given, in a shorter version, at the Institut Henri Poineare, in Paris, as well as at Queen's University, in 1977. I endeavoured to produee a text, readable by mathematieians in general, and not only by speeialists in number theory. However, due to a limitation in size, I am aware that eertain points will appear sketehy. Another book on Fermat's theorem, now in preparation, will eontain a eonsiderable amount of the teehnieal developments omitted here. It will serve those who wish to learn these matters in depth and, I hope, it will clarify and eomplement the present volume.

Modular Forms and Fermat   s Last Theorem

Modular Forms and Fermat s Last Theorem


  • Author : Gary Cornell
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-12-01
  • Genre: Mathematics
  • Pages : 582
  • ISBN 10 : 9781461219743


Modular Forms and Fermat s Last Theorem Book 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.

Fermat   s Last Theorem for Amateurs
Score: 2.5
From 3 Ratings

Fermat s Last Theorem for Amateurs


  • Author : Paulo Ribenboim
  • Publisher : Springer Science & Business Media
  • Release Date : 2000-03-10
  • Genre: Mathematics
  • Pages : 408
  • ISBN 10 : 0387985085


Fermat s Last Theorem for Amateurs Book 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.

Fermat s Last Theorem

Fermat s Last Theorem


  • Author : Harold M. Edwards
  • Publisher : Springer Science & Business Media
  • Release Date : 2000-01-14
  • Genre: Mathematics
  • Pages : 407
  • ISBN 10 : 0387950028


Fermat s Last Theorem Book Description :

This introduction to algebraic number theory via the famous problem of "Fermats Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummers theory of "ideal" factorization. The more elementary topics, such as Eulers proof of the impossibilty of x+y=z, are treated in an uncomplicated way, and new concepts and techniques are introduced only after having been motivated by specific problems. The book also covers in detail the application of Kummers theory to quadratic integers and relates this to Gauss'theory of binary quadratic forms, an interesting and important connection that is not explored in any other book.

CRC Concise Encyclopedia of Mathematics
Score: 4
From 2 Ratings

CRC Concise Encyclopedia of Mathematics


  • Author : Eric W. Weisstein
  • Publisher : CRC Press
  • Release Date : 2002-12-12
  • Genre: Mathematics
  • Pages : 3252
  • ISBN 10 : 9781420035223


CRC Concise Encyclopedia of Mathematics Book Description :

Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d

Elliptic Curves  Modular Forms   Fermat s Last Theorem

Elliptic Curves Modular Forms Fermat s Last Theorem


  • Author : John Coates
  • Publisher : International Pressof Boston Incorporated
  • Release Date : 1997
  • Genre: Mathematics
  • Pages : 340
  • ISBN 10 : UOM:39015043823981


Elliptic Curves Modular Forms Fermat s Last Theorem Book Description :

These proceedings are based on a conference at the Chinese University of Hong Kong, held in response to Andrew Wile's conjecture that every elliptic curve over Q is modular. The survey article describing Wile's work is included as the first article in the present edition.

Algebraic Number Theory

Algebraic Number Theory


  • Author :
  • Publisher : CRC Press
  • Release Date : 2011-01-05
  • Genre: Computers
  • Pages : 442
  • ISBN 10 : 9781439845998


Algebraic Number Theory Book Description :

Bringing the material up to date to reflect modern applications, Algebraic Number Theory, Second Edition has been completely rewritten and reorganized to incorporate a new style, methodology, and presentation. This edition focuses on integral domains, ideals, and unique factorization in the first chapter; field extensions in the second chapter; and

The Princeton Companion to Mathematics
Score: 4
From 17 Ratings

The Princeton Companion to Mathematics


  • Author : Timothy Gowers
  • Publisher : Princeton University Press
  • Release Date : 2010-07-18
  • Genre: Mathematics
  • Pages : 1056
  • ISBN 10 : 1400830397


The Princeton Companion to Mathematics Book Description :

This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, Béla Bollobás, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevi