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Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co.
Book Synopsis 13 Lectures on Fermat's Last Theorem by : Paulo Ribenboim
Download or read book 13 Lectures on Fermat's Last Theorem written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co.
Book Synopsis Thirteen 13 Lectures on Fermat's Last Theorem by : Paulo Ribenboim
Download or read book Thirteen 13 Lectures on Fermat's Last Theorem written by Paulo Ribenboim and published by . This book was released on 1979 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Fermat’s Last Theorem for Amateurs by : Paulo Ribenboim
Download or read book Fermat’s Last Theorem for Amateurs written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2008-01-21 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Three Lectures on Fermat's Last Theorem by : Louis Joel Mordell
Download or read book Three Lectures on Fermat's Last Theorem written by Louis Joel Mordell and published by . This book was released on 1921 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Modular Forms and Fermat’s Last Theorem by : Gary Cornell
Download or read book Modular Forms and Fermat’s Last Theorem written by Gary Cornell and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Excerpt from Three Lectures on Fermat's Last Theorem In March 1920, I gave at Birkbeck College, London, a course of three public lectures on Fermat's Last Theorem. The lectures were intended primarily for persons with a mathematical training, but not necessarily for those who bad made a special study of the Theory of Numbers. A general account was given of the various methods that have been devised for dealing with the question, more attention being paid to principles than to details. This booklet consists of the lectures in practically the form in which they were delivered. It also includes a few details which it was found convenient to omit from the lectures. I hope it may be of assistance in giving to the reader come idea, not only of the difficulties involved, but also of the progress made in dealing with this famous theorem. I have to acknowledge my indebtedness not only to the authors mentioned herein, but also to the works of Smith, Bachmann, Hilbert, Kronecker, Sommer, and Dickson, on the Theory of Numbers. Full references to the subject are given by Dickson in his very useful paper on "Fermat's Last Theorem" in the Annals of Mathematics, Vol. xviii. 1917 ;and in Vol. n.of his History of the Theory of Numbers,- which has just been published. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Book Synopsis Three Lectures on Fermat's Last Theorem by : L. J. Mordell
Download or read book Three Lectures on Fermat's Last Theorem written by L. J. Mordell and published by Forgotten Books. This book was released on 2015-06-25 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Three Lectures on Fermat's Last Theorem In March 1920, I gave at Birkbeck College, London, a course of three public lectures on Fermat's Last Theorem. The lectures were intended primarily for persons with a mathematical training, but not necessarily for those who bad made a special study of the Theory of Numbers. A general account was given of the various methods that have been devised for dealing with the question, more attention being paid to principles than to details. This booklet consists of the lectures in practically the form in which they were delivered. It also includes a few details which it was found convenient to omit from the lectures. I hope it may be of assistance in giving to the reader come idea, not only of the difficulties involved, but also of the progress made in dealing with this famous theorem. I have to acknowledge my indebtedness not only to the authors mentioned herein, but also to the works of Smith, Bachmann, Hilbert, Kronecker, Sommer, and Dickson, on the Theory of Numbers. Full references to the subject are given by Dickson in his very useful paper on "Fermat's Last Theorem" in the Annals of Mathematics, Vol. xviii. 1917 ;and in Vol. n.of his History of the Theory of Numbers,- which has just been published. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
In 1963 a schoolboy browsing in his local library stumbled across a great mathematical problem: Fermat's Last Theorem, a puzzle that every child can now understand, but which has baffled mathematicians for over 300 years. Aged just ten, Andrew Wiles dreamed he would crack it.
Book Synopsis Fermat's Last Theorem by : Simon Singh
Download or read book Fermat's Last Theorem written by Simon Singh and published by . This book was released on 1998-05 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1963 a schoolboy browsing in his local library stumbled across a great mathematical problem: Fermat's Last Theorem, a puzzle that every child can now understand, but which has baffled mathematicians for over 300 years. Aged just ten, Andrew Wiles dreamed he would crack it.
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.
Book Synopsis Fermat's Last Theorem by : Harold M. Edwards
Download or read book Fermat's Last Theorem written by Harold M. Edwards and published by Springer Science & Business Media. This book was released on 2000-01-14 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Three Lectures on Fermat's Last Theorem by : Louis Joel Mordell
Download or read book Three Lectures on Fermat's Last Theorem written by Louis Joel Mordell and published by . This book was released on 1962 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it
Book Synopsis Algebraic Number Theory and Fermat's Last Theorem by : Ian Stewart
Download or read book Algebraic Number Theory and Fermat's Last Theorem written by Ian Stewart and published by CRC Press. This book was released on 2001-12-12 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it