FermatÕs Last Theorem - Finding a new surprisingly simple demonstration?
FermatÕs Last Theorem - Finding a new surprisingly simple demonstration?

Author: Mercedes Orœs Lacort

Publisher: Lulu.com

Published: 2016

Total Pages: 80

ISBN-13: 1326589717

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A historical theorem finally proved by Andrew Wiles. He deserves all my deepest respect and admiration. I also extend this admiration and respect to all mathematicians of today and yesterday. I graduated in Mathematics from the Autonomous University of Barcelona since 1988. Currently I'm a teacher of different mathematics subjects at university level. During these years, I have published many books. These books are available around the world in university libraries and also in any bookstore. This book is a bit different from the previous ones, as it presents the discovery of what could be a surprisingly simple proof of Fermat's last Theorem. I developed this demonstration in 1998, but I never thought to disclose it until now. And I've decided to disclose it now because someone recently reminded me that it was kept in a drawer, and perhaps the world should know. Feel free to study it, analyze it and contact me with your opinions, if you want. For me, all your comments will be welcome.

Modular Forms and Fermat’s Last Theorem
Modular Forms and Fermat’s Last Theorem

Author: Gary Cornell

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 592

ISBN-13: 1461219744

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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.

13 Lectures on Fermat's Last Theorem
13 Lectures on Fermat's Last Theorem

Author: Paulo Ribenboim

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 306

ISBN-13: 1468493426

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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.

Local Fields
Local Fields

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 249

ISBN-13: 1475756739

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The goal of this book is to present local class field theory from the cohomo logical point of view, following the method inaugurated by Hochschild and developed by Artin-Tate. This theory is about extensions-primarily abelian-of "local" (i.e., complete for a discrete valuation) fields with finite residue field. For example, such fields are obtained by completing an algebraic number field; that is one of the aspects of "localisation". The chapters are grouped in "parts". There are three preliminary parts: the first two on the general theory of local fields, the third on group coho mology. Local class field theory, strictly speaking, does not appear until the fourth part. Here is a more precise outline of the contents of these four parts: The first contains basic definitions and results on discrete valuation rings, Dedekind domains (which are their "globalisation") and the completion process. The prerequisite for this part is a knowledge of elementary notions of algebra and topology, which may be found for instance in Bourbaki. The second part is concerned with ramification phenomena (different, discriminant, ramification groups, Artin representation). Just as in the first part, no assumptions are made here about the residue fields. It is in this setting that the "norm" map is studied; I have expressed the results in terms of "additive polynomials" and of "multiplicative polynomials", since using the language of algebraic geometry would have led me too far astray.

Fermat's Last Theorem
Fermat's Last Theorem

Author: Simon Singh

Publisher: Fourth Estate

Published: 2022-05-26

Total Pages: 0

ISBN-13: 9780008553821

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Introducing the Collins Modern Classics, a series featuring some of the most significant books of recent times, books that shed light on the human experience - classics which will endure for generations to come.

Fearless Symmetry
Fearless Symmetry

Author: Avner Ash

Publisher: Princeton University Press

Published: 2008-08-24

Total Pages: 308

ISBN-13: 0691138710

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Written in a friendly style for a general mathematically literate audience, 'Fearless Symmetry', starts with the basic properties of integers and permutations and reaches current research in number theory.

What's Happening in the Mathematical Sciences
What's Happening in the Mathematical Sciences

Author: Barry Cipra

Publisher: American Mathematical Soc.

Published:

Total Pages: 108

ISBN-13: 9780821890431

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Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.

The Last Theorem
The Last Theorem

Author: Arthur C. Clarke

Publisher: HarperCollins UK

Published: 2008-12-07

Total Pages: 23

ISBN-13: 0007308140

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The final work from the brightest star in science fiction’s galaxy. Arthur C Clarke, who predicted the advent of communication satellites and author of 2001: A Space Odyssey completes a lifetime career in science fiction with a masterwork.

Lie Algebras and Lie Groups
Lie Algebras and Lie Groups

Author: Jean-Pierre Serre

Publisher: Springer

Published: 2009-02-07

Total Pages: 180

ISBN-13: 3540706348

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The main general theorems on Lie Algebras are covered, roughly the content of Bourbaki's Chapter I.I have added some results on free Lie algebras, which are useful, both for Lie's theory itself (Campbell-Hausdorff formula) and for applications to pro-Jrgroups. of time prevented me from including the more precise theory of Lack semisimple Lie algebras (roots, weights, etc.); but, at least, I have given, as a last Chapter, the typical case ofal, . This part has been written with the help of F. Raggi and J. Tate. I want to thank them, and also Sue Golan, who did the typing for both parts. Jean-Pierre Serre Harvard, Fall 1964 Chapter I. Lie Algebras: Definition and Examples Let Ie be a commutativering with unit element, and let A be a k-module, then A is said to be a Ie-algebra if there is given a k-bilinear map A x A~ A (i.e., a k-homomorphism A0" A -+ A). As usual we may define left, right and two-sided ideals and therefore quo tients. Definition 1. A Lie algebra over Ie isan algebrawith the following properties: 1). The map A0i A -+ A admits a factorization A ®i A -+ A2A -+ A i.e., ifwe denote the imageof(x, y) under this map by [x, y) then the condition becomes for all x e k. [x, x)=0 2). (lx, II], z]+ny, z), x) + ([z, xl, til = 0 (Jacobi's identity) The condition 1) implies [x,1/]=-[1/, x).