invitation to the mathematics of fermat wiles

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Invitation To The Mathematics Of Fermat Wiles

Author : Yves Hellegouarch
ISBN : 0080478778
Genre : Mathematics
File Size : 48. 92 MB
Format : PDF
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Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context. This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat's last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically informed reader intrigued by the unraveling of this fascinating puzzle. Rigorously presents the concepts required to understand Wiles' proof, assuming only modest undergraduate level math Sets the math in its historical context Contains several themes that could be further developed by student research and numerous exercises and problems Written by Yves Hellegouarch, who himself made an important contribution to the proof of Fermat's last theorem

Modular Forms And Fermat S Last Theorem

Author : Gary Cornell
ISBN : 9781461219743
Genre : Mathematics
File Size : 53. 78 MB
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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.

Fermat S Last Theorem

Author : Simon Singh
ISBN : 9780007381999
Genre : Science
File Size : 40. 44 MB
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‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’

Groups Modular Mathematics Series

Author : Camilla Jordan
ISBN : 9780080571652
Genre : Mathematics
File Size : 51. 8 MB
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This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.

The Mathematical Career Of Pierre De Fermat 1601 1665

Author : Michael Sean Mahoney
ISBN : 0691036667
Genre : Biography & Autobiography
File Size : 64. 68 MB
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Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration". Along with formulating this proposition - x(superscript n) + y(superscript n) = z(superscript n) has no rational solution for n > 2 - Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

Notes On Fermat S Last Theorem

Author : Alfred J. van der Poorten
ISBN : 0471079405
Genre : Mathematics
File Size : 59. 58 MB
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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

Fearless Symmetry

Author : Avner Ash
ISBN : 0691124922
Genre : Mathematics
File Size : 86. 56 MB
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Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two hundred years ago by French mathematician Évariste Galois. They have been used extensively in the oldest and largest branch of mathematics--number theory--for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.

The Last Theorem

Author : Arthur C. Clarke
ISBN : 9780345509680
Genre : Fiction
File Size : 46. 65 MB
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Two of science fiction’s most renowned writers join forces for a storytelling sensation. The historic collaboration between Frederik Pohl and his fellow founding father of the genre, Arthur C. Clarke, is both a momentous literary event and a fittingly grand farewell from the late, great visionary author of 2001: A Space Odyssey. The Last Theorem is a story of one man’s mathematical obsession, and a celebration of the human spirit and the scientific method. It is also a gripping intellectual thriller in which humanity, facing extermination from all-but-omnipotent aliens, the Grand Galactics, must overcome differences of politics and religion and come together . . . or perish. In 1637, the French mathematician Pierre de Fermat scrawled a note in the margin of a book about an enigmatic theorem: “I have discovered a truly marvelous proof of this proposition which this margin is too narrow to contain.” He also neglected to record his proof elsewhere. Thus began a search for the Holy Grail of mathematics–a search that didn’t end until 1994, when Andrew Wiles published a 150-page proof. But the proof was burdensome, overlong, and utilized mathematical techniques undreamed of in Fermat’s time, and so it left many critics unsatisfied–including young Ranjit Subramanian, a Sri Lankan with a special gift for mathematics and a passion for the famous “Last Theorem.” When Ranjit writes a three-page proof of the theorem that relies exclusively on knowledge available to Fermat, his achievement is hailed as a work of genius, bringing him fame and fortune. But it also brings him to the attention of the National Security Agency and a shadowy United Nations outfit called Pax per Fidem, or Peace Through Transparency, whose secretive workings belie its name. Suddenly Ranjit–together with his wife, Myra de Soyza, an expert in artificial intelligence, and their burgeoning family–finds himself swept up in world-shaking events, his genius for abstract mathematical thought put to uses that are both concrete and potentially deadly. Meanwhile, unbeknownst to anyone on Earth, an alien fleet is approaching the planet at a significant percentage of the speed of light. Their mission: to exterminate the dangerous species of primates known as homo sapiens. From the Hardcover edition.

Uncle Petros And Goldbach S Conjecture

Author : Apostolos Doxiadis
ISBN : 9780571295692
Genre : Fiction
File Size : 20. 52 MB
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Uncle Petros is a family joke. An ageing recluse, he lives alone in a suburb of Athens, playing chess and tending to his garden. If you didn't know better, you'd surely think he was one of life's failures. But his young nephew suspects otherwise. For Uncle Petros, he discovers, was once a celebrated mathematician, brilliant and foolhardy enough to stake everything on solving a problem that had defied all attempts at proof for nearly three centuries - Goldbach's Conjecture. His quest brings him into contact with some of the century's greatest mathematicians, including the Indian prodigy Ramanujan and the young Alan Turing. But his struggle is lonely and single-minded, and by the end it has apparently destroyed his life. Until that is a final encounter with his nephew opens up to Petros, once more, the deep mysterious beauty of mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals.

An Invitation To Mathematics

Author : Dierk Schleicher
ISBN : 3642195334
Genre : Mathematics
File Size : 44. 18 MB
Format : PDF, ePub, Mobi
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This Invitation to Mathematics consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is about. We hope that it will also be of interest to teachers or more advanced mathematicians who would like to learn about exciting aspects of mathematics outside of their own work or specialization. Together with a team of young ``test readers'', editors and authors have taken great care, through a substantial ``active editing'' process, to make the contributions understandable by the intended readership.

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