Fermat S Last Theorem For Amateurs

Author: Paulo Ribenboim
Publisher: Springer Science & Business Media
ISBN: 0387216928
Size: 22.36 MB
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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.

Notes On Fermat S Last Theorem

Author: Alfred J. van der Poorten
Publisher: Wiley
ISBN: 9780471079408
Size: 29.30 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

Modular Forms And Fermat S Last Theorem

Author: Gary Cornell
Publisher: Springer Science & Business Media
ISBN: 1461219744
Size: 27.72 MB
Format: PDF
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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
Publisher: HarperCollins UK
ISBN: 0007381999
Size: 51.88 MB
Format: PDF, ePub, Mobi
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‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’

The Last Theorem

Author: Arthur C. Clarke
Publisher: Del Rey
ISBN: 0345509684
Size: 31.18 MB
Format: PDF, Mobi
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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.

Algebraic Number Theory And Fermat S Last Theorem

Author: Ian Stewart
Publisher: CRC Press
ISBN: 143986408X
Size: 80.37 MB
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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 is also eminently suited as a text for self-study.

Catalan S Conjecture

Author: Paulo Ribenboim
Publisher: Boston ; Toronto : Academic Press
ISBN:
Size: 53.51 MB
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In 1844, Catalan conjectured that 8 and 9 were the only consecutive integral powers. The problem of consecutive powers is more easily grasped than Fermats last theorem, so recently vanquished. In this book, Paulo Ribenboim brings together for the first time the diverse approaches to proving Catalans conjecture. These range from the elementary methods that apply in special cases (Part A) to powerful and general results in diophantine approximation (Part C) which yieldthe strongest results to date. In 1976, Tijdeman found a computable bound above which there are no consecutive powers. Langerin reduced this to an exponential: exp (exp (exp (exp (730)))). The enormous gap between such bonds-and the only known consecutive powers, 8 and 9-has been narrowed, but its immensity suggests the difficulty of such problems, as well as the interesting and fruitful methods developed for attacking them. Ribenboims book will appeal to anyone interested in how number theorists attack difficult problems. Its concrete focus on an easy to state problem is a relief from such generalities as the related A, B, C conjecture, and will prove to be a good point ofdeparture for seminars in number theory. The text includes many beautiful results of classical number theory not found in any other book. The treatment is fully accessible and self-contained, making this book as attractive as the authors 13 Lectures on Fermats Last Theorem, and his book, Book of Prime Records.

The Simpsons And Their Mathematical Secrets

Author: Simon Singh
Publisher: Bloomsbury Publishing USA
ISBN: 1620402777
Size: 41.22 MB
Format: PDF
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Based on interviews with the writers of The Simpsons and accompanied by images from the show, facsimiles of scripts, paintings and drawings and other imagery, this fascinating book reveals the meaningful mathematical concepts behind the most successful show in TV history.