Fermat¿s Last Theorem for Amateurs

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Beschreibung

ItisnowwellknownthatFermat¿slasttheoremhasbeenproved. For more than three and a half centuries, mathematicians ¿ from the greatnamestothecleveramateurs¿triedtoproveFermat¿sfamous statement. The approach was new and involved very sophisticated theories. Finallythelong-soughtproofwasachieved. Thearithmetic theory of elliptic curves, modular forms, Galois representations, and their deformations, developed by many mathematicians, were the tools required to complete the di?cult proof. Linked with this great mathematical feat are the names of TANI- YAMA, SHIMURA, FREY, SERRE, RIBET, WILES, TAYLOR. Their contributions, as well as hints of the proof, are discussed in the Epilogue. This book has not been written with the purpose of presentingtheproofofFermat¿stheorem. Onthecontrary, itiswr- ten for amateurs, teachers, and mathematicians curious about the unfolding of the subject. I employ exclusively elementary methods (except in the Epilogue). They have only led to partial solutions but their interest goes beyond Fermat¿s problem. One cannot stop admiring the results obtained with these limited techniques. Nevertheless, I warn that as far as I can see ¿ which in fact is not much ¿ the methods presented here will not lead to a proof of Fermat¿s last theorem for all exponents. vi Preface The presentation is self-contained and details are not spared, so the reading should be smooth. Most of the considerations involve ordinary rational numbers and only occasionally some algebraic (non-rational) numbers. For this reason I excluded Kummer¿s important contributions, which are treated in detail in my book, Classical Theory of Algebraic N- bers and described in my 13 Lectures on Fermat¿s Last Theorem (new printing, containing an Epilogue about recent results).

Zusammenfassung

Preliminary Booksellers Text: Do Not Use. In 1995, Andrew Wiles published two papers containing a proof of Fermat's Last Theorem. BRAVO FOR THIS GREAT MATHEMATICAL FEAT! Nevertheless, one shouldn't dismiss the earlier attempts to solve the problems. From giants in mathematics to clever amateurs, all did their best. In this book, aimed at amateurs, teachers, and mathematicians curious about the unfolding of the subject, the author restricts his attention exclusively to elementary methods. There are other books about Wiles' proof but the reader without an extended solid background may prefer to stay with this book.

Inhaltsverzeichnis

The Problem.- Special Cases.- 4 Interludes.- Algebraic Restrictions on Hypothetical Solutions.- Germain's Theorem.- Interludes 5 and 6.- Arithmetic Restrictions on Hypothetical Solutions and on the Exponent.- Interludes 7 and 8.- Reformulations, Consequences, and Criteria.- Interludes 9 and 10.- The Local and Modular Fermat Problem.- Epilogue.

Erscheinungsjahr:	1999
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xiii 407 S. 1 s/w Illustr.
ISBN-13:	9780387985084
ISBN-10:	0387985085
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Ribenboim, Paulo
Hersteller:	Springer New York Springer US, New York, N.Y.
Maße:	240 x 161 x 29 mm
Von/Mit:	Paulo Ribenboim
Erscheinungsdatum:	11.02.1999
Gewicht:	0,801 kg

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