Updated to reflect current research, Algebraic Number Theory and Fermat's Last Theorem, Fourth Edition introduces fundamental ideas of algebraic numbers and explores one of the most intriguing stories in the history of mathematics--the quest for a proof of Fermat's Last Theorem. The authors use this celebrated theorem to motivate a general study of the theory of algebraic numbers from a relatively concrete point of view. Students will see how Wiles's proof of Fermat's Last Theorem opened many new areas for future work.
New to the Fourth Edition
Provides up-to-date information on unique prime factorization for real quadratic number fields, especially Harper's proof that Z(√14) is Euclidean
Presents an important new result: Mihăilescu's proof of the Catalan conjecture of 1844
Revises and expands one chapter into two, covering classical ideas about modular functions and highlighting the new ideas of Frey, Wiles, and others that led to the long-sought proof of Fermat's Last Theorem
Improves and updates the index, figures, bibliography, further reading list, and historical remarks
Written by preeminent mathematicians Ian Stewart and David Tall, this text continues to teach students how to extend properties of natural numbers to more general number structures, including algebraic number fields and their rings of algebraic integers. It also explains how basic notions from the theory of algebraic numbers can be used to solve problems in number theory.
Автор: Koblitz Название: Number Theory Related to Fermat`s Last Theorem ISBN: 0817631046 ISBN-13(EAN): 9780817631048 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text on relativistic ray optics covers such topics as: light propagation in linear dielectric and permeable media; ray-optical structures on arbitrary manifolds; ray-optical structures on Lorentzian manifolds; and variational principles for rays.
Автор: W.K. B?hler; W. Scharlau; G. Cornell; H. Opolka Название: From Fermat to Minkowski ISBN: 1441928219 ISBN-13(EAN): 9781441928214 Издательство: Springer Рейтинг: Цена: 7260.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Tracing the story from its earliest sources, this book celebrates the lives and work of pioneers of modern mathematics: Fermat, Euler, Lagrange, Legendre, Gauss, Fourier, Dirichlet and more. Includes an English translation of Gauss`s 1838 letter to Dirichlet.
Автор: Yves Hellegouarch Название: Invitation to the Mathematics of Fermat-Wiles, ISBN: 0123392519 ISBN-13(EAN): 9780123392510 Издательство: Elsevier Science Рейтинг: Цена: 10162.00 р. Наличие на складе: Поставка под заказ.
Описание: Presents diverse concepts required to comprehend Fermat-Wiles` extraordinary proof. Placing these concepts in their historical context, this book contains several themes that could be developed by student research and numerous exercises and problems.
Автор: Paulo Ribenboim Название: Fermat`s Last Theorem for Amateurs ISBN: 1475772866 ISBN-13(EAN): 9781475772869 Издательство: Springer Рейтинг: Цена: 7965.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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).
Автор: Gary Cornell; Joseph H. Silverman; Glenn Stevens Название: Modular Forms and Fermat`s Last Theorem ISBN: 0387989986 ISBN-13(EAN): 9780387989983 Издательство: Springer Рейтинг: Цена: 10480.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Focuses on Andrew Wiles` proof of the Taniyama-Shimura-Weil conjecture for semistable elliptic curves and the works of Frey, Serre, Ribet showing that Wiles` Theorem would complete the proof of Fermat`s Last Theorem. This book reflects on the history of the problem. It describes the connections of Wiles` work with other parts of mathematics.
Автор: Harold M. Edwards Название: Fermat`s Last Theorem ISBN: 0387902309 ISBN-13(EAN): 9780387902302 Издательство: Springer Рейтинг: Цена: 11173.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Work on this book was supported in part by the James M. Vaughn, Jr., Vaughn Foundation Fund.
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