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OverviewItisnowwellknownthatFermat’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). Full Product DetailsAuthor: Paulo RibenboimPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1st ed. 1999. Corr. 2nd printing 2000 Dimensions: Width: 15.60cm , Height: 2.30cm , Length: 23.40cm Weight: 1.710kg ISBN: 9780387985084ISBN 10: 0387985085 Pages: 407 Publication Date: 11 February 1999 Audience: General/trade , Adult education , College/higher education , General , Further / Higher Education Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsThe 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.ReviewsFrom the reviews: MATHEMATICAL REVIEWS The history of elementary approaches to Fermat is very rich indeed, and Ribenboim has arranged these approaches in a way that makes them accessible to interested readers without extensive mathematical backgrounds...both readable and fairly comprehensive. This book would likely be of great interest to an enthusiastic undergraduate with a basic knowledge of rings and fields. In addition to describing the history of one of the great problems in number theory, the book provides a gentle and well-motivated introduction to some important ideas in modern number theory...any reader who spends a few hours with this book is guaranteed to learn something new and interesting about Fermat's last theorem. From the reviews: MATHEMATICAL REVIEWS The history of elementary approaches to Fermat is very rich indeed, and Ribenboim has arranged these approaches in a way that makes them accessible to interested readers without extensive mathematical backgrounds...both readable and fairly comprehensive. This book would likely be of great interest to an enthusiastic undergraduate with a basic knowledge of rings and fields. In addition to describing the history of one of the great problems in number theory, the book provides a gentle and well-motivated introduction to some important ideas in modern number theory...any reader who spends a few hours with this book is guaranteed to learn something new and interesting about Fermat's last theorem. From the reviews: MATHEMATICAL REVIEWS The history of elementary approaches to Fermat is very rich indeed, and Ribenboim has arranged these approaches in a way that makes them accessible to interested readers without extensive mathematical backgrounds!both readable and fairly comprehensive. This book would likely be of great interest to an enthusiastic undergraduate with a basic knowledge of rings and fields. In addition to describing the history of one of the great problems in number theory, the book provides a gentle and well-motivated introduction to some important ideas in modern number theory!any reader who spends a few hours with this book is guaranteed to learn something new and interesting about Fermat's last theorem. From the reviews: <p>MATHEMATICAL REVIEWS <p> The history of elementary approaches to Fermat is very rich indeed, and Ribenboim has arranged these approaches in a way that makes them accessible to interested readers without extensive mathematical backgroundsa ]both readable and fairly comprehensive. This book would likely be of great interest to an enthusiastic undergraduate with a basic knowledge of rings and fields. In addition to describing the history of one of the great problems in number theory, the book provides a gentle and well-motivated introduction to some important ideas in modern number theorya ]any reader who spends a few hours with this book is guaranteed to learn something new and interesting about Fermata (TM)s last theorem. Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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