Fermat’s Last Theorem for Amateurs by Paulo Ribenboim

Fermat’s Last Theorem for Amateurs by Paulo Ribenboim

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).

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 comprehensiveThis 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."

Well known for his contributions in number theory, Paulo Ribenboim has authored over 240 publications, including 13 books. He is now professor emeritus at Queen's University in Kingston, Ontaria. The Ribenboim Prize of the Canadian Number Theory Association is named after him.

SKU	NIN9781475772869
ISBN 13	9781475772869
ISBN 10	1475772866
Title	Fermat’s Last Theorem for Amateurs
Author	Paulo Ribenboim
Condition	New
Binding Type	Paperback
Publisher	Springer-Verlag New York Inc.
Year published	2013-03-14
Number of pages	407
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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