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Fermat’s Last Theorem for Amateurs - Hardcover

Ribenboim, Paulo

 
9780387985084: Fermat’s Last Theorem for Amateurs
Hardcover
ISBN 10: 0387985085 ISBN 13: 9780387985084
Verlag: Springer, 1999

Inhaltsangabe

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).

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Über die Autorin bzw. den Autor

Paulo Ribenboim ist emeritierter Professor der kanadischen Queen's University, Fellow der Royal Society of Canada und Träger des George Pólya-Preises der Mathematical Association of America. Er ist Autor von 13 Büchern und über 150 Forschungsartikeln.

Von der hinteren Coverseite

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).

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Verlag
Springer
Erscheinungsdatum
1999
Sprache
Englisch
ISBN 10 
0387985085
ISBN 13 
9780387985084
Einband
Gebundene Ausgabe
Anzahl der Seiten
420
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