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Number theory --- 511.5 --- Fermat's last theorem --- Last theorem, Fermat's --- Diophantine analysis --- Fermat's theorem --- Diophantine equations --- Fermat's last theorem. --- 511.5 Diophantine equations

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Assuming only modest knowledge of undergraduate level math, Invitation to the Mathematics of Fermat-Wiles presents diverse concepts required to comprehend Wiles' extraordinary proof. Furthermore, it places these concepts in their historical context.This book can be used in introduction to mathematics theories courses and in special topics courses on Fermat's last theorem. It contains themes suitable for development by students as an introduction to personal research as well as numerous exercises and problems. However, the book will also appeal to the inquiring and mathematically

Number theory --- Fermat's last theorem. --- Curves, Elliptic. --- Forms, Modular. --- Modular forms --- Forms (Mathematics) --- Elliptic curves --- Curves, Algebraic --- Last theorem, Fermat's --- Diophantine analysis --- Fermat's theorem

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This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem.

511.5 --- Curves, Elliptic --- -Fermat's last theorem --- -Forms, Modular --- -#WWIS:didaktiek --- Modular forms --- Forms (Mathematics) --- Last theorem, Fermat's --- Diophantine analysis --- Number theory --- Fermat's theorem --- Elliptic curves --- Curves, Algebraic --- 511.5 Diophantine equations --- Diophantine equations --- Congresses --- Forms, Modular --- Fermat's last theorem --- #WWIS:didaktiek --- Congresses. --- Number theory. --- Algebraic geometry. --- Number Theory. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Number study --- Numbers, Theory of --- Algebra

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Number theory --- Fermat's last theorem --- Théorie des nombres algébriques --- Fermat, Grand théorème de --- priem --- kwadraten --- dirichlet --- pell --- klasse --- geheel --- binair --- euler --- kummer --- deling --- 511.343 --- Last theorem, Fermat's --- Diophantine analysis --- Fermat's theorem --- Forms of higher degree. Fermat's last theorem --- Algebraic number theory. --- Fermat's last theorem. --- 511.343 Forms of higher degree. Fermat's last theorem --- Théorie des nombres algébriques --- Fermat, Grand théorème de --- Algebraic number theory --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- geschiedenis --- Gauss --- Nombres algébriques, Théorie des --- Nombres, Théorie des --- de Fermat, P.