{"title":"Joseph Silverman","description":null,"products":[{"product_id":"friendly-introduction-to-number-theory-a-book-joseph-silverman-9781292027098","title":"Friendly Introduction to Number Theory, A","description":"For one-semester undergraduate courses in Elementary Number Theory. A Friendly Introduction to Number Theory, Fourth Edition is designed to introduce students to the overall themes and methodology of mathematics through the detailed study of one particular facet-number theory. Starting with nothing more than basic high school algebra, students are gradually led to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing is appropriate for the undergraduate audience and includes many numerical examples, which are analyzed for patterns and used to make conjectures. 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The 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. Contributors to this volume include: B. Conrad, H. Darmon, E. de Shalit, B. de Smit, F. Diamond, S.J. Edixhoven, G. Frey, S. Gelbart, K. Kramer, H.W. Lenstra, Jr., B. Mazur, K. Ribet, D.E. Rohrlich, M. Rosen, K. Rubin, R. Schoof, A. Silverberg, J.H. Silverman, P. Stevenhagen, G. Stevens, J. Tate, J. Tilouine, and L. Washington. 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. 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This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry.  Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50177632370961,"sku":"GOR013881835","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ NEW \/ INGRAM","offer_id":51064063066385,"sku":"NIN9783319307572","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52455817543953,"sku":"NLS9783319307572","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/3319307576.jpg?v=1750933845"},{"product_id":"introduction-to-mathematical-cryptography-book-jeffrey-hoffstein-9780387779935","title":"An Introduction to Mathematical Cryptography","description":"An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises.  It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50189300465937,"sku":"CIN0387779930G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51356447932689,"sku":"GOR008752431","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":51694556938513,"sku":"CIN0387779930VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387779930.jpg?v=1750813465"},{"product_id":"friendly-introduction-to-number-theory-book-joseph-h-silverman-9780132637992","title":"A Friendly Introduction to Number Theory","description":"An introductory text designed to entice non-math majors to think mathematically. The reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples which are analyzed for patterns and used to make conjectures. The emphasis is on the methods used for proving theorems rather than on specific results.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50191665955089,"sku":"CIN0132637995G","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0132637995.jpg?v=1750843772"},{"product_id":"arithmetic-of-elliptic-curves-book-j-h-silverman-9780387962030","title":"The Arithmetic of Elliptic Curves","description":"The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields, and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y^2 = X^3 + DX. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50297378275601,"sku":"CIN0387962034G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51430352847121,"sku":"GOR010065311","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0387962034.jpg?v=1751196532"},{"product_id":"friendly-introduction-to-number-theory-a-classic-version-book-joseph-silverman-9780134689463","title":"Friendly Introduction to Number Theory, A (Classic Version)","description":"A Friendly Introduction to Number Theory, 4th Edition introduces students to the overall themes and methodology of mathematics through the detailed study of one particular facet–number theory. 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