About this product

Product Identifiers

PublisherSpringer International Publishing A&G

ISBN-10331918587X

ISBN-139783319185873

eBay Product ID (ePID)23038664880

Product Key Features

Number of PagesXxii, 332 Pages

LanguageEnglish

Publication NameRATIONAL Points on Elliptic Curves

SubjectGeometry / General, Number Theory, Databases / General, Geometry / Algebraic

Publication Year2015

TypeTextbook

Subject AreaMathematics, Computers

AuthorJohn T. Tate, Joseph H. Silverman

SeriesUndergraduate Texts in Mathematics Ser.

FormatHardcover

Dimensions

Item Weight231.6 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Edition Number2

Intended AudienceScholarly & Professional

Reviews"The two main changes for this edition are a new section on elliptic curve cryptography and an explanation of how elliptic curves played a role in the proof of Fermat's Last Theorem. ... the best place to start learning about elliptic curves." (Fernando Q. Gouvêa, MAA Reviews, maa.org, April, 2016) "The book is an excellent introduction to elliptic curves over the rational numbers and ideal textbook for an undergraduate course. ... This book is highly recommended to students and researches interested in elliptic curves and their applications. It provides a natural step to a more advanced treatment of the subject." (Andrej Dujella, zbMATH 1346.11001, 2016), "The two main changes for this edition are a new section on elliptic curve cryptography and an explanation of how elliptic curves played a role in the proof of Fermat's Last Theorem. ... the best place to start learning about elliptic curves." (Fernando Q. Gouva, MAA Reviews, maa.org, April, 2016) "The book is an excellent introduction to elliptic curves over the rational numbers and ideal textbook for an undergraduate course. ... This book is highly recommended to students and researches interested in elliptic curves and their applications. It provides a natural step to a more advanced treatment of the subject." (Andrej Dujella, zbMATH 1346.11001, 2016)

Dewey Edition22

Number of Volumes1 vol.

IllustratedYes

Original LanguageEnglish

Dewey Decimal516.352

Table Of ContentIntroduction.- Geometry and Arithmetic.- Points of Finite Order.- The Group of Rational Points.- Cubic Curves over Finite Fields.- Integer Points on Cubic Curves.- Complex Multiplication.

SynopsisThe theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. 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.

LC Classification NumberQA564-609