Rational Points on Elliptic Curves

Nonfiction, Science & Nature, Mathematics, Number Theory, Geometry
Cover of the book Rational Points on Elliptic Curves by Joseph H. Silverman, John T. Tate, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Joseph H. Silverman, John T. Tate ISBN: 9783319185880
Publisher: Springer International Publishing Publication: June 2, 2015
Imprint: Springer Language: English
Author: Joseph H. Silverman, John T. Tate
ISBN: 9783319185880
Publisher: Springer International Publishing
Publication: June 2, 2015
Imprint: Springer
Language: English

The 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

The 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.

More books from Springer International Publishing

Cover of the book Teacher Education in Lifelong Learning by Joseph H. Silverman, John T. Tate
Cover of the book The Uncertainty Analysis of Model Results by Joseph H. Silverman, John T. Tate
Cover of the book Posterior Cruciate Ligament Injuries by Joseph H. Silverman, John T. Tate
Cover of the book Risks and Resilience of Collaborative Networks by Joseph H. Silverman, John T. Tate
Cover of the book The Church of England in the First Decade of the 21st Century by Joseph H. Silverman, John T. Tate
Cover of the book Gypsies in Central Asia and the Caucasus by Joseph H. Silverman, John T. Tate
Cover of the book Fibre Bragg Grating and No-Core Fibre Sensors by Joseph H. Silverman, John T. Tate
Cover of the book Photons by Joseph H. Silverman, John T. Tate
Cover of the book Artificial Life and Computational Intelligence by Joseph H. Silverman, John T. Tate
Cover of the book Wilhelm Röpke (1899–1966) by Joseph H. Silverman, John T. Tate
Cover of the book Violence in Nigeria by Joseph H. Silverman, John T. Tate
Cover of the book The Digital Synaptic Neural Substrate by Joseph H. Silverman, John T. Tate
Cover of the book Overconfidence in SMEs by Joseph H. Silverman, John T. Tate
Cover of the book Brain Edema XVI by Joseph H. Silverman, John T. Tate
Cover of the book Automorphisms in Birational and Affine Geometry by Joseph H. Silverman, John T. Tate
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy