9783319185873 - rational points on elliptic curves (undergraduate texts in mathematics) von silverman, joseph h.; tate, john t. (7 Ergebnisse)
Sprache: Englisch
Verlag: Springer (edition 2nd 2015 ed.), 2015
Serie: Buch 144 von 170 - Undergraduate Texts in Mathematics
- Hardcover
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Hardcover. Zustand: Very Good. 2nd 2015 ed. It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting.
Sprache: Englisch
Verlag: Springer International Publishing AG, 2015
Serie: Buch 144 von 170 - Undergraduate Texts in Mathematics
- Hardcover
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Zustand: Very Good. Former library copy. Pages intact with possible writing/highlighting. Binding strong with minor wear. Dust jackets/supplements may not be included. Includes library markings. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good.
Sprache: Englisch
Verlag: Springer International Publishing AG, 2015
Serie: Buch 144 von 170 - Undergraduate Texts in Mathematics
- Hardcover
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Sprache: Englisch
Verlag: Springer International Publishing, 2015
Serie: Buch 144 von 170 - Undergraduate Texts in Mathematics
- Hardcover
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Gebunden. Zustand: New.
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Hardcover. Zustand: Brand New. 2nd ed. 2015 edition. 332 pages. 9.00x6.25x1.00 inches. In Stock.
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 un…ity 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.
