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- Author: Susanne Schmitt
- Pages: 380
- Language: English
- ISBN/ASIN: 3110168081
- ISBN13: 9783110168082
- Upload date: 26-02-2016, 12:50
- Category: Mathematics

The basics of the theory of elliptic curves should be known to everybody, be he (or she) a mathematician or a computer scientist. Especially everybody concerned with cryptography should know the elements of this theory. The purpose of the present textbook is to give an elementary introduction to elliptic curves. Since this branch of number theory is particularly accessible to computer-assisted calculations, the authors make use of it by approaching the theory under a computational point of view. Specifically, the computer-algebra package SIMATH can be applied on several occasions. However, the book can be read also by those not interested in any computations. Of course, the theory of elliptic curves is very comprehensive and becomes correspondingly sophisticated. That is why the authors made a choice of the topics treated. Topics covered include the determination of torsion groups, computations regarding the Mordell-Weil group, height calculations, S-integral points. The contents is kept as elementary as possible. In this way it becomes obvious in which respect the book differs from the numerous textbooks on elliptic curves nowadays available.

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Second Order Elliptic Equations and Elliptic Systems Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics) Partial Differential Operators of Elliptic Type (Translations of Mathematical Monographs) Jacobi Forms, Finite Quadratic Modules and Weil Representations over Number Fields (Lecture Notes in Mathematics) Iwasawa Theory 2012: State of the Art and Recent Advances Geometry of Algebraic Curves: Vol 1 Elliptic Tales: Curves, Counting, and Number Theory Elliptic Diophantine Equations: A Concrete Approach Via the Elliptic Logarithm Elementary Number Theory: Primes, Congruences, and Secrets: A Computational Approach (Undergraduate Texts in Mathematics) Elementary Number Theory, Cryptography and Codes (Universitext) Distributions, Sobolev Spaces, Elliptic Equations (EMS Textbooks in Mathematics) Direct Methods in the Theory of Elliptic Equations Complex Functions: An Algebraic and Geometric Viewpoint Biscuits of Number Theory (Dolciani Mathematical Expositions) Arithmetics (Universitext) An Introduction to the Theory of Numbers, 6 Edition Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography Algebraic Geometry Algebraic Functions and Projective Curves Advanced Topics in the Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) Making, Breaking Codes: Introduction to Cryptology Cryptography and Secure Communication An Introduction to Mathematical Cryptography, 2nd edition Algebraic Curves in Cryptography

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