Introduction To Applied Algebraic Systems
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Introduction to Applied Algebraic Systems
Author: Norman R Reilly
language: en
Publisher: Oxford University Press
Release Date: 2009-11-02
This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as well as a fairly complete discussion of major algebraic systems (such as rings, fields, and groups) with a view of their use in bar coding, public key cryptosystems, error-correcting codes, counting techniques, and elliptic key cryptography. This is the only entry level text for algebraic systems that includes an extensive introduction to elliptic curves, a topic that has leaped to prominence due to its importance in the solution of Fermats Last Theorem and its incorporation into the rapidly expanding applications of elliptic curve cryptography in smart cards. Computer science students will appreciate the strong emphasis on the theory of polynomials, algebraic geometry and Groebner bases. The combination of a rigorous introduction to abstract algebra with a thorough coverage of its applications makes this book truly unique.
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Author: Gérard Cohen
language: en
Publisher: Springer Science & Business Media
Release Date: 1995
This book constitutes the proceedings of the 11th International Conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-11, held in Paris, France in July 1995. The volume presents five invited papers and 32 full revised research papers selected from a total of 68 submissions; it is focussed on research directed to the exploitation of algebraic techniques and methodologies for the application in coding and computer algebra. Among the topics covered are coding, cryptoloy, communication, factorization of polynomials, Gröbner bases, computer algebra, algebraic algorithms, symbolic computation, algebraic manipulation.