Rings and Fields

Rings and Fields

by Graham Ellis
     
 

ISBN-10: 0198534558

ISBN-13: 9780198534556

Pub. Date: 12/28/1992

Publisher: Oxford University Press, USA

This accessible introduction to the mathematics of rings and fields shows how algebraic techniques can be used to solve many difficult problems. The book is carefully organized. Prerequisite mathematical skills are introduced at the beginning, and each chapter opens with an introduction to a problem followed by the development of the algebraic techniques necessary

Overview

This accessible introduction to the mathematics of rings and fields shows how algebraic techniques can be used to solve many difficult problems. The book is carefully organized. Prerequisite mathematical skills are introduced at the beginning, and each chapter opens with an introduction to a problem followed by the development of the algebraic techniques necessary for its solution, using concrete mathematical and non-mathematical examples. Although prior knowledge of group theory is not required, a chapter is included which states the axiom for a group and proves the group theoretic results needed in Galois theory. The work is intended for advanced students and researchers in mathematics, computer science, and electronic engineering.

Product Details

ISBN-13:
9780198534556
Publisher:
Oxford University Press, USA
Publication date:
12/28/1992
Series:
Oxford Science Publications
Pages:
184
Product dimensions:
9.50(w) x 6.31(h) x 0.63(d)

Table of Contents

1. Diophantine Equations: Euclidean Domains
2. Construction of Projective Planes: Splitting Fields and Finite Fields
3. Error Codes: Primitive Elements and Subfields
4. Construction of Primitive Polynomials: Cyclotomic Polynomials and Factorization
5. Ruler and Compass Constructions: Irreducibility and Constructibility
6. Pappus' Theorem and Desargues' Theorem in Projective Planes: Wedderburn's Theorem
7. Solution of Polynomials by Radicals: Galois Groups
8. Introduction to Groups
9. Cryptography: Elliptic Curves and Factorization

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