Rings and Fields

by Graham Ellis

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
Publication date:	01/28/1993
Series:	Oxford Science Publications
Pages:	178
Product dimensions:	9.50(w) x 6.31(h) x 0.63(d)

About the Author

University College, Galway

Table of Contents

1. Diophantine Equations: Euclidean Domains2. Construction of Projective Planes: Splitting Fields and Finite Fields3. Error Codes: Primitive Elements and Subfields4. Construction of Primitive Polynomials: Cyclotomic Polynomials and Factorization5. Ruler and Compass Constructions: Irreducibility and Constructibility6. Pappus' Theorem and Desargues' Theorem in Projective Planes: Wedderburn's Theorem7. Solution of Polynomials by Radicals: Galois Groups8. Introduction to Groups9. Cryptography: Elliptic Curves and Factorization

Editorial Reviews

"The coverage is broad enough and very interesting." —Mathematical Reviews

"Ellis makes available to students, in a clear, understandable fashion, many of the classic problems that are approachable through algebraic techniques. From Ellis's book, an interested student could easily obtain an understanding of the problem and be presented with a method of solution. An excellent choice for any undergraduate library and a very worthy resource for a "special" topics course for interested upper-division undergraduates and graduate students." —Choice

From the Publisher