A Concrete Introduction to Higher Algebra, 2nd Edition

by Lindsay N. Childs

An informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated in a well-motivated fashion and made relevant by many applications -- to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises, ranging from routine examples to extensions of theory, are scattered throughout the book, with hints and answers for many of them included in an appendix.

Genres: Mathematics, Textbooks, Algebra, Reference

522 pages, Paperback

First published December 1, 1978

Reviews

[Dave Neary · Rating 4 out of 5]

I really like this book! It switches from more elementary number theory (modular arithmetic, fundamental theorem of arithmetic) and more abstract algebra topics (groups, rings, fields). It has a light coverage of some applications like public key cryptography and primality tests, but does not give all the prerequisites for higher topics like elliptic curves and modular forms, which also depend on some complicated analysis too.