A Concrete Introduction to Higher Algebra

by Lindsay N. Childs

This book is written as an introduction to higher algebra for students with a background of a year of calculus. It has been used as a successful undergraduate text for more than 20 years. The objective of the book is to give students enough experience in the algebraic theory of the integers and polynomials to appreciate the basic concepts of abstract algebra. New sections on Luhn's formula, Cosets and equations, and detaching coefficients are included. 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 found throughout the book; hints and answers for many of them are included in an appendix.

Genres: Mathematics, Textbooks, Algebra, Reference

618 pages, Hardcover

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.