A Concrete Introduction to Higher Algebra

by Lindsay N. Childs

This book is 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. The new examples and theory are built 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 are found throughout the book.

Genres: Mathematics, Textbooks, Algebra, Reference

618 pages, Kindle Edition

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.