Introduction to Field Theory: Second Edition

by Iain T. Adamson

A fascinating branch of algebra with numerous applications, field theory leads the way to one of the most important theorems of mathematics, the fundamental theorem of Galois theory. This text ranges from field theory's basic definitions to its most significant results and applications, introducing both the spirit and techniques of abstract algebra. Appropriate for undergraduate students in pure mathematics, it presupposes minimal knowledge of elementary group theory.
Acclaimed by American Mathematical Monthly as "an excellent introduction," this treatment begins by developing the elementary properties of rings and fields and examining a variety of homomorphisms, vector spaces, and polynomials. Subsequent chapters explore extension fields and their classifications as well as Artin's approach to Galois theory. The concluding section focuses on applications, with considerations of finite fields, cyclotomic extensions, solution by radicals, generic polynomials, and much more.

192 pages, Hardcover

Published December 6, 2013

Reviews

[Kelly · Rating 2 out of 5]

Not what I was looking for in an introduction. I didn't mind the assumption about the level of knowledge, but the book itself is not well written, jumping into the subject with not real high-level intro or transitions. The book would probably work okay as part of a class, but it is not all that usable for self-study.