Field Theory and its Classical Problems

Carus Mathematical Monographs #19

by Charles R. Hadlock

Field Theory and its Classical Problems lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the construction of regular n-gons and the properties of roots of unity, and then on to the solvability of polynomial equations by radicals and beyond. The logical pathway is historic, but the terminology is consistent with modern treatments. No previous knowledge of algebra is assumed. Notable topics treated along this route include the transcendence of e and π, cyclotomic polynomials, polynomials over the integers, Hilbert's irreducibility theorem, and many other gems in classical mathematics. Historical and bibliographical notes complement the text, and complete solutions are provided to all problems.

Genres: Mathematics

340 pages, Paperback

First published January 1, 1978

Reviews

[Daniel Kelleher · Rating 4 out of 5]

One of the most readable math texts that I have read. If you want to understand Galois theory and its motivation, I recommend this text. Hadlock manages to keep in mind that this theory does not exist in a vacuum, which few authors manage.

The theory is presented with minimal technical concepts, which, while lending to accessibility, leaves the reader unprepared to deal with many of the concepts which pervade modern Galois theory. However, this book does include a proof of the Hilbert irreducibility theorem. Hilbert's theorem is central in (inverse) Galois theory, but is often excluded from basic texts.