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 $\pi$, 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.
By:
Charles Robert Hadlock Imprint: American Mathematical Soc Country of Publication: United States Weight: 415g ISBN:9781470449605 ISBN 10: 1470449609 Series:Carus Mathematical Monographs Pages: 323 Publication Date:30 December 2018 Audience:
Professional and scholarly
,
Undergraduate
Format:Paperback Publisher's Status: Active
Reviews for Field Theory and Its Classical Problems
The presented book is a clear and concise introduction to classical results of Galois theory. The book is an excellent reading for everyone, especially for instructors and first year graduate students in Galois theory. - Acta. Sci. Math.