Field Theory and Its Classical Problems (Carus Mathematical Monographs Series #19) / Edition 1by Charles Robert Hadlock
Pub. Date: 06/01/2000
Publisher: Mathematical Association of America
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.
Table of Contents1. Three Greek problems; 2. Field extensions; 3. Solution by radicals; 4. Polynomials with symmetry groups.
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