Beckenbach Book Prize Winner
Field Theory and its Classical Problems by Charles
Field Theory and its Classical Problems
I suggested the book as collateral reading in a one-semester course in Galois theory and the students found it very readable and most helpful in establishing a motivation and direction as we sifted through the modern abstract development. -Mathematical Reviews
lets Galois theory unfold in a natural way, beginning with the geometric construction problems of antiquity, continuing through the constructibility 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 groups, fields, or abstract algebra is assumed. Notable topics treated along this route include the transcendence of e and of 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. Field Theory and its Classical Problems
is a winner of the MAA Edwin Beckenbach Book Prize for excellence in mathematical exposition.