Field Theory and Its Classical Problems (Carus Mathematical Monographs) (Carus Mathematical Monographs, 35)

Charles Robert Hadlock

ISBN 10: 1470449609 / ISBN 13: 9781470449605

Editore: American Mathematical Society, 2018

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Titolo: Field Theory and Its Classical Problems (...

Casa editrice: American Mathematical Society

Data di pubblicazione: 2018

Legatura: paperback

Condizione: New

Tipologia articolo: book

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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.