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.
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