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  • Publisher:
    Mathematical Association of America
    Publication date:
    05 June 2014
    01 June 1975
    ISBN:
    9781614440192
    9780883850206
    9780883850329
    DOI:
    https://doi.org/10.1017/CBO9781614440192
    Dimensions:
    Weight & Pages:
    00kg,
    Dimensions:
    Weight & Pages:
    00kg,
    • Subjects:
    Mathematics, Algebra
    Series:
    Carus Mathematical Monographs
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Subjects:
Mathematics, Algebra
Series:
Carus Mathematical Monographs
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Book description

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 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.

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