Field theory and its classical problems
著者
書誌事項
Field theory and its classical problems
（The Carus mathematical monographs, no. 19）
Mathematical Association of America, c2000
- : pbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 , 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.
目次
- 1. Three Greek problems
- 2. Field extensions
- 3. Solution by radicals
- 4. Polynomials with symmetry groups.
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