| Softcover ISBN: | 978-1-4704-4960-5 |
| Product Code: | CAR/35 |
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| AMS Member Price: | $56.25 |
| eBook ISBN: | 978-1-4704-4961-2 |
| Product Code: | CAR/35.E |
| List Price: | $70.00 |
| MAA Member Price: | $52.50 |
| AMS Member Price: | $52.50 |
| Softcover ISBN: | 978-1-4704-4960-5 |
| eBook: ISBN: | 978-1-4704-4961-2 |
| Product Code: | CAR/35.B |
| List Price: | $145.00 $110.00 |
| MAA Member Price: | $108.75 $82.50 |
| AMS Member Price: | $108.75 $82.50 |
| Softcover ISBN: | 978-1-4704-4960-5 |
| Product Code: | CAR/35 |
| List Price: | $75.00 |
| MAA Member Price: | $56.25 |
| AMS Member Price: | $56.25 |
| eBook ISBN: | 978-1-4704-4961-2 |
| Product Code: | CAR/35.E |
| List Price: | $70.00 |
| MAA Member Price: | $52.50 |
| AMS Member Price: | $52.50 |
| Softcover ISBN: | 978-1-4704-4960-5 |
| eBook ISBN: | 978-1-4704-4961-2 |
| Product Code: | CAR/35.B |
| List Price: | $145.00 $110.00 |
| MAA Member Price: | $108.75 $82.50 |
| AMS Member Price: | $108.75 $82.50 |
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Book DetailsThe Carus Mathematical MonographsVolume: 35; 1975; 323 ppMSC: Primary 12Recipient of the Mathematical Association of America's Beckenbach Book Prize in 1984!
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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Table of Contents
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Chapters
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Introduction
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Chapter 1. The three Greek problems
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Chapter 2. Field extensions
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Chapter 3. Solution by radicals
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Chapter 4. Polynomials with symmetric groups
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Reviews
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The presented book is a clear and concise introduction to classical results of Galois theory. The book is an excellent reading for everyone, especially for instructors and first year graduate students in Galois theory.
Acta. Sci. Math.
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
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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.
-
Chapters
-
Introduction
-
Chapter 1. The three Greek problems
-
Chapter 2. Field extensions
-
Chapter 3. Solution by radicals
-
Chapter 4. Polynomials with symmetric groups
-
The presented book is a clear and concise introduction to classical results of Galois theory. The book is an excellent reading for everyone, especially for instructors and first year graduate students in Galois theory.
Acta. Sci. Math.
