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Galois Theory (4th edition) by Ian Nicholas Stewart
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About this book :-
Galois Theory (4th edition) written by
I. N. Stewart
Galois theory is a showpiece of mathematical unification, bringing together several different branches of the subject and creating a powerful machine for the study of problems of considerable historical and mathematical importance. This book is an attempt to present the theory in such a light, and in a manner suitable for second and third-year undergraduates.
The central theme is the application of the Galois group to the quintic equation. As well as the traditional approach by way of the 'general' polynomial equation I have included a direct approach which demonstrates the insolubility by radicals of a specific quintic polynomial with integer coefficients, which I feel is a more convincing result. Other topics covered are the problems of duplicating the cube, trisecting the angle, and squaring the circle; the construction of regular polygons; the solution of cubic and quartic equations; the structure of finite fields; and the 'Fundamental Theorem of Algebra'.
(I. N. Stewart)
Book Detail :-
Title: Galois Theory
Edition: 4th
Author(s): I. N. Stewart
Publisher: CRC Press
Series:
Year: 2015
Pages: 323
Type: PDF
Language: English
ISBN: 9781482245837,1482245833
Country: UK
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About Author :-
Author Ian Nicholas Stewart was born in 1945 in England. He was awarded a scholarship to study at the University of Cambridge as an undergraduate student of Churchill College, Cambridge.
After his PhD, Stewart was offered an academic position at Warwick. He is well known for his popular expositions of mathematics and his contributions to catastrophe theory.
While at Warwick, Stewart edited the mathematical magazine Manifold. He also wrote a column called "Mathematical Recreations" for Scientific American magazine from 1991 to 2001. This followed the work of past columnists like Martin Gardner, Douglas Hofstadter, and A.K. Dewdney. Altogether, he wrote 96 columns for Scientific American, which were later reprinted in the books "Math Hysteria", "How to Cut a Cake: And Other Mathematical Conundrums" and "Cows in the Maze".
Stewart has held visiting academic positions in Germany (1974), New Zealand (1976), and the US (University of Connecticut 1977–78, University of Houston 1983–84).
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Book Contents :-
Galois Theory (4th edition) written by
I. N. Stewart
cover the following topics.
Historical Introduction
1. Classical Algebra
2. The Fundamental Theorem of Algebra
3. Factorization of Polynomials
4. Field Extensions
5. Simple Extensions
6. The Degree of an Extension
7. Ruler-and-Compass Constructions
8. The Idea Behind Galois Theory
9. Normality and Separability
10. Counting Principles
11. Field Automorphisms
12. The Galois Correspondence
13. A Worked Example
14. Solubility and Simplicity
15. Solution by Radicals
16. Abstract Rings and Fields
17. Abstract Field Extensions
18. The General Polynomial
19. Regular Polygons
20. Finite Fields
21. Circle Division
22. Calculating Galois Groups
23. Algebraically Closed Fields
24. Transcendental Numbers
25 What Did Galois Do or Know?
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