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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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