Galois Theory

Galois Theory

4.15 (44 ratings by Goodreads)
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Description

Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose exceedingly well. Yet mathematics education has changed considerably since 1973, when theory took precedence over examples, and the time has come to bring this presentation in line with more modern approaches. To this end, the story now begins with polynomials over the complex numbers, and the central quest is to understand when such polynomials have solutions that can be expressed by radicals. Reorganization of the material places the concrete before the abstract, thus motivating the general theory, but the substance of the book remains the same.show more

Product details

  • Paperback | 328 pages
  • 152 x 232 x 20mm | 480.82g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • Revised
  • 3rd Revised edition
  • 40 black & white illustrations, 13 black & white halftones
  • 1584883936
  • 9781584883937
  • 641,981

Review quote

"This edition preserves and even extends one of the most popular features of the original edition: the historical introduction and the story of the fatal duel of Evariste Galois. These historical notes should be of interest to students as well as mathematicians in general. [A]fter more than 30 years, Ian Stewart's Galois Theory remains a valuable textbook for algebra undergraduate students." - Zentralblatt MATH, 1049 "The penultimate chapter is about algebraically closed fields and the last chapter, on transcendental numbers, contains 'what-every-mathematician-should-see-at-least-once', the proof of transcendence of pi. The book is designed for the second and third year undergraduate courses. I will certainly use it." - EMS Newslettershow more

Table of contents

Historical Introduction Classical Algebra The Fundamental Theorem of Algebra Factorization of Polynomials Field Extensions Simple Extensions The Degree of an Extension Ruler-and-Compass Constructions The Idea Behind Galois Theory Normality and Separability Counting Principles Field Automorphisms The Galois Correspondence A Worked Example Solubility and Simplicity Solution by Radicals Abstract Rings and Fields Abstract Field Extensions The General Polynomial Regular Polygons Finite Fields Circle Division Calculating Galois Groups Algebraically Closed Fields Transcendental Numbers References Indexshow more

Rating details

44 ratings
4.15 out of 5 stars
5 36% (16)
4 43% (19)
3 20% (9)
2 0% (0)
1 0% (0)
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