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Galois Theory
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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. RegularIan Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still ser...
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
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose very well, but mathematics education has changed considerably since 1973. The time has come to bring this presentation in line with more modern approaches. While preserving and extending the most popular features of the previous editions, the author has reorganized the material to place the concrete before the abstract. He has also added more technical history, incorporated several newer proofs, and revived some classical topics. There is simply no more engaging, no more accessible, no more outstanding introduction to the intriguing concepts of abstract algebra than Galois Theory.
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
Ian Stewart's Galois Theory has been in print for 30 years. Resoundingly popular, it still serves its purpose very well, but mathematics education has changed considerably since 1973. The time has come to bring this presentation in line with more modern approaches. While preserving and extending the most popular features of the previous editions, the author has reorganized the material to place the concrete before the abstract. He has also added more technical history, incorporated several newer proofs, and revived some classical topics. There is simply no more engaging, no more accessible, no more outstanding introduction to the intriguing concepts of abstract algebra than Galois Theory.
