Ebook: Galois theory

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1 Background.- 2 Factorization of polynomials.- 3 Field extensions.- 4 The degree of an extension.- 5 Ruler and compasses.- 6 Transcendental numbers.- 7 The idea behind Galois theory.- 8 Normality and separability.- 9 Field degrees and group orders.- 10 Monomorphisms, automorphisms, and normal closures.- 11 The Galois correspondence.- 12 A specific example.- 13 Soluble and simple groups.- 14 Solution of equations by radicals.- 15 The general polynomial equation.- 16 Finite fields.- 17 Regular polygons.- 18 Calculating Galois groups.- 19 The ‘fundamental theorem of algebra’.- Selected solutions.- References.- Symbol Index.