Classical Galois Theory, With Examples
Lisl Gaal · Medical Entomology and Zoology · 1973
Prerequisites: 1.1 Group theory 1.2 Permutations and permutation groups 1.3 Fields 1.4 Rings and polynomials 1.5 Some elementary theory of equations 1.6 Vector spaces Fields: 2.1 Degree of an algebraic extension 2.2 Isomorphisms of fields 2.3 Automorphisms of fields 2.4 Fixed fields Fundamental theorem: 3.1 Splitting fields 3.2 Normal extensions and groups of automorphisms 3.3 Conjugate fields and elements 3.4 Fundamental theorem Applications: 4.1 Solvability of equations 4.2 Solvable equations have solvable groups 4.3 General equation of degree $n$ 4.4 Roots of unity and cyclic equations 4.5 How to solve a solvable equation 4.6 Ruler-and-compass constructions 4.7 Lagrange's theorem 4.8 Resolvent of a polynomial 4.9 Calculation of the Galois group 4.10 Matrix solutions of equations 4.11 Finite fields 4.12 More applications Bibliography Index.