14/02/15 17:36:10.40
乙
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Course Syllabus
1 Introduction: description of the problem and some results on polynomials of one variable as heating.
2 Extensions body : algebraicity , algebraically closed , Lemma primitive element.
3 Minimal polynomial , combined elements.
4 Finite : Frobenius automorphisms , extensions of finite fields.
5 Group theory I: basic results , order of an element , Lagrange's theorem .
6 Galois : Lemma Artin , Galois groups , Galois .
7 Group Theory II: solvable groups , non solvability of the symmetric group Sn for n greater than or equal to 5.
8 Cyclotomy I: General cyclotomic extension, Kummer theory
9 Theorems of solvability of Galois : test solvability theorem, Galois degree p
10 Reduction mod p : calculating Galois groups of polynomials with integer coefficients by reduction modulo p
11 Supplements : cyclotomy Q ( through the reduction modulo p) and other applications