Date

Reading

Jan. 19, 21

13.1, 13.2: Basic theory of field extensions, Algebraic extensions

Jan. 26, 28

13.4, 13.5: Splitting fields and algebraic closures, Separable and inseparable extensions

Feb. 2, 4

More on inseparability. Finite fields.

Feb. 9, 11

13.6, 14.1: Cyclotomic fields, Galois Theory

Feb. 16, 18

14.2: The Fundamental Theorem of Galois Theory

Feb. 23, 25

14.2: Examples

Mar. 1, 3

14.3, 14.4: Galois theory for finite fields, Composite extensions and Simple extensions

Mar. 8, 10

14.5, 14.7 : Cyclotomic extensions, Abelian extensions, Solvable extensions

Mar. 22

Review

Mar. 24

Midterm

Mar. 29, 31

14.6, 14.8: Galois groups of polynomials, Computation of Galois groups over Q

Apr. 5,7

14.9: Examples,Transcendental extensions, Inseparable extensions

Apr. 12, 14

14.9, 18.1: Infinite Galois group, Introduction to the representation theory of finite groups,
Maschke's Theorem

Apr. 19, 21

18:1, 18:3: Schur's Lemma, Character theory and Orthogonality relations

Apr. 26, 28

19.1: Number of irreducible characters, Character tables, Lifted characters

May 3,5

19.3: Restriction of characters, Induced characters, Frobenius reciprocity.
