Date

Reading

Jan. 17, 19

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

Jan. 22, 24, 26

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

Jan. 29, 31, Feb. 2

More on inseparability. Finite fields.

Feb. 5, 7, 9

13.6, 14.1: Cyclotomic fields, Galois Theory

Feb. 12, 14, 16

14.2: The Fundamental Theorem of Galois Theory

Feb. 19, 21, 23

14.2, 14.3 : Examples, Galois theory for finite fields

Feb. 26, 28, Mar. 2

14.4, 14.5: Composite extensions and Simple extensions, Cyclotomic extensions

Mar. 5

Review

Mar. 7

Midterm

Mar. 9

14.7 : Abelian extensions, Solvable extensions

Mar. 19, 21, 23

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

Mar. 26, 28, 30

14.9: Examples,Transcendental extensions, Inseparable extensions

Apr. 2, 4, 6

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

Apr. 9, 11, 13

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

Apr. 16, 18, 20

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

Apr. 23, 25, 27

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

Apr. 30, May 2, 4

Additional topics depending on interest, and Review
