Date
|
Reading
|
Jan. 17, 19
|
13.1: Basic theory of field extensions
|
Jan. 22, 24, 26
|
13.2, 13.4: Algebraic extensions, Splitting fields and algebraic closures |
Jan. 29, 31, Feb. 2
|
13.5, 13.6: Separable & inseparable extensions, Finite fields, Cyclotomic fields
|
Feb. 5, 7, 9
|
14.1, 14.2: Intro to Galois Theory and the Fundamental Theorem of Galois Theory
|
Feb. 12, 14, 16
|
14.2: Examples
|
Feb. 19, 21, 23
|
14.3, 14.4: Galois theory for finite fields, Composite extensions and Simple extensions
|
Feb. 26, 28, Mar. 1, 4
|
14.5, 14.7: Cyclotomic extensions, Abelian extensions, Solvable extensions
|
Mar. 6
|
Review
|
Mar. 8
|
Midterm
|
Mar. 18, 20, 22
|
14.6, 14.8: Galois groups of polynomials, Computation of Galois groups over Q
|
Mar. 25, 27, 29
|
14.9: Examples,Transcendental extensions, Inseparable extensions
|
Apr. 1, 3, 5
|
14.9, 18.1: Infinite Galois group, Introduction to the representation theory of finite groups,
Maschke's Theorem
|
Apr. 8, 10, 12
|
18:1, 18:3: Schur's Lemma, Character theory and Orthogonality relations
|
Apr. 15,17, 19
|
19.1: Number of irreducible characters, Character tables, Lifted characters
|
Apr. 22, 24, 26
|
19.3: Restriction of characters, Induced characters
|
Apr. 29
|
19.3: Frobenius reciprocity.
|