Aug. 26, 28

1.1  1.5, 2.1 2.3, 3.1  3.2: Groups and subgroups, definition and examples; Cosets and quotient groups

Aug. 31, Sept. 2, 4

1.6  1.7, 3.3, 4.1: Homomorphisms and isomorphisms; Isomorphisms theorems; Group actions: orbits and stabilizers

Sept. 9, 11

4.2, 4.3, 4.5: Applications of groups actions; Sylow theory

Sept. 14, 16, 18

4.4, 4.5: Applications of Sylow theory; Representations induced by group actions; Automorphism group

Sept. 21, 23, 25

4.6, 5.1, 5.5: Automorphisms of S_{n}; The simplicity of A_{n}; Direct and indirect products

Sept. 28, 30, Oct. 2

5.4, 6.1, 5.2: Solvable and Nilpotent groups; Classification of finite abelian groups

Oct. 5, 7, 9

7.1  7.3: Rings, definition and examples; Ring homomorphisms and quotient rings; Ideals and their properties

Oct. 12, 14, 16

7.4  7.5: Properties of ideals, Rings of fractions

Oct. 19, 21, 23

7.6, 8.1  8.2: The Chinese Remainder theorem, Euclidean Domains, Principal ideal domains

Oct. 26, 28, 30

9.6, 8.3: Noetherian rings, Hilbert basis theorem, Unique factorization domains

Nov. 2, 4, 6

9.1  9.5: Polynomial rings

Nov. 9, 11, 13

10.110.4: Introduction to modules

Nov. 16, 18, 20

12.1: Modules over Principal Ideal Domains

Nov. 23

12.212.3: The Rational & Jordan Canonical forms

Nov. 30, Dec. 2, 4


Dec. 7

