This course will focus on Chapter 6 (Galois Theory), Chapter 7 (Extensions of Rings), Chapter 8 (Transcendental Extensions), Chapter 10 (Noetherian Rings and Modules), Chapter 20 (General Homology Theory), and Chapter 21 (Finite Free Resolutions). The course will also emphasize the interactions of algebra with other areas of mathematics. We will generally follow the structure of Serge Lang’s book

Representation theory (reference: Introduction to Representation Theory by Pavel Etingof et al)

• Chapter1: Introduction to Representation Theory
• Chapter2: General results of Representation Theory
• Chapter3: Representations of finite groups (Basic results)