# MAT 535

**Title: **Algebra II

**Description: **Vector spaces: Cayley-Hamilton Theorem, Jordon normal form, bilinear forms, signature, tensor products, symmetric and exterior algebras. Homological algebra: categories and functors, universal and free objects, exact sequences, extensions. Representation theory for finite groups: irreducible representations and Shur's Lemma, characters, orthogonality. Galois theory: splitting fields, finite fields, extension fields of various types, Galois polynomial and group, fundamental theorem of Galois theory, symmetric functions. **Offered:** Spring

**Credits: **3

**Textbook:**

- Abstract Algebra (3rd edition) by Dummit and Foote

**Note:**Subject to change - do not buy before confirming with the course instructor

Graduate Bulletin Course Information

**Course Webpages: **