# MAT 534

**Title: **Algebra I

**Description: **Groups: normal subgroups, quotient groups, Lagrange's theorem, class formula, finite p-groups and solvable groups, Sylow's theorems, finitely generated abelian groups. Rings and modules: subrings, fields, prime and maximal ideals, quotient rings, ID's, PID's, UFD's, polynomial rings, field of fractions, the Wedderburn theorem, Hilbert basis theorem, finitely generated modules over a PID. Vector spaces: basis, linear maps and matrices, dual spaces, determinants, eigenvalues and vectors, inner products, spectral theorem for normal operators. **Offered:** Fall

**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: **