Course Schedule and Catalog

Department: Mathematics

Meeting: 8:30AM - 9:25AM MWF FULLY ONLINE (24-AUG-2020 - 4-DEC-2020) 

Session: Full Term

Grade Mode: Standard Letter

Course Type: Lecture

Language of Instruction: Taught in English

Method of Instruction: Online

Credit Hours: 3

 

Prerequisites: MATH 357

Section Max Enrollment: 18

Section Enrolled: 7

Total Cross-list Max Enrollment: 25

Total Cross-list Enrolled: 7

Enrollment data as of: 30-SEP-2023 11:54PM

 

 

Final Exam: GR Course-Dept Schedules Exam

 

Description: A first graduate course in Algebra. Advanced topics in group theory: semi-direct products, dual groups, inverse limits and completions. Galois Theory, including infinite Galois Extensions. Advanced topics in ring theory: radicals, local rings, primary decomposition, the prime spectrum of a ring. Groebner Bases; elimination theory. Modules: the Cayley-Hamilton Theorem and Nakayama's lemma; localization and local properties; composition series and the Jordan-Hölder theorem; structure theorem for finitely generated modules over a PID. Tensor products: universal properties, multilinear algebra. Introduction to categories and functors. Cross-list: MATH 463. Mutually Exclusive: Cannot register for MATH 563 if student has credit for MATH 463.