Course Schedule - Fall Semester 2020

     

MATH 563 902 (CRN: 15925)

ADVANCED ALGEBRA I

Long Title: ADVANCED ALGEBRA I
Department: Mathematics
Instructor: Walton, Chelsea M.
Meeting: 8:30AM - 9:25AM MWF FULLY ONLINE (24-AUG-2020 - 4-DEC-2020) 
Session: Full Term
Grade Mode: Standard Letter
Course Type: Lecture
Method of Instruction: Online
Credit Hours: 3
Course Syllabus:
Course Materials: Rice Campus Store
 
Restrictions:
Must be enrolled in one of the following Level(s):
Graduate
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: 22-OCT-2020 12:57PM
 
Fees: None
 
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.