Math 721: Abstract Algebra II (Spring 2020)

Class: Tuesday and Thursday 10:15 - 11:30am, 222 Daniels Hall on Zoom
Instructor: Cynthia Vinzant (3260 SAS zoom, email)
Office Hours: Monday, Wednesday 1:30-2:30pm or by appointment
Textbook: Dummit and Foote (3rd edition), Abstract algebra, Wiley 2003

Class Syllabus

Algebra Qual Syllabus

Academic continuity plan and quick links:
Zoom class room
My Zoom "office"
Moodle page
Google group

Schedule (Tentative)
WeekTopicAssignments
Jan. 7, 9 Modules Intro (DF Ch. 10.1, 10.2, 10.3) Homework 1 (.pdf, .tex, solutions), due Jan. 16
Jan. 14, 16 Tensors (DF Ch. 10.4) (Worksheet) Homework 2 (.pdf, .tex, solutions), due Jan. 23
Jan. 21, 23 Exact sequences, Hom (DF Ch. 10.5) Homework 3 (.pdf, .tex, solutions), due Jan. 31
Jan. 28, 30 Tensor, symmetric, and exterior algebras (DF Ch. 11.5) Homework 4 (.pdf, .tex, solutions), due Feb. 7
Feb. 4, 6 Modules over PIDs (DF Ch. 12.1)
Feb. 11, 13 Midterm I (Solutions), Structure theory (DF Ch. 12.2) Homework 5 (.pdf, .tex, solutions), due Feb. 21
Feb. 18, 20 Canonical forms, applications (DF Ch. 12.2, 12.3) (Worksheet) Homework 6 (.pdf, .tex, solutions), due Feb. 28
Midterm 1 revisions, due Feb. 28
Feb. 25, 27 Primary decomposition (DF Ch. 15.1, 15.2) Homework 7 (.pdf, .tex, solutions), due March 6
March 3, 5 Homological algebra (DF Ch. 17.1, 17.2)
March 10, 12 No class - Spring Break
March 17, 19 No class - Extended Spring Break
March 24, 26 Midterm II (pdf, Solutions)
Homological algebra (DF Ch. 17.1)
Notes: Class 3/26		 Homework 8 (.pdf, .tex, solutions), due April 3
March 31, April 2 Homological algebra and cohomology of groups (DF Ch. 17.1, 17.2)
Notes: Class 3/31, Class 4/02 		Homework 9 (.pdf, .tex, solutions), due April 10
Sat. April 4 Representation theory basics (DF Ch. 18.1)
Notes: Class 4/04
April 7, 9 Representation theory and Wedderburn's Theorem (DF Ch. 18.1, 18.2)
Notes: Class 4/07, Class 4/09
Homework 10 (.pdf, .tex, solutions), due April 17
April 14, 16 Wedderburn's Theorem and character theory (DF Ch. 18.2, 18.3)
Notes: Class 4/14, Class 4/16
 Good practice problems:
DF 18.2 Exercises 16, 17
DF 18.3 Exercises 2, 3, 4, 5, 9, 11, 12
Sat. April 18 Character theory (DF Ch. 18.3)
Notes: Class 4/18
April 21, 23 Character theory and representation theory of Sn (DF 18.3, 19.1) (Worksheet)
Notes: Class 4/21, Class 4/23, OH 4/27
April 28 Final Exam (pdf, solutions)