MATH 5112 (Spring 2026)

• Welcome to the homepage for MATH 5112: Advanced Algebra II!
• Send questions to eric.marberg@gmail.com.
• For office hours, send me an email to arrange an appointment.
• For information about prerequisites, grades, and so forth, consult the syllabus.

Lectures:

• Time: Tuesdays and Thurdays from 1:30PM to 2:50PM.
• Location: Room 2132B, near Lift 19.

Textbooks:

• The first 6 weeks will follow Introduction to Representation Theory by Etingof et al.
  We will only discuss selected topics, rather than the whole book.
• The second 6 weeks will cover the notes on Galois Theory by Rössler.
  See also Chapter 6 in Ip's lecture notes for MATH 5111

Schedule:

• Week 1:
  • Lecture 1: algebras and representations
  • Lecture 2: ideals, quotients, generators, relations
• Week 2:
  • Lecture 3: tensor products
  • Lecture 4: semisimple representations, density theorem
• Week 3:
  • (no lectures)
• Week 4:
  • Lecture 5: matrix algebras, filtrations, finite-dimensional algebras
  • Lecture 6: semisimple algebras, characters, two general theorems
• Week 5:
  • Lecture 7: Krull-Schmidt theorem, tensor products of algebras
  • Lecture 8: Group representations, Maschke's theorem, characters
• Week 6:
  • Lecture 9: orthogonality relations, unitary representations, character tables
  • Lecture 10: representations of product groups, restriction and induction

Assignments:

• You are allowed to use any resources to do the assignments.
  But your solutions must be hand-written and delivered in-person during lecture.
  No electronic submissions.
• Homework 1 due Tuesday, February 24
• Homework 2 due Tuesday, March 3