Math 470-3, Algebra

Instructor: Mihnea Popa

Mihnea Popa
Office: Lunt 226
Tel: 847-491-5576
email: mpopa@math.northwestern.edu
  • Meeting times: MWF 12-12:50, Lunt 101
  • Office hours: Friday 2.30-3.30, or by appointment; Mingyi Zhang's office hour Wednesday 2-3
  • Textbook: P. Aluffi, "Algebra: Chapter 0", GSM 104, American Mathematical Society, 2009. Errata for the book can be found here.
Brief course description: This is the third quarter graduate algebra course, intended to serve as an introduction to: solvability of polynomials, representations of finite groups, higher linear algebra, and homological algebra. The course will prepare you for more advanced graduate courses relying on abstract algebra.
Other useful references: S. Lang "Algebra"; M. Artin "Algebra"; D. Dummit and R. Foote "Abstract Algebra"; J.-P. Serre "Linear Representations of Finite Groups"; M. Atiyah and I.G. MacDonald "Introduction to Commutative Algebra"; W. Fulton and J. Harris "Representation theory: a first course".
Prerequisites: Math 470-1 and 470-2.
Requirements: There will be weekly homework, posted posted on this page every Monday, and due in class the following Monday (if you cannot attend class, you can leave it in my mailbox in Lunt before class). The grader is Mingyi Zhang. Homework is the most important component of this course, counting for 60% of your grade. No late homework will be accepted. You may collaborate on the homework problems, but you must write your own solutions and properly acknowledge any help you receive from others. There will be a take-home final exam counting for 40% of your grade. The Algebra prelim (a three hour exam) will be on Friday, June 14.
Homework:
Syllabus:
  • April 1: VII.7
  • April 3: VII.7
  • April 5: VII.7
  • April 8: Serre Ch.1 or Artin Ch.9
  • April 10: Serre Ch.1 or Artin Ch.9
  • April 12: Serre Ch.2 or Artin Ch.9
  • April 15: Serre Ch.2 or Artin Ch.9
  • April 17: Serre Ch.2 or Artin Ch.9
  • April 19: Serre Ch.2 or Artin Ch.9
  • April 22: Serre Ch.2 or Artin Ch.9, VIII.1
  • April 24: VIII.1
  • April 26: VIII.2
  • April 29: VIII.2
  • May 1: VIII.3
  • May 3: VIII.4
  • May 6: VIII.4 and VIII.5
  • May 8: VIII.5 and VIII.6
  • May 10: VIII.6
  • May 13: VIII.6 and IX.3
  • May 15: IX.3 and IX.4
  • May 17: IX.4
  • May 20: IX.5
  • May 22: IX.5 and IX.6
  • May 24: IX.6
  • May 29: IX.7
  • May 31: IX.7