MAT 535  Algebra II   Spring 2022 

Tue & Thu 9:45am-11:05am in Math Tower 4-130

Instructor: Ljudmila Kamenova

Office: Math Tower 3-115
Office hours: LK's web card
Grader: Alexandra Viktorova
Grader's office hours: Viktorova's web card

Feel free to send me an e-mail or drop by my office with questions.

The main goal of this course is to study in detail fundamental concepts and methods of algebra that are used in all branches of mathematics. During the second term we cover elements of homological algebra, field theory and foundations of algebraic geometry. We also study Galois theory and representations of finite groups.

Text: Abstract Algebra, by Dummit and Foote (3rd Edition), John Wiley and Sons, Inc., 2003

Additional references:

Grading: There will be one midterm test given in class (on 3/29/22) and a final exam (on 5/10/22, 8:00am-10:45am). The final course grade will be determined as follows: homework = 40%, midterm = 20%, final = 40%.


HW 1 (due on Feb 3): [DF] 17.1. Problems 2, 3, 4 and 5

HW 2 (due on Feb 10): [DF] 17.1. Problems 7, 10, 12 and 13

HW 3 (due on Feb 17): [DF] 13.1. Problem 8, 13.2. Problems 1, 7 and 10

HW 4 (due on Feb 24): [DF] 13.2. Problems 19, 20 and 21, 13.3. Problem 5

Spring Break: March 14--20, 2022

HW 5 (due on March 22): [DF] 13.4. Problem 5, 13.5. Problems 6 and 11, 13.6. Problem 8

Midterm: Tuesday, March 29, in class.

HW 6 (due on April 12): [DF] 14.2. Problems 3 (over Q), 7, 17 and 18

HW 7 (due on April 19): [DF] 14.3. Problems 3, 8 and 10 (p here is prime), 14.4. Problem 5

HW 8 (due on April 26): [DF] 14.6. Problems 5 (over Q), 11 and 19, 14.7. Problem 3

HW 9 (due on May 5): Click here for the problems.

Final: Tuesday, May 10, in Math Tower 4-130, 8:00am-10:45am.

Syllabus: What follows is a tentative syllabus for the class, taken from the Graduate Handbook:
  1. Linear and multilinear algebra (4 weeks)

    References: Lang, chapters XIII and XIV; Dummit and Foote, Chapter 11.

  2. Rudiments of homological algebra (2 weeks)

    References: Lang, chapter XX; Dummit and Foote, Part V, 17.

  3. Representation Theory of Finite Groups (2 weeks)

    References: Lang, chapter XVII; Dummit and Foote, Part VI; Serre.

  4. Galois Theory (6 weeks)

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