MAT 535  Algebra II   Spring 2012 

Tue & Thu 11:20 a.m. - 12:40 p.m. Physics P125

Instructor: Ljudmila Kamenova

Office: Math Tower 3-115
Office hours: Wednesday 4-6 p.m. in 3-115
Grader: Xin Zhang, e-mail:

Feel free to send me or Xin Zhang an e-mail or drop by.

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 linear and multilinear 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. The final course grade will be determined as follows: Homework: 40%, Midterm Test: 20%, Final Exam: 40%.

Midterm: Thursday, March 22nd in class

Final: Take-home final. Pick up the problems on Monday, May 7th between 2:30 and 3:30 p.m. in my office (Math 3-115). Return your final on Tuesday, May 8th by 3:30 p.m. in Math 3-115.


HW 1 (due on February 2nd): [DF] 10.5. Problems 8, 14 and 17

HW 2 (due on February 9th): [DF] 17.1. Problems 2, 3, 4 and 5

HW 3 (due on February 16th): [DF] 17.1. Problems 7, 10, 12 and 13

HW 4 (due on February 23rd): [DF] 13.1. Problem 8, 13.2. Problems 1, 7 and 10

HW 5 (due on March 1st): [DF] 13.2. Problems 19, 20 and 21, 13.3. Problems 4 and 5

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

HW 7 (due on March 15th) [DF] 13.6. Problems 14, 15, 16 and 17, 14.1. Problem 8

Midterm: Thursday, March 22nd, in class.

HW 8 (due on April 10th) [DF] 14.2. Problems 2, 3, 7, 17 and 18

HW 9 (due on April 12th) [DF] 14.3. Problem 8, 14.4. Problem 5, 14.6. Problems 5 (over Q) and 19, 14.7. Problem 3

HW 10 (due on April 19th) [DF] 12.1. Problems 9, 11 and 12

HW 11 (due on April 26th) [DF] 12.2. Problem 4, 12.3. Problem 12

HW 12 (due on May 3rd): Click here for the problems.

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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DSS advisory. If you have a physical, psychiatric, medical, or learning disability that may affect your ability to carry out the assigned course work, please contact the office of Disabled Student Services (DSS), Humanities Building, room 133, telephone 632-6748/TDD. DSS will review your concerns and determine what accommodations may be necessary and appropriate. All information regarding any disability will be treated as strictly confidential.

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