MAT 535  Algebra II   Spring 2011 

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: Yi Zhu, e-mail:

Feel free to send me or Yi Zhu 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: Tuesday, March 15th in class

Final: Tuesday, May 17th from 2:15 p.m. to 4:45 p.m. in Physics P125


HW 1 (due on Feb 15th): [DF] 17.1. Problems 2, 3, 4 and 5

HW 2 (due on Feb 22nd): [DF] 17.1. Problems 7, 10, 12, 13 and 16

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

HW 4 (due on March 8th): [DF] 13.2. Problems 19, 20 and 22, 13.3. Problem 4

HW 5 (due on March 29th): [DF] 13.4. Problem 6, 13.5. Problems 6 and 11, 13.6. Problem 8

HW 6 (due on April 5th): [DF] 13.6. Problems 14, 15, 16 and 17, 14.1 Problem 8

HW 7 (due on April 12th): [DF] 14.2. Problems 2, 3, 5, 7 and 16

HW 8 (due on April 26th): [DF] 14.2. Problems 17, 18 and 23, 14.3. Problem 8, 14.4. Problem 5, 14.6. Problems 5 (over Q) and 19, 14.7. Problem 3

HW 9 (due on May 3rd): Click here for the problems.

HW 10 (due on May 10th): 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.

Students who might require special evacuation procedures in the event of an emergency are urged to discuss their needs with both the instructor and DSS. For important related information, click here.