MAT 535  Algebra II   Spring 2017 

Mon & Wedn 11:30am-12:50pm in Math Tower 4-130

Instructor: Ljudmila Kamenova

e-mail: kamenova@math.sunysb.edu.
Office: Math Tower 3-115
Office hours: Wed 1-4pm in Math 3-115
Grader: John Sheridan
Grader's office hours: Thu 1-2pm in Math 2-118, Tue 1-2pm and Wed 12-1pm in the MLC

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 3/20/17) and a final exam (on 5/11/17, 11:15am-1:45pm). The final course grade will be determined as follows: homework = 40%, midterm = 20%, final = 40%.


Homework:

HW 1 (due on Feb 1): [DF] 10.5. Problems 4, 8, 14 and 17

HW 2 (due on Feb 8): [DF] 17.1. Problems 2, 3, 4 and 5

HW 3 (due on Feb 15): [DF] 17.1. Problems 7, 10, 12 and 13

HW 4 (due on Feb 22): [DF] 13.1. Problem 8, 13.2. Problems 1, 7 and 10

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

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

Midterm: Monday, March 20, in class.

HW 7 (due on March 29): [DF] 14.2. Problems 3 (over Q), 7, 17 and 18

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

HW 9 (due on April 19): [DF] 14.6. Problems 5 (over Q), 11 and 19, 14.7. Problem 3

HW 10 (due on April 26): Click here for the problems.

Final: Thursday, May 11, in Math Tower 4-130, 11:15am-1:45pm.


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)


Stony Brook University expects students to maintain standards of personal integrity that are in harmony with the educational goals of the institution; to observe national, state, and local laws as well as University regulations; and to respect the rights, privileges, and property of other people. Faculty must notify the Office of Judicial Affairs of any disruptive behavior that interferes with their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.


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.