MAT 535  Algebra II   Spring 2014 

Tue & Thu 1-2:20 p.m. Math Tower 4-130

Instructor: Ljudmila Kamenova

e-mail: kamenova@math.sunysb.edu.
Office: Math Tower 3-115
Office hours: Wed 11 am - 12 noon in the MLC, Wed 1:30 - 3:30 p.m. in Math 3-115
Grader: Dingxin Zhang, e-mail: dzhang@math.sunysb.edu
Grader's office hours: Mon 3-4 pm in Math 2-114, Mon 4-6 pm in the MLC
Feel free to send me or Dingxin 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 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 two midterm tests given in class (on 3/6 and on 4/17). The final exam will be a take-home final to be picked up on 5/12 between 2 and 3 pm in Math Tower 3-115 and to be returned on 5/13 by 3pm. The final course grade will be determined as follows: homework = 30%, midterms = 20% each, final = 30%.


Homework:

HW 1 (due on Feb 6): 10.1. Problem 8; 10.2. Problem 6; 10.3. Problems 4 and 9.

HW 2 (due on Feb 18): 10.4. Problems 5 and 24; 10.5. Problems 8 and 17.

HW 3 (due on Feb 25): 12.1. Problems 11 and 12; 12.2. Problem 4; 12.3 Problem 12.

HW 4 (due on March 4): 17.1. Problems 2, 3, 4 and 5.

Midterm 1: Thursday, March 6, in class.

HW 5 (due on March 13): 17.1. Problems 7, 10, 12 and 13.

HW 6 (due on March 27): 15.1. Problems 13, 16, 24 and 26.

HW 7 (due on April 3): 15.2. Problems 11, 15 and 26; 15.3. Problem 18 (in part (a) prove that I and J are radical ideals, not prime).

HW 8 (due on April 10): 13.1. Problem 8, 13.2. Problems 1, 7 and 10.

Midterm 2: Thursday, April 17, in class.

HW 9 (due on April 24): 13.2. Problems 19, 20 and 21, 13.3. Problem 5.

HW 10 (due on May 1): 13.4. Problem 5, 13.5. Problems 6 and 11, 13.6. Problem 8.

Take-home final to be picked up on 5/12 between 2 and 3 pm in Math Tower 3-115 and to be returned on 5/13 by 3pm.

Practice problems: 14.1. Problem 8, 14.2. Problems 2, 3, 7, 17 and 18, 14.3. Problem 8, 14.4. Problem 5, 14.6. Problem 19.


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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