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.
Additional references:
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.
References: Lang, chapters XIII and XIV; Dummit and Foote, Chapter 11.
References: Lang, chapter XX; Dummit and Foote, Part V, 17.
References: Lang, chapter XVII; Dummit and Foote, Part VI; Serre.
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