Instructor: Ljudmila Kamenova
Office: Math Tower 3-115
Office hours: Tuesday 2-4 p.m. in 3-115
Grader: Jaimie Thind, office hours: Monday 4-6 p.m. in 2-122,
Wednesday 10-11 in MLC, e-mail: jthind...
Feel free to send me or Jaimie Thind an e-mail or drop by outside of
office hours.
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.
Additional references:
Midterm 1: Monday, March 9th in class
Midterm 2: Friday, April 24th in class
Final: Wednesday, May 13th from 8 a.m. to 10:30 a.m. in Math 4-130
On Monday, May 4th, there will be no lecture. Check out the Clay Research Conference held at Harvard. Hironaka is going to present a resolution of singularities in positive characteristic!
HW 1 (due Feb 11): [DF] 10.1. Problem 8, 10.2. Problems 6 and 9, 10.3. Problems 9 and 11
HW 2 (due Feb 18): [DF] 10.3. Problems 24 and 27, 10.4. Problems 4, 5 and 24
HW 3 (due Feb 25): [DF] 12.1. Problems 9 and 12, 12.2. Problems 4 and 11, 12.3 Problem 12
HW 4 (due March 4): [DF] 11.3. Problems 3 and 5, 11.5. Problems 5 and 13, 10.5 Problem 1
HW 5 (due March 18): [DF] 10.5. Problems 8, 14 and 17, 17.1. Problems 3 and 4
HW 6 (due March 25): [DF] 15.1. Problems 5, 10 and 24, 15.2. Problem 8, 15.3. Problem 1
HW 7 (due April 1): [DF] 13.1. Problem 8, 13.2. Problems 1, 7, 10 and 22
HW 8 (due April 15): [DF] 13.3. Problem 4, 13.4. Problem 6, 13.5. Problems 6 and 11, 13.6. Problem 8
HW 9 (due April 29): [DF] 14.1. Problem 8, 14.2. Problems 5 and 7, 14.3. Problem 8, 14.4. Problem 5
HW 10 (due May 6): [DF] 14.5. Problems 7 and 10, 14.6. Problems 5 and 19, 14.7. Problem 3
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.
The Instructor may be reached by e-mail at kamenova@math.sunysb.edu.
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