640:551 - Abstract Algebra I

Rutgers University, Fall 2017

Anders Buch (asbuch ⊗ math • rutgers • edu)


Resources:

Course web site:
http://sites.math.rutgers.edu/~asbuch/alg551_f17/

Prerequisites

Algebra Boot Camp Notes

Algebraic geometry class notes

PID modules class notes (TBC)

Syllabus

Text:
Brundan and Kleshchev: A Graduate Course in Algebra.

Lectures:
Monday and Wednesday 3:20 - 4:40 PM in Hill 425.

Office hours:
Tuesday 11-12 noon and Wednesday 11-12 noon in Hill 234.

Final exam:

Wednesday December 13, 3:20-4:40 PM in Hill 425.
Exam from 2015 (designed for 3 hours).

Assigned homework:

Homework policy

Homework 1: Due Friday September 22.
Solve all of the following problems, then choose 5 of them to write up to perfection.
2.2.16, 2.2.18, 2.4.2, 2.4.6, 2.4.7, 2.4.8, 2.5.8, 3.3.3, 3.3.7, 3.3.18, 3.4.7, 3.6.9, 3.6.15, 5.4.1.
Homework 2: Due Friday September 29.
Solve all of the following problems, then choose 5 of them to write up to perfection.
4.1.7, 4.1.9, 4.1.15, 4.1.16, 4.1.17, 4.2.8, 4.3.2, 4.3.5, 4.3.10, 4.3.13, 4.3.14, 4.4.2, 4.4.7, 26.2.7, 19.2.7, 19.2.8 (for the last two problems you may assume that R is commutative if desired).
Homework 3: Due Friday October 6.
Solve all of the following problems, then choose 5 of them to write up to perfection.
4.1.3, 4.1.4, 4.1.9, 4.2.12, 4.2.13, 4.3.1, 4.3.7, 4.3.15, 4.4.9, 4.4.10, 4.4.11, 4.4.14.
Homework 4: Due Friday October 13.
Solve all of the following problems, then choose 5 of them to write up to perfection.
6.1.2, 6.1.4, 6.1.8, and SPP Exercises 3.9, 6.9, 6.11, 6.12, 6.13, 6.14, 7.3, 7.4, 8.12.
Homework 5: Due Friday October 20.
Solve all of the following problems, then choose 5 of them to write up to perfection.
6.1.12, 6.2.2, 6.2.4, 6.2.5, 6.3.5, 6.3.8, 6.4.2, 6.5.5, 6.5.6, 6.6.2, 6.6.6.
Homework 6: Due Friday October 27.
Solve all of the following problems, then choose 5 of them to write up to perfection.
6.7.8, 6.7.9, 6.8.4, 6.8.9, 6.8.10, 7.1.4, 7.1.8, 7.2.3, 7.2.11, 7.3.9 (use n colors).
Homework 7: Due Friday November 3.
Solve all of the following problems, then choose 5 of them to write up to perfection.
7.5.8, 7.5.11, 7.5.14, 7.5.15, 7.5.17, 7.5.18, 7.6.3, 7.6.7, 8.1.8, 8.1.10, 8.1.11, 8.2.2, 8.2.6, 8.2.13, 8.2.14.
Homework 8: Due Friday November 10.
Solve all of the following problems, then choose 5 of them to write up to perfection.
9.2.1, 9.2.11, 9.2.13, 9.2.22, 10.1.11, 10.1.15, 10.1.16, 10.1.17, 10.1.21, 10.1.22, 10.2.10, 10.2.11.
Homework 9: Due Friday November 17.
Solve all of the following problems, then choose 5 of them to write up to perfection.
11.1.5, 11.1.10, 11.1.12, 11.1.18, 11.1.19, 11.1.20, 12.1.3, 12.1.8, 12.1.9, 12.2.8.
Homework 10: Due Friday December 1.
Solve all of the following problems, then choose 5 of them to write up to perfection.
12.3.6, 26.3.2, 26.3.3, 26.3.4, 29.1.4, 29.2.4. Exercises on pages 4-6 of Alg. geo. notes. Algebraic geometry problems.
Homework 11: Due Friday December 8.
Solve all of the following problems, then choose 5 of them to write up to perfection.
12.3.6, 12.4.5, 12.5.2, 12.5.5, 12.5.7, 12.6.2, 16.2.6, 16.2.7, 16.2.9, 16.2.12, 16.3.11.