# 640:551 Abstract Algebra I

### Resources:

Course web site:
`http://sites.math.rutgers.edu/~asbuch/alg551_f22/`

Prerequisites

Algebra Boot Camp Notes

Working with tensor products

Algebraic Geometry Notes

Syllabus

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

Lectures:
Monday and Thursday 8:30-9:50 AM in Hill 423.

Office hours:
Week before final: Wednesday 3:30-4:30 PM and Thursday 1-2 PM.
Monday and Thursday 10:00-10:30 AM
Wednesday 4:30-5:30 PM on colloquium days.
Wednesday 3:30-4:30 PM when no colloquium.
No office hours Wednesday September 28.

Exams:
Midterm: Thursday, October 27 in class. Covered sections and instructions.
Takehome Midterm: Due Thursday November 3 in class.
Final: Monday, December 19, 8:30 AM in Hill 005.

### Assigned homework:

Homework policy

Homework 1: Due Monday September 19.
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.
Homework 2: Due Monday September 26.
Solve all of the following problems, then choose 5 of them to write up to perfection.
3.4.7, 3.6.9, 3.6.15, 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, 5.4.1, 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 Monday October 10.
Solve all of the following problems, then choose 5 of them to write up to perfection.
4.3.13, 4.3.14, 4.4.2, 4.4.7, 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 Monday October 17.
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, 6.1.12, and Boot Camp Exercises 1.7, 3.9, 6.9, 6.12, 6.13, 6.14, 7.3, 7.4, 8.12.
Homework 5: Due Monday October 24.
Solve all of the following problems, then choose 5 of them to write up to perfection.
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, 6.8.4, 6.8.9, 6.8.10.
Homework 6: Due Monday November 7.
Solve all of the following problems, then choose 5 of them to write up to perfection.
6.7.8, 6.7.9, 7.1.4, 7.1.8, 7.2.3, 7.2.11, 7.3.9 (use n colors), 7.5.8, 7.5.11, 7.5.14.
Homework 7: Due Thursday November 17.
Solve all of the following problems, then choose 5 of them to write up to perfection.
7.5.15, 7.5.17, 7.5.18, 7.6.3, 7.6.7, 10.1.11, 10.1.15, 10.1.16, 10.1.17, 10.1.21, 10.1.22.
Homework 8: Due Monday November 28.
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, 10.2.10, 10.2.11, 26.3.2, 26.3.4, 29.1.4, 29.2.4. Exercises on pages 4-6 of Alg. geo. notes. Algebraic geometry problems.
Homework 9: Due Monday December 5.
Solve all of the following problems, then choose 5 of them to write up to perfection.
16.2.6, 16.2.7, 16.2.9, 16.2.12, 16.3.11, 16.4.2, 17.1.5, 17.1.8, 17.1.12, 17.1.14, 17.1.16, 17.1.20.
Homework 10: Due Monday December 12.
Solve all of the following problems, then choose 5 of them to write up to perfection.
16.1.15, 16.1.16, 16.1.17, 16.2.1, 16.4.3, 16.4.13, 16.4.17, 16.4.19, 16.4.20.