640:551 Abstract Algebra I

Resources:

Web sites:

Course web site: http://sites.math.rutgers.edu/~asbuch/alg551_f25/

Canvas site (homework and announcements)

Prerequisites

Algebra Boot Camp Notes

Working with tensor products

Text:

Brundan and Kleshchev: Foundations of Graduate Algebra

Lectures:

Monday and Thursday 12:10-1:30 PM in Hill 525.

Office hours:

Monday and Thursday 3PM in Hill 702.

Midterm:

Monday, October 27 in class.

Covered sections and instructions.

Final Exam:

Thursday, December 18, 8:00-11:00 AM.

Place: TBA

Assigned homework:

Homework policy. Turn problems in using Canvas.

Homework 1: Due Monday September 15.

Solve all of the following problems, then choose 5 of them to write up to perfection.

2.2.25, 2.3.6, 2.4.5, 2.4.12, 2.4.13, 2.4.15, 2.5.11, 3.3.5, 3.3.16, 3.3.32.

Homework 2: Due Monday September 22.

Solve all of the following problems, then choose 5 of them to write up to perfection.

3.4.5, 3.6.9, 3.6.12, 3.6.17, 3.6.18, 3.6.20, 3.6.22, 3.7.13, 3.7.15, 26.2.7.

Homework 3: Due Monday September 29.

Solve all of the following problems, then choose 5 of them to write up to perfection.

4.1.8, 4.1.9, 4.1.15, 4.1.17, 4.1.19, 4.1.20, 4.1.21, 5.2.4, 5.2.5, 5.2.6, 5.2.7.

Homework 4: Due Monday October 6.

Solve all of the following problems, then choose 5 of them to write up to perfection.

4.2.7, 4.2.12, 4.2.14, 4.3.3, 4.3.4, 4.3.7, 4.3.9, 4.3.15, 4.3.16, 4.3.17.

Homework 5: Due Monday October 13.

Solve all of the following problems, then choose 5 of them to write up to perfection.

Boot Camp Exercises 1.7, 2.7, 2.8, 3.9, 6.10, 6.13, 6.15, 7.3, 7.4, 8.10.

Homework 6: Due Thursday October 23.

Solve all of the following problems, then choose 5 of them to write up to perfection.

Group Exercises: 6.1.4, 6.1.8, 6.1.12, 6.2.2, 6.2.5, 6.3.5, 6.3.8, 6.4.2, 6.7.9, 9.3.8.

Homework 7: Due Monday November 3.

Solve all of the following problems, then choose 5 of them to write up to perfection.

Group Exercises: 6.2.4, 6.5.5, 6.5.6, 6.6.2, 6.6.6, 6.8.4, 6.8.9, 6.8.10, 9.2.1, 9.2.13.

Homework 8: Due Monday November 10.

Solve all of the following problems, then choose 5 of them to write up to perfection.

Group Exercises: 7.1.4, 7.1.8, 7.2.3, 7.2.11, 7.3.9 (use n colors), 7.5.11, 7.5.14, 7.5.15, 7.5.17, 7.5.18.

Homework 9: Due Monday November 17.

Solve all of the following problems, then choose 5 of them to write up to perfection.

Groups Exercises: 6.7.8, 7.3.12, 7.5.8, 7.5.13, 7.5.22, 7.6.3, 7.6.7, 9.2.11.
Boot Camp Exercises: 1.8, 1.9.

Homework 10: Due Wednesday November 26.

Solve all of the following problems, then choose 5 of them to write up to perfection.

5.2.13, 5.3.9, 5.3.13, 5.3.16, 5.3.18, 5.3.20, 5.3.21, 5.3.27, 5.3.28, 5.3.31.
Note: There is a typo in 5.2.13(i). The condition for equality should be s''s v' = s''s'v for some s'' in R-{0}.

Homework 11: Due Monday December 8.

Solve all of the following problems, then choose 5 of them to write up to perfection.

5.1.18, 5.1.20, 5.1.32, 5.2.26, 5.3.34, 5.3.36, 5.4.8, 5.4.9, 5.4.10, 5.4.14, 5.4.17, 5.4.20, 5.4.21, 5.4.22, 5.4.32, 5.5.3, 8.1.1.
Boot Camp Exercises 4.9, 4.10, 4.13, 4.14.