640:551 Abstract Algebra I
Rutgers University, Fall 2022
Anders Buch (asbuch ⊗ math • rutgers • edu)
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.