Graduate Algebra; 505

Instructor: Julia Pevtsova

Place: Padelford Hall, C36

Time: 9:30-10:20, MWF

Office Hours: by appointment (that is, I am happy to talk between classes, just need an advance notice)

Course Description. This is the second quarter of the first-year algebra sequence. Here is the Syllabus including recommended texts.

Class Notes (Courtesy of Chad and Nate)

Grading system. Grades will be determined based on homework assignments, a midterm and a final as follows:

· Homework 40%

· Midterm 20%

· Final 40%

Exams. Midterm – Friday, February 12^th, in class.

List of “theoretical” questions for the midterm.

Midterm and Solutions.

List of potential “theoretical” questions for the final.

Final exam -- Wednesday, March 17^th, 8:30-10:20am
Final exam and Solutions.

Homework. Assignments will be posted on this website on a weekly basis. You are encouraged to tex your homework especially if you did not take a calligraphy course in the past. The homework will be collected on Wednesday unless specified otherwise.

Worksheets. This is a special homework assignment. It counts towards the total homework grade. The format is different from the regular homework. The worksheet is designed as an independent study (or review) of a particular topic. You’ll get a short written introduction to the topic with the proofs missing. You’ll need to ``fill in the blanks”, that is, supply the proofs. Once the worksheet is graded and returned to you, it should be added to your notes. You may attach your proofs to the original worksheet, or download the tex file and add the proofs right where they belong so that you get a nice and continuous exposition. The material from the worksheets will be used later in the course and relied on in exams in the same way as the material presented in lecture.

References.

o Algebra, Lang

o Algebra, Hungerford

o Abstract Algebra, Dummit and Foote

o Abstract Algebra: The Basic Graduate Year, Ash (online textbook)

o Introduction to Commutative Algebra, M. Atiyah and I. Macdonald

o Associative Algebras, R. Pierce

1. Homework 1 (Tex), due Wednesday, January 13.

2. Homework 2 (Tex), due Wednesday, January 20.

Solution to Problem 5 (Courtesy of Cody, with an addition by Julia)

3. Homework 3 (Tex), due Wednesday, January 27.

4. Homework 4 (Tex), due Wednesday, February 3.

5. Worksheet 1 (Tex), due Wednesday, February 10
updated Friday, February 5

6. Worksheet 2: Artinian modules (Tex), due Friday, February 19
Proofs (courtesy of Cody)
Homework 6, due Wednesday, February 17

7. Homework 7, (Tex) due Wednesday, February 24

8. Homework 8, (Tex) due Wednesday, March 3

9. Homework 9, (Tex) due Friday, March 12