Graduate Algebra; 504A

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 first quarter of the first-year algebra sequence. Here is the Syllabus including recommended texts.

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

· Homework 40%

· Midterm 20%

· Final 40%

Midterm will be take home, assigned on Friday, October 30th, due Monday, November 2^nd. Scroll down for details.

Final exam is in-class on Wednesday, December 16^th, 8:30-10:20am

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 due in class on TBA. No late homework is accepted.

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 the topic with all 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 An Introduction to the Theory of Groups, Rotman

o Linear Algebra Done Right, 2^nd edition, S. Axler (Recommended by Alan as a reference to review Jordan canonical forms which came up in HW 2)

Homework 1, due Wednesday, October 7

Homework 2, due Wednesday, October 14, tex, pdf.

Worksheet 1: Symmetric groups, Tex, pdf. Due Friday, October 23

You’ll need this file to tex the worksheet and subsequent homework assignments (the file might get updated later on). Add it to the same directory with your tex homework.

Homework 3, due Wednesday, October 21, tex, pdf.

Homework 4, due Wednesday, October 28, tex, pdf. (Updated 12pm on Friday; one more problem added)

Take-home midterm: distributed Friday, October 30^th, in class, due Monday, November 2^nd, also in class (or in my mailbox by 9:25am). It is a 2-hour individual offline exam. In particular, no trick-or-treating your neighbors into solving your exam problems. You may use your class notes. If you miss class on Friday, e-mail me to get a copy of the exam.

Homework 5 (optional), due Friday, November 6, tex, pdf.

Solution to 2b, thanks to Jim Stark

NO LECTURE on NOVEMBER 9 and 11

Homework 6, due Friday, November 13, tex, pdf.

Homework 7, due Wednesday, November 18, tex, pdf. Note: this homework is a ``worksheet”. It contains theoretical material for independent study that will not be presented in lectures. The homework WILL be graded out of 40 points. When you get it back, please attach it together with your proofs to your notes.

Solution to the problem 3b) on HW7 (algebraic independence of the power sums). There are two approaches: a complete solution which is a courtesy of Nate Bottman, and an appendix by Julia with a somewhat different method.

Attention: homework 8 consists of two assignments: Homework 8 Tex, pdf, due Wednesday, December 2 and Worksheet 3 on ”Polynomial Rings and Gauss Lemma” tex, pdf, due Friday, December 4.

Homework 9, due Wednesday, December 9, sharp, tex, pdf.

Final exam and Solutions.

HAVE A NICE HOLIDAY!