Graduate Algebra; 506

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)

Announcements: There is no lecture on Friday, April 13.  There will be a homework discussion session on Tuesday, April 17, at 3:30pm.

 

Course Description.  This is the third (and last!) 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%

 

TA/Grader. Jim Stark

 

Exams.  Midterm – in class, May 4, 8:30-10:20am.

Solutions to the midterm

 

Final exam -- Wednesday, June 6th, 8:30am, Padelford C-36

Notes allowed but no other external sources

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 in class 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. 

 

Textbooks.  

1. Commutative algebra:

o   Introduction to Commutative Algebra, M. Atiyah and I. Macdonald (main reference)

o   Commutative algebra with a view towards algebraic Geometry, D. Eisenbud

o   ``Undergraduate commutative algebra” and “Undergraduate algebraic geometry”, M. Reid

2. Homological algebra:

o   An introduction to homological algebra, C. Weibel

3. General references:

o   Abstract Algebra, D. Dummit and R. Foote

o   Algebra,  S. Lang

 

Homework assignments:

1.      Worksheet on symmetric polynomials ( .pdf, .tex, MyDefn.tex), due Wednesday, April 4

2.      Homework 2: radicals, irreducible components, Noetherian spaces ( .pdf, .tex), due Wednesday, April 11

                           Solution to problem 5: pdf

3.      Worksheet on Artinian rings ( .pdf, .tex), due Wednesday, April 18.

                           Solutions (courtesy of Reid Dale and Jim Stark): pdf

4.      Homework 4: principal open sets, algebraic subsets in A2, normal rings and normalizations, due Wednesday, April 25. Files: pdf, tex.

5.      Homework 5: regular functions and morphisms; examples of algebraic sets in A3 with decompositions into irreducible components, due Wednesday, May 2. Files: pdf, tex.

6.      Worksheet on primary decomposition (pdf, tex), due Wednesday, May 16.

7.      Homework 7: Tensor product and localization, Dedekind domains, faithful flatness (pdf, tex), due Wednesday, May 23

8.      Homework 8: Homological algebra (assigned by Steve Mitchell) pdf, due Wednesday, May 30. If you’d like the tex file please talk to Steve.