Galois Theory notes

Official Syllabus

Prerequisites: Math 541 (please review this carefully)
Course description:Math 542
Textbooks:
- Abstract Algbera - Dummit and Foote

Grades:

- 35% Midterm (In class, Thursday March 26 - Modules)
- 35% Final (10:05 - 12:05, Tuesday May 7 - Galois Theory )
- 30% Homework/Quizzes (Due Thursdays in class)

Homework: I will assign homework every week and it will be due at the beginning of class on Tuesday. Additionally there may occasionally be a small quiz based on the homework material after the homework is handed in. Late homework will not be accepted for any reason but your lowest homework score will be dropped. You are encouraged to work on homework problems in groups but each assignment must be written up individually.

Course content:
Modules: submodules, homomorphisms, quotients, simple modules, cyclic modules, free modules, linear transformations
Matrices: determinants, elementary matrices, Smith normal form over a PID, characteristic roots
Finitely generated modules over a PID
Classification of Finite abelian groups
Normal forms for matrices: rational canonical form, Jordan canonical form
Field extensions, roots of polynomials
Galois Theory

Honors option: There will be extra starred problems on homework assignments throughout the course. There will also be an oral exam based on a final homework assignment. You must complete 75% of the honors homework problems to receive honors.

Important dates: See the registrar's web page for drop deadlines etc.