Math 250A - Groups, rings, and fields

Instructor: Bjorn Poonen

Lectures: TTh 8:10-9:30am, 70 Evans

Course Control Number: 55170

Office: 879 Evans, e-mail: poonen@math

Office Hours: M 2:10-3pm, Th 11:10-12 (last one 12/4/03) or by appointment.

Teaching assistant: Brian Rothbach, 1042 Evans, e-mail: rothbach@math, office hours: WF 11-12

Prerequisite: Math 114 (or equivalent undergraduate abstract algebra) or consent of instructor.

Syllabus: We will cover Appendix 2 and most of Chapters I-VI in Lang's text: a little set theory (Zorn's lemma and cardinality), groups (including the Sylow theorems and the Jordan-Hölder theorem), rings, modules, polynomials, algebraic field extensions, Galois theory (including infinite Galois theory, and an introduction to Galois cohomology, if there is time). There is a lot of material, so students will be expected to read the text for definitions and theorems not covered in class. Class time will serve to emphasize important points, to clarify difficult topics, and to supplement the text as needed.

Required Text: Lang, Algebra (revised third edition, Springer, 2002). Errata

Other books (not required):

(I don't have firsthand experience with the last three texts, but others have recommended them.)

Grading: There will be no exams. Grades will be based on weekly homework.

Homework: Assignments will be due in class on Tuesdays. Late homeworks will not be accepted. You are free to consult any sources (animate or inanimate) while doing your homework, but if you use anything (or anyone) other than your class notes or the texts listed above, you should say so on your homework. Staple loose sheets!!!

Click here for reading and homework assignments. You may need to clear the caches in your browser to force it to reload the current version.

Solutions will be posted on Brian Rothbach's website.