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):

• Jacobson, Basic algebra I and II
• Shafarevich, Basic notions of algebra (this is not a text or a reference, but a fun collection of 20 or so 10-page introductory essays on various topics)
• Bourbaki, Algebra and Commutative algebra volumes (these are encyclopedic references, not intended as texts - they have been translated from the French)
• Hungerford, Algebra
• Isaacs, Algebra, a graduate course
• Mac Lane and Birkhoff, Algebra

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.