Algebra
Announcements
Announcements will be posted here from time to time. Please check regularly. The most recent announcement(s) will always be in green.
Lecturer
Ken Brown, Malott 521, 5-3598, kbrown@cornell.edu, office hours Mondays 10:00–11:00, Wednesdays 1:30–2:30, Fridays 3:00–4:00, and by appointment.
The class meets Tuesdays and Thursdays, 8:40–9:55, in Malott 206.
Teaching assistant
Anna Bertiger, annab@math.cornell.edu, office hours Thursdays 12:00–2:00, in Malott 112.
Course mailing list
Mail sent to math6310@math.cornell.edu will reach everyone in the class (including Anna and me). We will use this for announcements, but students can also use it for questions of general interest, discussion, etc.
Course description and prerequisites
See the syllabus.
Text
David S. Dummit & Richard M. Foote, Abstract Algebra, 3rd ed., John Wiley & Sons, 2004 (ISBN 0-471-43334-9). A list of errata is available.
Other references
You can find a huge number of books on algebra in the math library (start browsing around QA150). I've put a few on reserve:
- T. W. Hungerford, Algebra, 1974.
- I. M. Isaacs, Algebra, a graduate course, 1994.
- N. Jacobson, Basic algebra, two volumes, 2nd edition, 1985–1989.
- S. Lang, Algebra, 3rd edition, 2002.
- B. L. van der Waerden, Algebra, two volumes, 1991 reprinting.
Course requirements and grading
There will be weekly homework assignments due on Mondays by 4:30pm. Please leave your homework in Anna's mailbox if you have access to the mailroom. Otherwise bring it to my office.
I expect that most of your learning will take place while doing the homework, and it will count heavily toward your final grade. The remainder of your grade will be based on a take-home prelim and a final exam on Tuesday, December 13, 9:00–11:30, in Malott 203.
I try very hard to design the homework to go along with what is happening in class. I might, for example, give you a problem due Monday that is intended to motivate a theorem I'll prove on Tuesday. For this reason I will not accept late homework except in very unusual circumstances. I will, however, drop the lowest homework grade.
See the homework page for the assignments and some guidelines as to how I want your homework written.
Due to constraints on our resources, it is possible that not all problems will be graded.
Working together
I have no objection in principle to collaboration on the homework, provided that it is done in a way that maximizes the benefit of the homework to all people involved. (One person simply telling another how to do a problem totally defeats the purpose of the problem.) It is my opinion that you get maximum benefit from a homework problem if you work hard on it alone before combining your ideas with someone else's. In any case, the paper that you turn in with your name on it should represent your own solutions, written in your own words, regardless of whether you arrived at some of those solutions in collaboration with others.
Handouts
- Student questionnaire
- The butterfly lemma
- Introduction to category theory
- Solution to Exercise 50 on p. 148
- The Todd–Coxeter procedure
- Computation in permutation groups
- Todd–Coxeter software
- Zorn's lemma
- Ordinal numbers
- The primitive element theorem
- Take-home prelim; solutions
- Solutions to problems on principal open sets