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Honors Introduction to Algebra

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  • Solutions to the final exam available in the handouts section.

Lecturer

K. Brown, Malott 521, 5-3598, kbrown@cornell.edu, office hours Tuesdays 10:45–11:45, Thursdays 3:00–4:00, and by appointment.

See the course and room roster for class meeting times and places.

Teaching assistant

Ho Hon Leung, 5-9351, hohonleung@math.cornell.edu, office hours Wednesdays 3:30–5:30 in Malott 218.

Course mailing list

Mail sent to math4340@math.cornell.edu will reach everyone in the class (including the teaching staff). We will use this for announcements, but students can also use it for questions of general interest, discussion, etc.

Course description

We will study the basic abstract structures of modern algebra: Groups, rings, fields, and modules. See the course catalogue for more details.

Since this is an honors course, we will move quickly and cover the material at a high level. If you want a less demanding version of the course, consider Math 4320.

Prerequisite

The prerequisite is Math 4330 or permission of the instructor. [The catalogue says something different, but that resulted from a clerical error and will be fixed in the next catalogue.] Here are some things I expect:

  • You should have experience reading and writing proofs.
  • You should be willing to persevere on a hard problem.
  • You should be able to tolerate failing to solve a hard problem.
  • You should be willing to learn things on your own by reading the text.

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.

The course will cover most of what's in Chapters 1–8, followed by a selection of topics from Chapters 9–14.

Software

A large part of the course will deal with group theory, which lends itself to computational experimentation. There is a lot of software (both free and commercial) that can aid you in this. My favorite is gap. If you want to use this (either in conjunction with the homework or to do a project), I'll be glad to try to help.

Other references

You can find a huge number of books on this subject in the math library (start browsing around QA150). I've put a few of my favorites on reserve:

  • M. Artin, Algebra, 1991.
  • G. Birkhoff and S. MacLane, A survey of modern algebra, 4th edition, 1977.
  • I. N. Herstein, Topics in algebra, 2nd edition, 1975.
  • N. Jacobson, Basic algebra I, 2nd edition, 1985.
  • B. L. van der Waerden, Algebra, two volumes, 1991 reprinting.

Course requirements and grading

There will be weekly homework assignments due on Fridays. You can turn them in in class or bring them to my office by 3:00pm. I expect that most of your learning will take place while doing the homework, and it will count heavily toward your final grade (35%). The remaining 65% will be based on two prelims (20% each) and a final (25%).

The first prelim will be in class on Wednesday, February 25. The second prelim will probably be a take-home exam. The final is scheduled for period H: Monday, May 11, 9:00–11:30am, Malott 253. I am willing to consider a final project in lieu of a final exam. See me if this interests you.

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 Friday that is intended to motivate a theorem I'll prove on Monday. 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.

In particular, you may not simply copy someone else's homework and turn it in as your own. This will be treated as a violation of Cornell's Academic Integrity Code. Similarly, copying solutions that you might find on the internet or in some other source is illegal.

Academic integrity

I take academic integrity very seriously and will follow university procedures in all cases of suspected cheating. Details are spelled out in the Academic Integrity Handbook, cited above.

Handouts