MWF 10:30-11:20 am in Eckhart TBA, Problem Session TBA in Eckhart TBA
Please pay attention to the detailed list of Reading and Homework Assignments. It may be subject to change.
Math 25700 is an honors-level course in abstract algebra taught at a high level of abstraction. Its subject matter (groups, rings, fields, etc.) is similar to that of Math 25400, but there is a greater emphasis in 25700 on proving theorems, by the students themselves as well as by the instructor. A good deal of the learning will come from the weekly problem sets, and students in 25700 should be prepared to devote considerable time to them.
|Office||Eckhart 226||Eckhart TBA|
|Phone||Who uses phones?|
|Office Hours||Tuesday 11:30-12:30 and Friday 12:30-1:30||Mon-Wed 12:30-1:30, Fri 1:30-2:30.|
*The easiest way to make an appointment is to see Prof. Calegari after class.
The main text, which you should buy, is David S. Dummit and Richard M. Foote, Abstract Algebra, Third edition, John Wiley & Sons, 2004.
In addition, you might want to consult several other books, such as
Gallian, Joseph A., Contemporary abstract algebra
Lang, Serge, Algebra
Herstein, I. N., Abstract algebra
Fraleigh, John B, A first course in abstract algebra
Any student with a documented disability needing accommodations is requested to speak directly to Student Disability Services (773-702-6000, or email@example.com) and to the instructor as early as possible in the quarter (preferably within the first two weeks of class). All discussions will remain confidential.
Working together with someone else on the exercises is an excellent way to enhance your learning and your understanding. Nevertheless, all written work you hand in must be strictly your own. In other words, you are encouraged to work together with others in understanding and solving the problems, but when you actually write them up, you must work alone.
When you hand in your homework, list the names of others you have collaborated with just under your own name at the top of the page.
Your homework should be written in clear mathematical style. You should clearly state what is to be proved in its own sentence; progress sequentially, justifying or explaining each step; write in complete sentences; use notation correctly; and state that you have completed a proof. What you hand in should be a legible final version, not a first draft.
The exercises will be collected during the first 5 minutes of the Monday lecture following the date on which the exercise appears on the schedule (unless otherwise indicated). Late homework will not be accepted; this includes homework which is put in the TA's mailbox rather than handed in during lecture. Exceptions may be made for illness or other exceptional circumstances.
There are a total of 600 possible points in the course, distributed as follows:
Note that homework points cannot be made up. There is a simple reason for this: the only way to master the material and pass the course is to do the homework.
If a piece of work is regraded by the TA, be sure to bring it to Prof. Calegari so the change can be recorded.