Algebra I (Math 611)

Overview

This is a course in the basics of abstract algebra, with the goal of helping you prepare to take the graduate qualifying exam. This semester covers groups, rings, and modules. The final goal is the classification of modules over principal ideal domains.

Instructor

Prof. Paul Gunnells, LGRT 1115L, 545–6009, gunnells at math dot umass dot edu. The best way to contact me is by email. Please don’t leave a message on my office phone; I almost never listen to messages there.

Textbook

Abstract Algebra, 3rd Edition by David S. Dummit and Richard M. Foote. Table of contents.

The textbook is very readable; the authors put a lot of work into their exposition, and there are many examples given in detail. It will be presumed that you are investing significant time with the textbook outside of class, since not every topic we need can be covered in class.

Other valuable references:

Grading

The grading for the course will be as follows. There will be a final exam worth 40%, and one exam during the semester worth 30%. The remaining 30% will be based on homework exercises.

Final Exam

The final will be cumulative, with some emphasis placed on topics covered after the midterm exam.

Exams

The date of the midterm exam will be the following:

This exam date does not conflict with any religious observances, as determined by the
2018 NYC Alternate Side Parking Rules Suspension Calendar, which is the most complete list of holidays I know.

Problem Sets

Problem sets will be assigned on the main course page and will be collected in-class. Late problem sets will not be accepted for any reason. At the end of the term, a few problem set grades will be dropped, so missing one or two problem set submissions shouldn’t affect your grade. Only selected problems (randomly chosen by me) will be graded.

I encourage you to form study groups and to work on the problem sets together. In fact you will learn a lot more about the material through discussing it with your fellow students. However, there are a few guidelines to follow:

Successful completion of the problem sets is essential to help you monitor your progress in the course. The homework problems will be very similar to problems that appear on exams. Please don’t postpone working on the problems; try to take a look at them shortly after the material is covered in class.

Help

I try to answer as many questions as possible during lecture. If you have a question, don’t be afraid to ask. Chances are other students also have the same question. I also usually stick around a few minutes after class to answer quick questions (such as questions about parts of the lecture, a homework problem you’ve tried, etc.). Most students find this to be a good way to clear up confusion.

Outside of class, the best way to get help is through my office hours. Sometimes only a little bit of consultation is all that’s needed to deal with difficulties. One thing to remember is that you will get much more out of office hours if you make a serious effort to do the problem on your own first.

Although I like to get a lot of questions from students, it is not possible to answer mathematical questions by email. Please don’t be offended if you ask me a mathematical question by email and I don’t respond. I’ve found in the past that trying to discuss mathematics by email rarely helps anyone, and usually only causes more confusion. It’s much more effective to ask me such questions during class or office hours.