Mathematics 351, Abstract Algebra
Fall 2003

Text: Hungerford, Abstract Algebra, an Introduction, 2nd edition

Instructor: Professor Gregory L. Cherlin


Examination dates (expected):

Any changes to the midterm schedule will be announced in class.
The final examination will probably be given in our usual classroom, but we will be told the location at the end of the semester.

Homework and quizzes:
Regular homework will be assigned from the book (in class). In the Workshop sessions we will work in groups on more difficult problems, under your professor's supervision. Some of these problems, but not all, come from the book. Quizzes will be given in the workshop, based on the homework. Questions concerning the homework should be raised in class.

In the workshops we will have a short quiz and then work on the workshop problems, which will be given to you there. Selected problems will be written up and collected.

Notice regarding collaboration vs. plagiarism1 :
The workshop involves a mixture of two very different kinds of work: collaborative and independent. It is important to understand what this means in practice.

Material covered:
Rings, Fields, Groups, Abstract Vector Spaces

The material will not be taken in exactly this order. We will jump around a good deal in the second half of the course. For the exact sequence of material, see this document.

The course is about the general theory of algebraic operations. You have studied numbers, polynomials, functions, vectors and matrices and you have observed that one can compute with them in broadly similar ways. This course goes into the theory common to these examples. One of our goals is to show how very classical problems can be solved using these very modern ideas.

Course level:
This is a high level course, much of it quite different from anything you will have seen before. You will be expected to follow proofs which are given in the text, and in lectures, and to construct your own proofs. You should expect to become more experienced in this as the term progresses. The course is one of two that satisfies the algebra requirement for the mathematics major. The alternative is mathematics 350 (advanced linear algebra).

As a general rule, undergraduates should expect to spend approximately two hours outside of class for every hour spent in class. As Mathematics 351 is a 4-credit course, and is one of our more challenging courses,

students in Mathematics 351 should be prepared to spend 8 to 10 hours per week on the course, in addition to the class meetings.

Writing proofs may be particularly time consuming at first. In such cases, paying a visit to office hours after devoting a reasonable amount of time to the problems will probably save time and effort. For this to be useful, you should plan to discuss a couple of specific problems that you have thought about carefully.

A numerical calculator will certainly be useful. Graphing is irrelevant. When working with numerical data you will usually need to keep everything in exact terms (21/2 rather than 1.414 for example), so the usefulness of the calculator is limited to rather simple calculations. We do need to do some substantial arithmetic occasionally, of the sort you would not want to do by hand.

Main page, 351.

1Acknowledgement: Substantial portions of this page are adapted from Professor Sim's 351 page.