Fall 2003

**Text:** Hungerford, *Abstract Algebra, an Introduction*,
2^{nd} edition

**Instructor:** Professor Gregory L. Cherlin

*Office:*Hill Center 244, Tel. 445-5921*Office hours:*

Wednesday 2:50-4:00, Thursday 1:30-2:30; and by appointment*Home page:*http://sites.math.rutgers.edu/~cherlin*Email:*cherlin@math.rutgers.edu*Department phone:*445-2390

**Grading**

- Two in-class midterm examinations: 20% each (40% total)
- Final examination: 40%
- Workshops: 10%
- Homework and quizzes: 10%

**Examination dates (expected):**

- Midterm I: Oct 8
- Midterm II: Nov. 12
- Final examination: Dec. 16, 12-3 PM. Location to be announced.

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*.

**Workshops:**

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. plagiarism ^{1
}:*

The workshop involves a mixture of two very different kinds of work:

**During the workshop session**you are expected to collaborate fully with your group. The goal here is not only to solve the problems, but to develop a range of skills relating to technical communication and group work, and to reach a*common understanding*of the issues with your classmates.**Outside the classroom**you may also discuss these problems with your classmates, but you should*mention explicitly*any such collaboration in your write-up. Unacknowledged collaboration is considered*plagiarism*, which is a serious violation of the principles of academic honesty.

We want to encourage collaboration as far as possible, but we do not want to blur the line between legitimate collaboration and plagiarism! Unlike most other forms of academic dishonesty, this one is subtle and can result from carelessness.**The final write-up is your own.**

This means it is entirely written in your own words, even if you like someone else's words better, and even if a classmate has come up with the key idea!

If you have trouble with the presentation, you should see your professor, who is the only one authorized to help you with the actual write-up.

Again, if the rules are unclear in practice, you should consult your professor in specific cases.

**Material covered:**

*Rings, Fields, Groups, Abstract Vector Spaces*

- Chapters 1-7, omitting 1.4, 6.3, 7.8, 7.10
- Sections 9.1, 10.1, 11.1, 11.3, 15

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.

**Calculator**

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 (2^{1/2} 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.

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