- Write clear mathematical arguments,
- Think mathematically,
- Appreciate how writing and thinking depend on each other, and
- Understand the roles of:
- Proofs,
- Definitions,
- Examples,
- Creativity,
- Precision, and
- Sustained effort

- Basic set theory
- Rational and irrational numbers
- Functions
- Mathematical induction
- Equivalence relations and partitions
- Sizes of infinity

The course will include a considerable amount of writing, and thinking about writing. You will find this quite different from past mathematics courses you have taken, and you may find it frustrating; that is natural. This course is intended to help you bridge the gap between performing mathematical algorithms by rote memorization and actually doing mathematics yourself. This is a major change in thinking for many people, and it does not come easily.

One important thing to recognize is that you will not know how to do a problem when you first look at it. It frequently will take several sittings to come to a solution to a problem, and this is contrary to your experience in math classes to date. Expect this to happen; it is the way that most real mathematical thinking occurs, and it is one of the things we are going to practice in this course. Uncertainty is not a bad thing; the methods of transforming the unknown into something understood are central to the study of mathematics, and will be a guiding theme for this class.

See also the course outline for the timing of these topics.

Comments to: dpvc@union.edu

Created: Mar 24 1999 --- Last modified: Mar 26, 1999 11:01:01 AM