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Course Description

Summary

This course is intended to serve as a foundation, and it will be a prerequisite for most other advanced mathematics courses. "Pure" mathematics generally refers to mathematics studied for its own sake rather than for any particular application. There is a particular focus on logic and proof. However, this distinction is a bit artificial, since most of the advanced applications of mathematics depend on this sort of reasoning - which is why this class is a prerequisite for many other mathematics classes. Pure mathematical questions are usually not only about how to compute something (e.g. how to find prime numbers), but also about how we know something for certain (e.g. that there are infinitely many prime numbers). Typical questions we will consider: Are there infinitely many prime numbers? How can we know? How do we know for certain that the infinitely many digits in the decimal expansion of the square root of 2 never repeat? Can we ever have definite knowledge about abstractions like infinite sets or the fourth dimension? This class is an introduction to the type of reasoning which lets one answer such questions. We will look at some fundamental ideas of mathematics: rational and irrational numbers, infinite sets, geometric axioms, and some classic questions about them. We will also cover the fundamentals of logic, so this should be of interest to students of philosophy as well. This is an introductory class. Students will be expected only to have a good facility with high school algebra. Students without this solid background can still take the course if they are willing to work on this as the course progresses.