Set Theory and Logic
Spring Quarter 2007-2008
Period 7, MTRF
Professor Steve Carlson
Course Description: The notions of set theory and logic provide a necessary foundation of all areas of pure mathematics, including abstract algebra, analysis, and topology. They also interface nicely with other areas among the applied and computational sciences and are of tremendous interest within the symbolic logic and philosophy disciplines.
This course is intended as a first introduction to axiomatic set theory and the elements of logic necessary to express and analyze it. The only real prerequisite is some experience with doing proofs and working with descriptive set theory (e.g., unions, intersections, complements, etc.), roughly at or beyond the Discrete and Combinatorial Algebra level. Any student intending to pursue graduate study in mathematics will benefit greatly from this experience. But any student interested in knowing more about the area will find the course interesting and quite accessible.
In a nutshell, we shall address how mathematics may be built up “from scratch.” We will be motivated by attempting to answer questions like:
“How can we start with nothing and develop mathematics?”
“What is a number?”
“What is ‘infinity’ and in what ways can it be represented?”
“Are all statements decidable?”
“What does it mean for a theory to be complete or consistent?”
Some Specific Comments: We will be using a textbook (to be announced later) that will be made available in the bookstore. A student’s course grade will be based on demonstration of interest via class participation, etc.; performance on assigned homework exercises; and possibly completion of a project and/or giving a presentation in class. There will be no hour tests or exams.
Questions? E-mail, call, or visit the instructor: