| Meetings | TTh 9:30-11:00, 2-255 |
|---|---|
| Instructor | Eric Rosen |
| Office | 2-172 |
| rosen (at) math (dot) mit (dot) edu | |
| Office Hours | Wed. 2-3, Thur. 11-12, and by appointment |
| Prerequisites | 18.100, 18.700, or 18.701. The course
will be essentially self-contained. In particular, no prior knowledge of logic is required. |
| Syllabus |
Set theory is one of the main branches of mathematical
logic (the others being model theory and recursion theory). This course
will provide an introduction to the basic aspects of the subject, including the
axioms of ZFC, ordinal and cardinal numbers, transfinite induction,
and equivalents of the axiom of choice.
The notion of set is also fundamental to mathematics as many central concepts are defined in terms of sets. During the semester, we will also explain how set theory provides a unifying foundation or framework for mathematics. Specifically, mathematical practice can be modeled within, or reduced to, set theory. More information about set theory can be found here or on wikipedia. Possible topics for student projects include infinitary combinatorics, descriptive set theory (set theory of the reals), cardinal exponentiation and the continuum hypothesis, new axioms for set theory, and applications to algebra and analysis. |
| Calendar | Here is the course schedule. |
| Text | Notes on Set Theory, by Yiannis Moschovakis (Springer 2006). Information about the book can be found on amazon. |
| Format | The course will be seminar format, which means that classes will consist of student presentations. Participants will also be required to write a ten page paper, in LaTeX, on a related topic. |
| Grading | Grades will be based mainly on class presentations and the term paper. Homework and class participation will also be factored into the final grade. |
| Paper | Information about the final project for
the class can be found here.
Here are some student papers from the seminar. |
| Homework | Homework will be assigned on a regular
basis, and will be collected but not graded. The purpose of these assignments is
to help students develop a better understanding of basic concepts in the lectures.
In particular, problem sets will be less demanding than in a typical lecture
course, and will generally be fairly routine. All problems are
from the text.
|
Last updated June 2007