Math 432. Set Theory and Topology
Instructor Syllabus

Text: Irving Kaplansky, Set Theory and Metric Spaces, 2nd Edition, 1977.

Chapter 1 - Basic Set Theory
1.1 Inclusion
1.2 Operations on Sets
1.3 Partially Ordered Sets and Lattices
1.4 Functions
1.5 Relations; Cartesian Products
.5 hr.
.5 hr.
1 hr.
1 hr.
1 hr.
Chapter 2 - Cardinal Numbers
2.1 Countable Sets
2.2 Cardinal Numbers
2.3 Comparison of Cardinal Numbers; Zorn�s Lemma
2.4 Cardinal Addition
2.5 Cardinal Multiplication
2.6 Cardinal Exponentiation
2 hr.
1 hr.
3-4 hr.
1 hr.
1 hr.
1-2 hr.
Chapter 3 - Well-ordering: The Axiom of Choice
3.1 Well-ordered Sets
3.2 Ordinal Numbers
3.3 The Axiom of Choice
3.4 The Continuum Problem
4 hr.
1-2 hr.
3-4 hr.
1 hr.
Chapter 4 - Basic Properties of Metric Spaces
4.1 Definitions and Examples
4.2 Open Sets
4.3 Convergence; Closed Sets
4.4 Continuity
1 hr.
2 hr.
2-3 hr.
2 hr.
Chapter 5 - Completeness, Separability, and Compactness
5.1 Completeness
5.2 Separability
5.3 Compactness
4 hr.
2 hr.
2-3 hr.
Total 37-43 hr.

Notes:

  1. You will need to fit two or three hour exams into the above schedule.
  2. The text is very readable. Much of the content of the text is in the exercises, so many of the exercises should be covered, either during discussion/problem-solving sessions in class or as work done outside of class.
  3. This class often has a small enrollment; 10-15 students. It is both possible and very useful to have students present their work at the board on a regular basis.