**Prerequisites & Bulletin Description**

## Course Objectives

The course is intended as an introduction to the Foundations of Mathematics. It begins with Cantor's initial work in set theory, followed by a description of the paradoxes found within his approach and approaches to set theory which avoid the paradoxes. The construction of cardinal and ordinal numbers and operations on those classes are studied. Finally the axiom of choice is discussed with some of its principle equivalences.

## Evaluation of Students

Students will be graded on regular problem sets, in-class or take-home examination and a written final examination.

## Course Outline

Topics |
Number of Weeks |

Cantor's plan, the paradoxes, and remedies for the paradoxes | 2 |

Cardinal numbers and operations on cardinals | 4 |

Ordinal numbers and operations on ordinals | 4 |

Equivalences of the axiom of choice | 3 |

Axiom systems for set theory | 2 |

## Textbooks & Software

None required.

Submitted by: Diane Resek

Date: April 28, 2003