MA482 FOUNDATIONS OF MATHEMATICS (3 Cr.)

COURSE DESCRIPTION

Prerequisite: Permission of instructor.

Offered:  On Demand

Course Description
Informal axiomatic set theory, cardinal and ordinal arithmetic, transfinite induction, and issues in the philosophy of mathematics.

Course Content Outline

1. Axiomatic Method
   1. Description and applications
   2. Consistency, independence and completeness of an axiomatic system
2. Theory of Sets
   1. Background
   2. Russell paradox
   3. Relations and operations
   4. Cardinality: finite, ordinary infinite, Dedikind infinite
   5. Countable and uncountable sets
   6. Ordering of countable numbers
3. Ordinal Numbers
   1. Order types
   2. General well ordered set
   3. Choice Axiom, Well Ordering Theorem, and Comparability
4. The System of Real Numbers
   1. Complete ordered field
   2. Operations
   3. Peano axioms
   4. Complex number system