Mathematics 161: Set Theory

(Philosophy 161--Enroll in Math 161)

Winter 2005-2006

Syllabus

2. http://en.wikipedia.org/wiki/Set_theory

3.

4.

5.

6.

Motivation: Cantor and the notion of infinity

GEORG CANTOR: THE BATTLE FOR TRANSFINITE SET THEORY (by Joseph W. Dauben)

**Jan 12**

Basic principles (axioms)

Elementary operations

(Handout1, Ch 1)

(Homework1 to be handed in by Wed 18)

**Jan 17**

Ordered pairs

Relations

(Handout2, Ch 2, Sect 1 and 2)

**Jan 19**

Functions

(Handout3, Ch 2, Sect 3)

(Homework2 to be handed in by Wed 25)

**Jan 24**

Equivalences and partitions

Orderings

(Handout4, Ch 2, Sect 4 and 5)

**Jan 26**

Orderings (cont.) (Hasse diagram)

(Homework3 to be handed in by Feb 1)

**Jan 31**

The natural numbers

Properties of natural numbers

(Handout5, Ch 3, Sect 1 and 2)

**Feb 2**

The recursion theorem

(Handout6, Ch 3, Sect 3)

(Homework4 to be handed in by Feb 8)

**Feb 7**

The recursion theorem (cont.)

Arithmetic of natural numbers

(Handout7, Ch 3, Sect 4)

**Feb 9**

Midterm

**Feb 14**

Cardinality of sets

Finite sets

(Handout8, Ch 4, Sect 1 and 2)

**Feb 16**

Countable sets

(Handout9, Ch 4, Sect 3)

(Homework5 to be handed in by Feb 22)

**Feb 21**

Linear orderings

(Handout10, Ch 4, Sect 4)

**Feb 23**

Complete linear orderings

Uncountable sets

(Handout11, Ch 4, Sect 5 and 6)

(Homework6 to be handed in by Mar 6)

**Feb 28**

Complete linear orderings (cont.)

Uncountable sets (cont.)

**Mar 2**

Cardinal arithmetic

The cardinality of the continuum

(Handout12, Ch 5, Sect 1 and 2)

(Homework7 to be handed in by Mar 10)

**Mar 7**

Well-ordered sets

Ordinal numbers

(Handout13, Ch 6, Sect 1 and 2)

**Mar 9**

The axiom of replacement

(Handout14, Ch 6, Sect 3)
The Zermelo-Fraenkel axiom system

**Mar 14**

(No class)

**Mar 16**

(No class)

**Mar 20** (confirmed!)

Final exam

*Last updated: March 9, 2006, 09:25am PST*