Last updated: Thu 4/15/08 11:48 p.m.

Math 3312 Set Theory

CATALOG DESCRIPTION:  Topics include sets and set operations, relations and their properties, partition of sets and equivalence relations, axioms of set theory, partially and totally ordered sets and their properties, mappings, cardinals and ordinals.

PREREQUISITE:  A grade of C or better in Math 2305.

GOALS/OBJECTIVES:  At the end of the course, a student should be able to: (1) give examples of set relations (mappings) and be familiar with some of their properties; (2) give examples of equivalence relations and be familiar with some of their properties; (3) be familiar with some axioms of set theory; (4) describe the properties of partially and totally ordered sets and give examples; (5) be familiar with the definition of cardinal numbers and some of their properties; (6) be familiar with the definition of ordinal numbers and some of their properties; (7) construct correct proofs of some set theoretic propositions.

TEXTBOOK: No required book however you may wish to use the following as a supplement (it is not complete) to my notes that will not be emphasized until about a third of way through the semester.

• As time permits read Introductory Chapter in Reinhard Laubenbacher and David Pengelley book Math Expeditions

GRADES

• 3 tests 20% each & final Exam 25%
• Homework and class participation 15%

TEST DATES

• Test 1. Thu Mar 6th
• Test 2  Thu Apr 3rd
• Test 3  Thu Apr 24th
• Final Exam Thu May 8th, 2008

COURSE NOTES & SCHEDULE

• Tue 1/15/2008: Introduction, Set notation and some definitions. Homework at the end of the notes due 1/22/08
• Thu 1/17/2008: continued Introduction, Set notation and some definitions. Homework at the end of the notes due 1/22/08
• Tue 1/22/2008: Finish Introduction, Students present homework &  Set Operations. Homework at the end of the notes due 1/29/08
• Thu 1/24/2008: Finish  Set Operations. & Sets of Numbers Homework at the end of the notes due 1/31/08
• Tue 1/29/2008: Students present homework over Set Operations & Finish Discussion of  Sets of Numbers reminder Homework at the end of the notes due 1/31/08 & we will begin the discussion of Relations.
• Thu 1/31/2008: Students present homework over Sets of Numbers
• Tue 2/5/2008: Finish Discussion of  Relations & Students present corrections of homework over Sets of Numbers
• Thu 2/7/08: Student homework presentations
• Tue 2/12/08: H1: Turn-in all previously assigned homework & Discuss Functions
• Thu 2/14/08: Student homework presentations
• Tue 2/19/08: Discuss Functions (homework part 1 due on paper Thu the 2/21/08)
• Tue 2/26/08: Student homework presentations
• Thu 2/28/08: Finish Functions & begin Cardinality
• Tue 3/04/08: Finish Cardinality & mention Countability
• Thu 3/06/08: Test 1: Sets: definitions, notation, operations, subsets of real numbers, relations, functions and cardinality.
• Tue 3/11/08: Countable Sets
• Thu 3/13/08: Countable Sets (Cont'd)

  H2: Test 1 Corrections Due Tue 3/25/08

  H3: Homework for Countable sets on handout Due Thu 3/27/08

Test 1 10 pt Bonus. Due 4/8/08 Read the article Taming the Infinite. Give a 2-3 page summary of the article, including items such as its purpose, the main events that took place and their significance, and your impression of these events.

• Tue 3/25/08: Countable Sets (Cont'd)

• Thu 3/27/08: Countable Sets (Cont'd)

• Thu 4/10/08: Uncountable Sets
• Tue 4/15/08: Uncountable Sets (Cont'd) & Cantor-Bernstein