Course

Home

Syllabus

Lecture Topics

Homework

Policies



Links

Problem of the Month

Math Club (QED)

Summer Research in Mathematics

Putnam Competition

Math Department Tutor List


Math 6730-001: Set Theory, Spring 2023


Syllabus


Course description: 
Presents logic, the axioms of ZFC, cardinal and ordinal arithmetic, infinite combinatorics, and the independence of the continuum hypothesis. Department enforced prerequisites: MATH 4000 or MATH 5000 and MATH 4730 or MATH 5730. Instructor consent required for undergraduates.

For MATH 4000/5000 (Foundations of Mathematics), please be familiar with with the subject at the level of Chapters 0-3 of A mathematical introduction to logic by Herbert Enderton. For electronic access to this text through Chinook follow this link and click on Full Text (via ScienceDirect).

For MATH 4730/5730 (Set Theory), please be familiar with with the subject at the level of Chapters 1-9 of Introduction to Set Theory by Karel Hrbacek and Thomas Jech. For electronic access to this text through Chinook follow this link and click on Full Text (via Taylor & Francis).

Requisites:
Restricted to graduate students only.

Texts/Resources: 
The texts and resources for this course are freely available:
Lectures on set theory; solutions for exercises (J. D. Monk)
Notes on set theory (J. D. Monk)
Set Theory, The Third Millennium Edition, revised and expanded (T. Jech)
Notes on Jech (J. D. Monk)

Homework: 
If you are enrolled for a grade I will ask you to solve some problems. You will be asked to work on the problems in small sets of 2-3. Different sets will be assigned different problems, and sets will change with each assignment. You will typically have a week for your group to solve its assigned problem(s) and submit the solution(s). (This deadline is not strict. but I'll check in with you if I don't get solutions within a couple days of the due date.)

If you are solving Problem M of HW assignment N, please submit the solution as a PDF file called "setsNpM.pdf" (which abbreviates "set theory assignment N, problem M"). At the top of the first page of the solution please include the assignment number and the names of all group members/authors who are responsible for the work. After receiving your solution I will correspond with you about improvements and corrections, if I can think of any. This step in the process should take at most one week. You are not obligated to take any of my advice, but if one of my comments involves a correction, then you should correct that part in some way. For example, if I say "Here is a shorter way to do it", you don't have to change anything unless you want to. If I say "The first displayed equation is wrong. Here is how to fix it …", then you should fix the error, not necessarily along the lines of my suggestion. If you believe that one of my criticisms is incorrect, then you do not have to change your work, but you do have to explain why the criticism is incorrect.

New assignments will be posted regularly starting the second week. Solutions to old assignments will be posted when they are in final form. You should read your classmates' solutions.

Dates: 
MLK Jr (no class): Jan 16 (Monday)
First day of class: Jan 17 (Tuesday)
Last day to drop without penalty: Feb 1 (Wednesday)
Spring Break (no class): Mar 27-31 (Monday-Friday)
Last day of class: May 4 (Thursday)

WWW: 
Information concerning our class will be posted on my teaching web page under the link for Teaching. A copy of any document I hand out in class will be accessible from this page.