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Math 6730-001: Set Theory,
Spring 2023
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Syllabus
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Catalogue description:
Presents cardinal and ordinal arithmetic,
and basic combinatorial concepts, including stationary sets,
generalization of Ramsey's theorem, and ultrafilters,
consisting of the axiom of choice and the generalized
continuum hypothesis.
Department enforced prerequisites: MATH 4000 or MATH 5000
and MATH 4730 or MATH 5730.
Instructor consent required for undergraduates.
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Requisites:
Restricted to graduate students only.
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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)
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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.
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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)
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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.
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