Math 4200: Point Set Topology, Spring 2015
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Instructor: Associate Professor Pete L. Clark, Ph.D., pete (at) math (dot) uga (dot) edu

Course webpage: http://www.math.uga.edu/~pete/MATH4200S15.html (i.e., right here)

Office Hours: Boyd 502, MWF 1:05 - 2 pm, and by appointment

Course Text (strongly recommended) Set Theory and Metric Spaces by Irving Kaplansky

For information on grades, exams and other procedural matters, please consult the course syllabus.
LECTURE NOTES ON SETS

Several years ago I wrote an introduction to set theory for a general mathematical audience at the advanced undergraduate / basic graduate level. I reproduce all of them here. In our course, apart for occasional (and optional) isolated examples and exercises, only the first part will be needed.

Part 1: Finite, countable and uncountable sets. (pdf) (11 pages)
Part 2: Order and Arithmetic of Cardinalities. (pdf) (8 pages)
Part 3: Ordinalities and their arithmetic; von Neumann's ordinals and cardinals. (pdf) (18 pages)
Part 4: Cardinality Questions. (pdf) (3 pages)
LECTURE NOTES ON TOPOLOGY

Real Induction (11 pages)
Ordered Spaces (10 pages)
Metric Spaces (47 pages)
(These last notes are both rough and incomplete and should be updated relatively soon. But I thought you would appreciate having them before the end of the course!)
Tietze and Urysohn (3 pages)
A Manifold Embedding Theorem (4 pages)
Tychonoff's Theorem and Filters (9 pages)
HOMEWORK

Problem Set 0: Tedium on Sets and Functions: Due in class, Friday January 9th, 2015
Problem Set 1: Real Induction: Due in class, Friday January 23rd, 2015
Problem Set 2: First Steps in Space: Due in class, Monday, February 2nd, 2015
Problem Set 3: Ordered Spaces: Due in class, Wednesday, February 11th, 2015
Problem Set 4: Metric Spaces (No More Lulz): Part one due in class Monday, February 23, 2015. Part two due in class Monday, March 2, 2015
Problem Set 5: General Topological Spaces: Due in class, Wednesday, March 25, 2015.
Problem Set 6: Products, Quotients and Manifolds: Due in class, Wednesday, April 8, 2015.
Problem Set 7: More Separation, Connectedness and Local Compactness: Due in class, Monday, April 19, 2015.
Problem Set 8: This is the End: Due in office hours Wednesday, April 29, 2015.

Some interesting -- and perhaps relevant -- links:

Why You Should Be A Math Major

Why Major in Mathematics?

What Can a Math Degree Do For You?, Jaqueline Jensen, Sam Houston State University.