Instructor         Ron Freiwald
Office               203A Cupples I
Office Hours    Tu-Th 2:45-3:30, W 1:30-2:30, and by appointment
Phone               935-6737

Text   General Topology, Steven Willard (out of print; I'll have loaner copies available for everyone.) There are a number of good books available but Willard is the closest to the way I want to handle the material.

In Math 417 we covered most of the material in Chapters 1,2,4,5,6 of Kaplansky's Set Theory and Metric Spaces. Topics we skipped will be covered in Math 418. We have also covered Sections 1.1-3.7, as well as some material from Chapter 7
of Willard's text.   You should probably quickly read Sec. 1.1-3.7 of Willard, to warm up and to get used to the book.

Topics for Math 418 include connectedness, products and quotients, embedding theorems, separation axioms, some of the major classical theorems of general topology (for example, Urysohn's Lemma, Tietze's Extension Theorem, and the Tychonoff Product Theorem), and some additional set theory (ordinal numbers and transfinite methods such as transfinite induction and Zorn's Lemma), and compactifications.  If time permits, we may also do a brief look at some "nonstandard" analysis (theory of infinitesimals) as an interesting "application" of set theoretic methods.

Exams    As in Math 417, there will be the equivalent of four exams:

                        1) Exam 1       In class, Tuesday, February 27
                        2) Exam 2       Take-home, given out in class on Thursday, March 29 and
                                                                  due on Tuesday, April 3
                        3) Exam 3      See under Homework
                        4) Exam 4       Final exam, on Friday, May 4, 1-3 pm

Exams 1 and 4 will consist of such things as definitions, statements of theorems, examples and counterexamples, and true/false questions. The "take-home" exam will consist of more substantial questions, analogous to homework problems.

Homework

There will be 6-8 homework sets during the semester.  Some of problems are fairly routine, but many are quite challenging. During the course of the semester, I will choose approximately 6 homework problems at random after the homeworks are submitted and grade those problems myself.  The remaining homework problems will be handled by a grader.

Your total accumulated score on the homework problems I grade will count as "Exam 4".  Your accumulated score on the remainder of the homework problems will count as your homework score.
 

Basis for Grading

The four exams and the homework will each count about 20% of your grade. Homework assignments are an essential part of the course. If a student neglects these, the course grade may be dramatically lowered (regardless of test scores) at my discretion.  There may be an additional requirement of an oral presentation of a paper as a necessary condition (not necessarily sufficient) for a grade of A- or better.  This would not happen, in any event, until about the last month of the course, so I'll let you know what I decide by sometime before spring break.
 

Academic Integrity

In an examination room and on take-home Exam 2, no discussion or consultation of any kind with any other person is permitted.

It is understood that on any take-home work (tests or homework)  you may consult class notes, the text, or any other references, provided the other references are explicitly documented. Any solutions taken from other sources without documentation will result in a grade of 0 for the test or assignment. If you have questions about what is appropriate, please ask me.

Students are encouraged to discuss homework assignments with each other, to share questions and ideas. This is a powerful way to explore the material. Each student, however, must write up the homework solutions independently in his/her own words and notation. Suspicious similarities between solutions sets may be noted and may result in a grade of 0 for the homework.
 

Web Pages

The following web pages may be give some interesting sidelights on the material.

The MacTutor History of Mathematics Archive

George Cantor
Bertrand Russell
Ernst Zermelo
Adolph Fraenkel
Kurt Godel
Paul Cohen
Felix Hausdorff
Kazimierz Kuratowski
Ernst Lindelof
Augustin-Louis Cauchy
Rene-Louis Baire
Pavel Alexandroff
Andrei Tychonoff
Paul Urysohn
Heinrich Tietze
Ernst Zermelo
Max Zorn
Julius Konig
Richard Dedekind

The Beginnings of Set Theory
Home Page for the Axiom of Choice
Axiom of Choice (the music)
Topology Enters Mathematics

Bibliography

The following is a brief bibliography you may find useful. The first two books are probably more helpful for Math 417 than the others, which are more suited to Math 418.  I have requested that the boldfaced books be placed on reserve at Olin Library.
 

Dugundji        Topology
Eisenberg      Topology
Munkres        Topology
Sierpinski        Cardinal and Ordinal Numbers
Wilansky       Topology for Analysis
Willard            General Topology