Department of Mathematics Department of Mathematics
Math 4171 Topology I
Syllabus Fall 2013

& Office

Ron Freiwald,
Cupples I, room 201

Tuesday 9:30-10:30, Thursday 10:30-11:30, Friday 9:30-10:30

The office hours may change during the next few weeks, in which case I'll notify the class.  If you're planning to stop by, it may be best to check with me by email in advance.  Because of some home remodelling, I may need to rearrange office hours on short notice to work with my contractors.  Usually, I'll know my shedule at least a few days in advance.  This inconvenience will end after about a month.

You're also welcome to ask whether I have some time whenever the lights are on in my office; or to email me about a possible special appointment.


Homework and Exams

There will be 6-8 homework sets during the semester. Homework assignments will be posted on this web page. Usually, an assignment will be due in class at the third lecture after the assignment is posted online: for example, an assignment posted on Tuesday is due in class a week from the following Thursday. 

Some of the homework problems are fairly routine, but others are more challenging. Usually, you can't put them off until the night before they're due.

Most homework problems will be read by a grader. However, on several homework sets during the semester, I will select a problem (after homework is turned in) that I will grade myself.  Your total accumulated score on the homework problems that I grade will count as "Exam 4."  Your accumulated score on the remaining homework problems will count as your homework score.

Homework I: Due in class on Tuesday, September 10
Solutions for Homework 1
Homework 2: Due in class on Thursday, September 19
Solutions for Homework 2
Homework 3: Due in class on Tuesday, October 1Solutions for Homework 3
Homework 4: Due in class on Tuesday, October 15Solutions for Homework 4
Homework 5: Due in class on Thursday, October 24Solutions for Homework 5
Homework 6: Due in class on Tuesday, November 5Solutions for Homework 6
Homework 7: Due in class on Tuesday, November 19Solutions for Homework 7
Homework 8: Due in class on Thursday, December 5Solutions for Homework 8
Some practice problems about connectedness

Other Materials

An Alternate Slick Proof of the Cantor Schroeder Bernstein Theorem

One Way Not to Write a Proof

Example with Baire Category Theorem


There will be the equivalent of four exams in the course:

Exam 1 Solutions for Exam 1
Exam 1 Scores
Exam 2 Solutions for Exam 2
Exam 2 Scores
Exam 3 (Final Exam) Final exam, on Tuesday, December 17, 1-3 pm  
OPTIONAL because of extra lectures in reading period
Here's a copy of the final exam from an earlier year. Those taking the final exam can use it as practice; everyone might consider working through it just to tie things together, or to refocus for the second semester.
Final Exam, Math 417 Fall 2009
Final Exam, Math 417 Fall 2009 Solutions
"Exam 4" See description above, under Homework

The dates for Exams 1 and 2) could be moved slightly if a substantial majority of the class wants the change. But if there's an important reason for a change, then I'd like to decide that within about a week so that some students aren't upset by making a change closer to the exam date. 

The "in-class" exam and the final will be "short-answer" -- such things as definitions, statements of theorems, providing examples or counterexamples, and true/false questions.

The “take-home" exam will consist of more substantial questions, analogous to homework problems. On the take home exam, there will usually be some options for you: "answer m of the following n questions

Basis for Grading

The four exam scores and the homework score will each count 20% of your grade.  However, homework assignments are an essential part of the course.  If you neglect the homework, your course grade may be dramatically lowered (regardless of test scores) at my discretion.   I will not have a scale for converting numeric scores into letter grades until the end of the semester.

Academic Integrity

Exams:  During all examinations, both "in class" and "take-home," no discussion or consultation of any kind with any other person or sources, whether in person, electronically, or via the internet, is allowed. The only exception is for questions of clarification that you can request from me.

For the take-home exam, you may consult class notes, the texbook, or any other references for ideas—but any such references must be explicitly documented in your solutions and solutions must be completely written up in your own words.

You should avoid trying to "find" solutions to problems elsewhere: that just undercuts your learning.  Any solutions taken from other sources without good documentation will result in a grade of 0 for the test or assignment and might be cause for a referral to the Academic Integrity Committee.  If you have questions about what is appropriate, please ask me.  

Homework: Students are encouraged to discuss homework assignments with each other; you should share questions and ideas. It is a powerful way to learn the concepts. Each student, however, must write up the homework solutions independently in his/her own words and notation.  One good way to avoid "borrowing too much" from discussions with others is to talk together but not take away any written notes from the conversation.  Suspicious similarities between solution sets may be noted by the grader and may result in a grade of 0 for the homework.

and Biography 

These web pages may be give some interesting historical sidelights on the material.

The MacTutor History of Mathematics Archive
George Cantor
Bertrand Russell
Kazimierz Kuratowski
Kurt Godel
Paul Cohen
Felix Hausdorff
Robert Sorgenfrey
Ernst Lindelof
Augustin-Louis Cauchy
Rene-Louis Baire

Pavel Alexandroff

The Beginnings of Set Theory
The Axiom of Choice

Topology Enters Mathematics

The "Kuratowski 14 Problem"

Background Information

This link will give you some background information about the course.  I e-mailed this link to everyone enrolled a few days before the course began. Read the document now if you didn't receive it earlier.
TuTh 1-2:30 in Cupples I, room 215.  We can also schedule occasional additional meetings to talk about problems if enough people are interested.  Let me know.  

For all lectures, you should be up to date on reading from the textbook, or even a bit ahead. Make notes to yourself about anything you don't understand so you can raise questions.

Textbook & References

The textbook for the course is one that I have written.  It is photocopied, spiral bound and is available at Hi/Tec Copy Center (at the intersection of Big Bend and Forest Park Parkway).  The cost is approximately $16.80 + tax.  The price is set by Hi/Tec to cover the cost of copying and binding + whatever markup they add for selling the notes (and nothing goes to me).

In addition three fairly standard reference texts are:

1. Munkres, James        Topology   QA611 .M82 2000
2. Willard, Stephen        General Topology   QA611 W55 1970
3. Kaplansky, Irving       Set Theory and Metric Spaces  QA248 K36 1977 

Munkres and Willard are standard General Topology texts;  Kaplansky is a nicely written little book; it is a "softer" introduction to set theory and metric spaces, with not much material about topological spaces in general.
Munkres and Willard may be of more interest next semester. These three books should be on two day reserve at Olin Library. 

A few other books that might be useful. They are available in Olin Library but not on reserve:

4. Eisenberg, Murray     Topology  QA611 E53
5. Kahn, Donald            Topology: An Introduction to the Point-Set and Algebraic Areas  
QA611 K32

6. Simmons, George      Introduction to Topology and Modern Analysis  QA611 S49  

Each of these has different emphases and perspective, and none follows the material as I'll present it.