Arts and Sciences

Department of Mathematics
Fall 2009
Math 417 Syllabus
Introduction to Topology and Modern Analysis (I)


Homework 1: Due in Class Thursday, September 10Homework 1 Solutions
Homework 2: Due in Class Tuesday, September 22Homework 2 Solutions
Homework 3: Due in Class Thursday, October 1Homework 3 Solutions
Exam 1 and Solutions
Exam 1 Scores
Homework 4: Due in Class Thursday, October 15
Hint for HW 4
Homework 4 Solutions
Homework 5: Due in Class Tuesday, October 27Homework 5 Solutions
Homework 6: Due in Class Thursday, November 5Homework 6 Solutions
Exam 2 and SolutionsExam 1 and 2 Scores
Homework 7: Due in Class Thursday, November 19Homework 7 Solutions
Homework 8: Due in Class Thursday, December 3Homework 8 Solutions
Some Optional Problems on Connectedness


The Final Exam will be given on Wednesday, December 16, from 1-3 p.m. in the usual classroom (Cupples I, room 218).

The style of the exam will be similar to Exam 1:  for example, statements of definitions and theorems, example, lots of true/false questions.  All questions will be of the "short-answer" variety.

Questions will focus on Chapters 3-4 and the material we covered in 5. Of course, there are things that you will need to know from Chapters 1-2 in order to answer these questions but I will not be "directly targeting" material from Chapters 1-2.


I will keep my regular office hours (see below) up until the day of the final.  But there will probably be other times when I'm available too.  E-mail me if you need an appointment.


InstructorRon Freiwald
My OfficeCupples I, room 203A
My Office Hours
Special: 3-4 on each of:  Thursday August 27;  Tuesday, Thursday September 1, 3; and Tuesday September 8.  

Thereafter, until the end of the first semester:  M 10:30 - 12:00  and W 11:30 - 12:30 on days when classes are in session, and by appointment.

Lectures 
TuTh 1-2:30 in Cupples I, room 218.  We can also schedule special meetings to talk about problems if enough people are interested.  Let me know.  

For all lectures, you should have read through all the notes handed out in the preceding class.  Make a note to yourself about anything you don't understand, particularly for the part of those notes that I have already covered in a lecture.

Background Information
This link connects you to a document with background information about the course.  I e-mailed this document to everyone enrolled a few days before the course began. Read the document now if you didn't receive it earlier.

Textbook
The textbook for the course is one that I have written.  It will be photocopied two-sided, on punched paper and distributed by installments in class (since I continue revising and correcting each time I use it).  I recommend that you get a three-ring binder to hold these pages.  There will be about 100-125 sheets (so, 200-250 printed sides) each semester. 

There will be a charge of $10.00 each semester to cover the cost of paper, toner and copying time.  You can pay this charge to the secretary in the Mathematics Department Office (Cupples I, room 100). She will give me a list of the people who have paid.  The office will accept a check made out to “Washington University Department of Mathematics” or cash  (but the exact cash amount is required; the Office cannot “make change”).  I will distribute the first 20 pages or so free of charge so that there's no rush; but please try to make your payment by Friday, September 4. 

Some fairly standard reference texts that are available in the library are

Kaplansky, Irving        Set Theory and Metric Spaces
Willard, Stephen        General Topology
Munkres, James        Topology
Kahn, Donald            Topology: An Introduction to the Point-Set and Algebraic Areas
Simmons, George      Introduction to Topology and Modern Analysis       

Eisenberg, Murray     Topology

Each of these is quite different, and none follows the material as I'll present it.

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

         1)   Exam 1    Tuesday, October 6  (in class)
         2)   Exam 2    Take-home, given out in class on Thursday, November 5 and due in class
              Tuesday,   November 10.
         3)   Exam 3    Final exam, on Wednesday, December 16, 1-3 pm
         4)  "Exam 4"   See description under "Homework"

The dates for 1) and 2) can be moved slightly if a majority of the class wants the change.  However, if there's going to be a change, I'd like to decide that within about a week so that some students aren't upset by a sudden change later.

The "in-class" exam and the final will be "short-answer", consisting of such things as definitions, statements of theorems, giving examples/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.  Usually these will be distributed in class and will be due in class three lectures later.  Some of the homework problems are fairly routine, but many are quite challenging.

Most homework problems will be read by a grader. However, on about 5-6 homework sets during the semester, I will select a problem (after homework is collected) and grade that problem myself. 
Your total accumulated score on the homework problems I grade will count as "Exam 4".  Your accumulated score on the remaining homework problems will count as your homework score.

Homework assignments will be posted on this web page.


Basis for Grading
The four exam scores and the homework score will each count about 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

During examinations "in class" and on take-home Exam 2,  no discussion or consultation of any kind with any other person (including internet or other electronic communication) is permitted.  You may consult class notes, the text, 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 referral to the Academic Integrity Committee.  If you have questions about what is appropriate, please ask me.

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 handy way to avoid "borrowing too much" from sessions with others is to talk together but not take any written notes away 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.

Web Pages

The following 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"