Arts and Sciences


Department of Mathematics
Spring 2007
Math 418 Syllabus
Introduction to Topology and Modern Analysis (II)

Instructor               Ron Freiwald

My Office               203A Cupples I
My Office Hours     M 2:30-3:30, W 9:30-10:30 (between January 16 and May 9), and by appointment
Office Phone         314-935-6737

Lectures                TuTh 1-2:30 in Cupples I, Room 111
                              We can also schedule special meetings to talk about problems if enough people are interested.

   
Announcements, Homework, etc.

If you have a copy of the Kaplansky textbook, you should read (if you haven't)
Chapter 1 (omitting Section 1.3)

Chapter 2 up through p. 34.
  (You can read the rest of Chapter 2 if you like.  But it coveres and uses Zorn's Lemma -- an important too but one which I won't discuss until later.  With Zorn's Lemma, some of the results about cardinal arithmetic that (for now) I omitted can be proven).

Chapter 4 and Chapter 5

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.

Homework 1
Homework 1 Solutions
Grader Comments
Homework 2
Homework 2 Solutions

Homework 3
Homework 3 Solutions


Homework 4
Homework 4 Solutions

Homework 5
Homework 5 Solutions

Homework 6
Homework 6 Solutions
Homework 7
Homework 7 Solutions


Exam 1 and Solutions
Exam 2 and Solutions
Final Exam and Solutions


          


"Textbook"            Notes will be given out, just as last semester.  There may be an occasional recommended reading from Set Theory and Metric Spaces, Kaplansky (Chelsea Publishing)


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

                        1)  Exam 1    Tuesday, February 27  (in class)
                        2)  Exam 2    Take-home, given out in class on Thursday, March 22 and due in class
                        Tuesday,  March 27..
                        3)  Exam 3    Final exam, on Tuesday, May 8, 1-3 p.m. (Location TBA)
                        4) "Exam 4"   See description under "Homework"

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 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, about 6 times during the semester, I will select a problem from your most recent homework (after it's handed in) 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.


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 a student neglects these, the 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 is permitted.

It is understood that on any take-home work (tests or homework) a student may consult class notes, the text, or any other references—provided the other references are explicitly documented.  Generally speaking, you should avoid trying to "find" solutions to problems elsewhere.  Any solutions taken from other sources without 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
Robert Sorgenfrey
Felix Hausdorff
Ernst Lindelof
Augustin-Louis Cauchy
Rene-Louis Baire
Pavel Alexandroff
August Ferdinand Moebius             
Andrei Tychonoff
Paul Urysohn
Heinrich Tietze
Ernst Zermelo
Max Zorn
Julius Konig
Richard Dedekind


The Axiom of Choice


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 all of the books be placed on overnightreserve at the Math Library (in the basement of Cupples I).

Dugundji: Topology
Eisenberg, Murray:  Topology
Gillman & Jerison: Rings of Continuous Functions
Kahn, Donald W:  opology: An Introduction to the Point-Set and Algebraic Areas
Munkres, James: Topology  
Sierpinski: Cardinal and Ordinal Numbers
Willard,Stephen: General Topology    
Some of these books are "old classics" and some (such as Munkres) are more recent.