## Spring 2007 Introduction to Topology
Math 4710/5710

Dr. Sarah J. Greenwald

### Where to Get Help

**Office Hours**
326 Walker Hall,
262-2363.
I am always happy to help you in office hours. An open door
means that I am on the floor somewhere, so come look for me.

**
http://www.mathsci.appstate.edu/~sjg/class/4710/s07.html**
**Check this main web page often for work due (at least twice a week).**

**WebCT Postings** This is the
easiest way to ask a math question outside of class and office hours. At
times I will respond to the entire class, so **you are
responsible for reading all posts**.
I prefer that you use office hours since it is easier to discuss
material in person, but if you can not make them, then the newsgroup
is a great alternative.
### Required Resources

*Topology* by Munkres (2nd edition)
rental text available in the bookstore

*Introduction to Topology* by Mendelson available for purchase
in the bookstore.

Access to a web browser at least once every 36 hours.
### Catalog Description

A study of the basic concepts of general topological space including such topics as compactness, connectedness, product spaces, metric spaces, and continuous functions.
Prerequisite: MAT 3110 or MAT 3220 (SPEAKING).
### Course Goals

An introduction to point set topology, including exposure to the history,
usefulness, and applications of topology.

Develop problem solving, proof-writing, and mathematical communication
skills

Mat 4710
has been designated as a
speaking intensive designated (S)
course, which means that
"a substantial
amount of the graded work be in oral presentations prepared outside of class".
### Receiving Graduate Credit

In order to receive credit for 5710, graduate students who are enrolled
will complete extra grad problems on the problem sets as well as
an additional paper based on their semester long project
topic.
### Grades

### Other Policies

Material is covered very quickly.
**Plan to spend 6-10 hours
per week, outside of class, on average, on this course.**
You are responsible for all material covered and all announcements
and assignments made at each class, whether
you are present or not. You are also responsible for announcements
made on the web pages, so check them often.
When writing up work, be sure to give acknowledgment where it is due.
Submitting someone else's work as your own (PLAGIARISM) is a serious
violation of the University's Academic Integrity Code.

### Methodology

Asking questions, and explaining things to others, in or out of class,
is one of the best ways to improve your understanding of the material.
This course is to be an environment in which everyone
feels comfortable asking questions,
making mistakes, offering good guesses and ideas, and is respectful to
one another.
You should explore each problem
and write out your
thinking in a way that can be shared with others.
Focus on your own ideas.
Turn in projects or prepare to present problems
even if it they are not complete, even if only to say, "I do not
understand such and such" or "I am stuck here."
Be as specific as possible. Conjecture.

In this course, you will be challenged with problems that you have never
seen before. I do not expect you to be able to solve all the issues
immediately. Instead, I want to see what you can do on your own.
Out in the real world, this is important, since no matter what job
you have, you will be expected to seek out information and answers
to new topics you have not seen before.
This may feel uncomfortable and frustrating. I understand this
and want to help you through the process.
It helps to remember that
there are no mathematical dead-ends!
Each time we get stuck, it teaches us
something about the problem we are working on, and leads us to a
deeper understanding of the mathematics.

In the real world though, you are not expected to face your work alone.
You will be allowed to talk to other people
and you
may even be expected to work with other people.
In this class, you are also not expected to face your work alone.
I encourage you to talk to me often in class, office hours,
and the bulletin board.

I am always happy to help you in class, during office hours (or by
appointment), or on the WebCT bulletin board, and will
try to give you hints and direction.
At times though, to encourage the exploration process,
I may direct you to rethink a problem
and to come back to discuss it with me again afterwards. This occurs
when I believe that the struggle to understand is imperative for your
deep understanding of the material.