Fall 2003 Introduction to Topology
Dr. Sarah J. Greenwald
Where to Get Help
326 Walker Hall,
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.
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.
You are responsible for reading all posts - you should check the bulletin
board at least once a week.
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.
I usually check the newsgroup numerous times every day including the
Foundations of Topology by Patty
text available in the bookstore
Access to a web browser at least once every 36 hours.
An introduction to topology via a selection of topics from
chapters 1-4 of the textbook and additional topics as time allows.
Develop problem solving and proof-writing skills
Be exposed to the history, usefulness and applications of topology.
has been designated as a
speaking intensive designated (S)
course, which means that
amount of the graded work be in oral presentations prepared outside of class".
Review proof-writing techniques
via puzzles and games related to topology and/or
specific proof-writing goals
Technical language of topology - the language of mathematics. Metric spaces and topological spaces, bases, closure, interior and boundary, convergence,
continuous functions and homeomorphisms, subspaces, products and quotients, connected and compact spaces (additional topics as time allows).
Semester long project - Each person will choose a
related to topology. There will be numerous
oral and written assignments during the course
of the semester related to the project
which will culminate in a final presentation.
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
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.
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
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
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.