Dr. Sarah J. Greenwald

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

Develop problem solving and proof-writing skills

Be exposed to the history, usefulness and applications of topology.

Math 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".

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 project topic 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.

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.

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.