Fall 2003 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/ 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 weekends.

Required Resources

Foundations of Topology by Patty text available in the bookstore
Access to a web browser at least once every 36 hours.

Course Goals

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.
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".


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 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.

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.


  • Participation in Classroom Activities 20% There will be days when the activities are designed to be completed during class. Thus, attendance is required at ALL classes. Missing more than 2 classes (official and/or unofficial absences) will result in a lower participation grade. Missing more than 6 classes will result in a grade of F. An incomplete will be granted only in university justified cases. Save your absences for emergencies. As part of the speaking designator, you are expected to contribute to discussions and may be called on to participate.
  • Problem Sets 35% You may be required to present and/or turn in your work in writing. Work will not be accepted without explanation and must also be turned in on or before the due date. If there is some reason you must miss a class, then obtain the assignment from the web pages. The lowest problem set will be dropped - save this for emergencies. Every other problem set will be equally weighted regardless of the total number of points. If all of your problem sets are turned in on time AND you have received at least 65% credit for all work, then you will receive an on-time credit of +1 added on to your final average. No late work will be accepted. May occur the last week of classes.
  • Tests 15% Tests may be oral, written or on WebCT and are designed to reinforce the material. May occur the last week of classes.
  • Semester Long Project 30% -- Final Project Presentations Tuesday December 16 3-5:30 pm No make-ups allowed. Part of this project may occur the last week of classes.
  • Extra credit There will extra credit opportunities during the semester for which points will accumulate. When final grades are given, extra credit points are taken into account in the determination of -, nothing, or + attached to a letter grade. Undergraduates can receive extra credit by successfully completing grad problems.
  • 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.


    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.