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.


  • Participation in Classroom Activities 20% You are expected to contribute to discussions in a meaningful way and actively engage the material in class and lab. You must be prepared for each class and check the main web page regularly for hw. Attendance is required. This means that when we are doing a calculation, you must also do this, and you are expected to take notes since the book does not contain everything you need to know. These kinds of baseline activities will result in a participation grade of 16/20. Other activities can increase or decrease this grade. Asking and answering thought provoking questions, coming up with creative ways of thinking about the material, and explaining the material to others are some examples of positive participation that will increase your grade. On the other hand, performing activities that detract from the professional classroom environment will result in a lowered participation grade. Many activities and class discussions are designed to be completed during class. Thus, attendance is required at ALL classes, and will form a portion of your grade. Missing more than 9 credit hours will result in an automatic F in the course. Save your absences for emergencies. If the university is open and you miss a class, then that counts as an absence. If you must be late to a class, or must leave early, then do still attend. As part of the speaking designator, you are expected to contribute to discussions and may be called on to participate.
  • Homework and Projects 40% You may be required to present and/or turn in your work. 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 project will be dropped - save this for emergencies. If all of your problem sets are turned in on time AND you have received at least 75% credit for all work, then you will receive an extra credit of +1 added on to your final average. No late work will be accepted. May occur the last week of classes. Final Project Presentations Monday April 30th from 12-2:30 (as we agreed upon in class - we have permission from the dean's office).
  • Tests 40% Tests are designed to reinforce the material. May occur the last week of classes. No make-up exams will be given.

    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.

    * Work may occur during the last week of classes. Accommodations in the determination of your final grade will be made for extenuating circumstances that are documented to prevent you from completing work early/on time.
  • 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.