Fall 2011 Introduction to Topology Math 4710/5710
Dr. Sarah J. Greenwald

Where to Get Help

Office hours, 326 Walker Hall, 262-2363. Sometimes, if no one comes to office hours, I go down the hall to the mailroom, photocopy machine, or to talk to another professor. If I am not in my office during office hours, you should walk down the hall to look for me, and interrupt to tell me that you are there. I am always around and happy to help you during office hours unless otherwise posted to the webpage. You do not need to make an appointment to use office hours - just drop by! If you can't make office hours, message me on ASULearn, which will be answered at least once a day.

ASULearn Messages are the easiest way to ask a math question outside of class and office hours. I prefer that you use office hours since it is easier to discuss material in person, but if you can not make them, then this is a great alternative. Sometimes I may respond to questions of interest with a message to the entire class, so you are responsible for reading all posts by me. I usually check the posts at least once a day, including the weekends.

Required Resources

Topology by Munkres (2nd edition) rental text available in the bookstore
i-clicker available for rental from the bookstore.
Introduction to Topology by Mendelson available for purchase in the bookstore.

Check the tentative course calendar often for work due and any changes (at least twice a week).

Catalog Description

A study of the basic concepts of general topological spaces including such topics as metric spaces, continuous functions, connectedness, product spaces, and compactness. Prerequisite: MAT 3220. (SPEAKING)
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 as well as an additional paper based on their semester long project topic.


  • Participation in Classroom Activities 15% You are expected to contribute to discussions in a meaningful way and actively engage the material in class. 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 12/15. 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 6 classes 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 30% 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. No late work will be accepted. The lowest homework will be dropped - save this for emergencies. If all of your work is 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. Work may occur the last week of classes.*
  • Tests 30% Tests are designed to reinforce the material. No make-up exams will be given*
  • Final Project 25% No make-ups allowed* You must participate in the final project to pass the class.

    Undergraduates can receive extra credit by successfully completing grad problems. When final grades are given, extra credit points are taken into account in the determination of -, nothing, or + attached to a letter grade.

    *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. The grading scale is the same as the one in ASULearn grades: A ≥93; 90≤ A- < 93; 87 ≤ B+ <90...

    Also see the University-wide syllabus and policy statements which we adhere to.

  • 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 in an ASULearn message, 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.