Syllabus for Math 461

Fall Semester 2006

Background and goals: This course is designed primarily for undergraduates intending to go to graduate school in mathematics, statistics, or engineering. Some beginning graduate students in these areas may also take this course. Although students will need some background in writing proofs, one of the principal goals of the course is to improve proof-writing skills.

Textbook: Elementary Topology, by Michael Gemignani. We will cover most of Chapters 2-4 and 7-9 of the book.

Prerequisites: MTH 320 or MTH 428H. Recommended: MTH 310.

Grading Scheme

The main components of the final grade are homework, exams, and an in-class presentation. (The test dates are tentative for now.)

Component Date Worth
Homework Wednesdays 30%
Midterm Exam October 13 25%
Presentation Various 15%
Final Exam December 12 30%

Policy on missed work. The only valid reasons for missing an exam are: (1) illness, or (2) a conflicting University activity that cannot be rescheduled. Claims involving such contingencies must be supported by verifiable documentation signed by: (1) your physician in case of illness, or (2) your faculty supervisor in case of a non-rescheduleable University activity. Each case will be handled on an individual basis.

No late homework will be accepted. However, I will drop your lowest homework score.

Homework Policy

Homework assignments will be posted on the course webpage, and will typically be due on Wednesdays. No late homework will be accepted. I encourage you start early and work in groups. There are only a couple of caveats to group work:
  • You should try to do all of the problems on your own before getting together with others. It does not benefit you (on exams and in the real world when you need to use math) to simply get solutions from your classmates! In fact, there is research suggesting that group work is much more productive when everyone has thought about the problems before getting together.
  • Everyone must turn in their own solutions. In other words, you should write up your final solutions in the privacy of your own room (or your own library, cafe, bar, roof, etc.).

Here are a few guidelines for how to write up the proofs:

  • Write up the problems in order, using only one side of the page and leaving lots of space for me to write comments. Please staple your sheets together.
  • Begin each problem with a statement of that problem.
  • Proofs should be written in complete sentences, with appropriate use made of mathematical notation (your textbook will serve as a guide to how to do this). Proofread what you've done to be sure that it's complete and makes sense. Remember that proof-writing is above all an act of communication, and that the ultimage goal is clarity.
  • If you leave a small gap in a proof that you're not able to fill in, note this down. I'll try to indicate how to fill it in my comments.
  • Start early! This way, if you are stuck, you can still discuss the problem with other students or with me.


Toward the end of the semester, every student will have to give a 20-minute in-class presentation on a self-contained topic in topology. The purpose of this is two-fold. First of all, this field of math has many interesting examples and special topics that don't fit neatly into a linear exposition. These presentations are a way for all of us to be exposed to these ideas. Second of all, these presentations are intended to help you practice the art of explaining difficult concepts. The ideas of mathematics and the related quantitative sciences are hard enough that it becomes very important to communicate them clearly. In fact, I've found that having to explain something makes me understand it on a much deeper level.

We will start scheduling student presentations in late October or early November. You should definitely discuss the topic with me before presenting it. I would also be more than happy to suggest topics for presentations.

Academic Integrity

Students are reminded that the University's policy concerning academic integrity is covered in the Spartan Life booklet, General Student Regulations. According to the handbook, "no student shall claim or submit the work of another as one's own".

Important Dates

9/1/06 Open add period by computer enrollment ends.
9/21/06 Last day to drop with no record of course on transcript; end of tuition refund period.
10/17/06 Last day to drop a course or withdraw from all courses with no grade reported.

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dfuter at temple edu
Last modified: Wed Aug 23 14:31:53 PDT 2006