Information for Math 348 Students
Prof. Jill Dietz
Fall '98
About Topology
Goals
I have three main goals for this course. First, you
will learn about three areas of topology: point-set, geometric, and
algebraic. Point-set topology lays the foundation, it sets up the
language used in all areas of topology as well as fields such as
analysis and dynamics. Geometric topology studies how spaces are
built out of complexes (glorified triangles!), and properties of
spaces such as Euler number, genus, etc. Finally, algebraic topology
relates topological spaces to groups and other algebraic objects.
Group theory can then lead to an
understanding of the nature and behavior of a topological space.
A second goal is to help you refine your ability to read and write
proofs. Theorem/proof writing is the method by which high-level
mathematics is communicated. In addition, mastering the logic and
language that are
involved in proof-writing is a skill that
will certainly help you in whatever career you choose to have after you
leave St. Olaf.
Finally, you will be asked to do a project on any one of a number of
topological topics. Doing research and then presenting your findings
is another skill that will help you in your future career.
Prerequisites
You need to have taken either ERA or Abstract
Algebra. If you have not taken algebra, I will teach the group theory
necessary for understanding the algebraic topology we will cover.
Class Structure
As with most 300-level courses, topology will be driven by lectures.
There will be some opportunities for in-class problem solving as well
as presenting. Most exciting of all will be the days when we get to
play with Fisher Price toys, softballs and donuts!
Requirements
Your final grade will be based on the following: homework
assignments, a final project, and three exams.
Homework is likely to be assigned weekly. I'm guessing that it will be
due on Tuesdays.
Project
We will end the semester with presentations of projects. Early in the
semester I will give you some topic ideas, or you may choose one of
your own. The only stipulation is that the project relate to topology
in some tangible way.
Throughout the semester I will ask about your progress on the
project. First I will ask for your idea and sources, later I will
want an outline, a first draft, etc. Dates for these assignments will
be determined later.
There will be three take-home exams during the semester. Dates for
these will be determined later.
Your final grade will be determined by:
| Homework | 20%
|
| Project | 20%
|
| 3 Exams | 60%
|
Miscellaneous Items
Participation
In order for this particular course to be successful, I hope that you
all will fully participate in the class activities. I would like you to
- be prepared for class,
- be willing and able to work on problems in class as required,
- submit homework assignments on time,
- be willing and able to ask and answer questions,
- bring a good attitude to class everyday.
As you might guess, the math clinic does not provide support for
topology students. Your only hope for help is me. Check my
office
hours
for official times I'll be available during the semester, or
simply swing by my office when you're in the neighborhood and see if I
have time to answer a question or two.
Honor Code
There is an honor system by which all St. Olaf students must abide. I
expect you to follow the system in conjunction with my particular
course, homework and exam guidelines written throughout this document
and discussed in class.
Make-up Policy
If you are absent because of an extra-curricular activity, homework
and exams should be submitted early rather than late. If you
are sick or have some other sort of emergency,
you must notify me immediately. In such a (legitimate) case,
homework will be due two days after you return to class and
exams must be made-up within one week. Note that a make-up exam will
potentially be harder than the original exam.
E-Mail
I expect all of you to read your e-mail on a regular basis. From
time to time, I will send you notes regarding homework, exams, etc.
You are responsible for reading these notes.
Disclaimer