What to Expect
Here is some additional information about the class about what to
expect, how to enjoy the course and do well, and help you decide
whether or not this class is for you.
- I've taught this class twice before, and each time it's gone quite
well. This is a moderately revised version of the course, but it's
sufficiently similar to the old version that I'm pretty confident of
how most things will go.
- This class is listed as an intermediate/advanced (I/A) class.
It's not I/A because we'll be doing super hard, super tricky
math. Rather, it's I/A because of what you'll be asked
to do with some mostly straightforward math. You'll be asked to
think with math and to use math creatively. You will also be
expected to think about the structure of research and improve research
- This class makes extensive use of ideas from calculus. It's
important that you've had both differential and integral calculus
before and felt reasonably good about the experience, although it's ok
if you've forgotten much of it.
- Falling behind in this course is not a good idea. If you're
confused about something, it's very important that you seek help
sooner rather than later. There are many people around who can offer
help. However, we can't offer assistance if we don't know who needs
it when. You need to take responsibility to seek help if you need
- I do not expect all of the homework assignments to be easy; I don't
expect you to be able to sit down and do them easily the first time.
The style of homework assignments in this class might be very
different from what you're used to. Don't let yourself get frustrated
-- I strongly suggest working with others and seeking help if you
- There will be few, if any, quick plug-in assignments. This class
is not so much about mathematical calisthenics. Rather, there will be
only a few problems, but they will be longer, requiring multiple
steps. On many occasions you will be asked to form your own
mathematical model as part of a problem.
- This course is structured to allow you to do a significant project
as part of the coursework. You'll want to start early on this and
keep moving throughout the term. There will be numerous check-points
throughout the term, including an oral presentation during week five.
Falling behind in your project can be disastrous.
- The text we use is "modern" in the sense that the authors
emphasize qualitative, global analysis of differential equations,
rather than specialized analytic tricks. This book makes full use of
available technology; we will use computers without guilt or apology
to help us do mathematics and science. I think these modernizations
are excellent, especially for COA students. However, this might give
the course a different (and hopefully better) feel than other math
classes you've taken.