Informal Description

This is the eighth time I have taught this class. So I have a pretty good idea of how this course will go. Here are some thoughts on the class and how to do well and learn a lot.

  1. Most students find the material in Calculus III to be less difficult and more interesting that that of Calculus I and II. Calculus III basically re-does all of calculus, except with functions of two or three variables instead of just one variable. In the last third of the class we re-re-do calculus for vector fields. This means that along the way we will review and re-affirm concepts and techniques from the first two terms of calculus.
  2. Students who take this class should have had roughly a full year (or two college terms) of calculus. It is important that you've seen both differential and integral calculus and felt like you understood these topics reasonably well at some point. If you feel like you've forgotten a lot of calculus, that's ok.
  3. This class is a lot of work and will move at a fairly brisk pace. However, the workload is steady; you'll be doing approximately the same amount of work each week. We'll hit the ground running and try to get lots of stuff done the next few weeks. The workload may taper off some toward the end of the term, although the material at the end might be a bit more difficult.
  4. This class meets three times a week instead of the usual two. The Wednesday meeting is a normal class session, not a lab. This extra time will let us cover more material and have classtime be a bit more relaxed. It also gives us a buffer in case we miss a day or two due to snow or other winter nastiness.
  5. 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 it.
  6. 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. Don't let yourself get frustrated. I strongly suggest working with others and seeking help if you need it. I also strongly suggest that you start the homework well before it's due.
  7. This year I would like to try using an online homework system. We will use WeBWorK, a system developed by the Mathematical Association of America. It has been in use for quite a few years and is used at many colleges and universities. There are several advantages to an online system:
    1. You get instant feedback while doing the work, so you can learn right away from your mistakes. And on most problems you can submit solutions many times until you get everything correct.
    2. Since the problems are automatically marked, the TAs and I can spend more time helping you and won't have to spend as much time grading.
    3. Some problems are randomized so that you will all get slightly different versions of the questions. This means that collaborating with other students will be maximally effective, since you'll have to share solution methods and not just the final answer.
    I am not certain how WeBWorK will work, but I'm optimistic. I expect there will be some initial hiccups as we get used to the system, but let's give it a few weeks and see how it goes.
  8. In many more traditional math classes the textbook has a ton of examples in them. The book we'll be using doesn't. The result is that students sometimes find the homework to be challenging, frustrating, and occasionally even annoying. However, I'm convinced that this style of homework -- where there's not an example just like the problem you're trying to do -- is much better pedagogically. You'll learn a lot more this way.
  9. Our textbook emphasizes graphical and verbal understanding in addition to being able to work with symbols and numbers. Much of mathematics -- both theory and application -- is graphical or geometrical in nature. The graphical problems are not "lite" problems but are an essential part of the course. The graphical problems are most definitely "real math." Some of you may find graphical work difficult, as it's likely different than some of what you've been asked to do in math classes before.
  10. You will actually need to read the textbook in order to do some of the homework. I won't be able to cover everything in class, and/or you'll just want to see a topic explained in a different way.
  11. I very strongly recommend getting your own copy of the textbook. I think you'll learn more if you have your own copy to take notes in and always have with you when you're doing problems. An important part of introductory science and math classes is forming a strong, long-term relationship with some textbooks.
  12. We will make use of computers to help us do math. We will use the website WolframAlpha. I think you'll like it. These days pretty much anyone who uses math in some meaningful way in research needs to be good at "pencil-and-paper" math and overall mathematical thought, and facile with a variety of computer programs and applications.