Good advice

I've just finished typing up my 280 students' responses to the final question on their exam: "Please compose a brief statement detailing any advice you would like to give to someone taking 280, to be given to the student on the first day of class. You can be as specific or as general as you like, but please be sure that your response offers honest and thoughtful advice to a new 280 student." The advice will indeed by posted on the website for the Fall 2009 MATH 280 class, and it will be the first reading required of the new 280 students.

The advice ranges from comical ("I recommend keeping a running total of how many times Professor Bahls yells, throws a chair, drops a table, ...or does anything else that startles or amuses you") to metaphysical ("I also found that meditation helps out a lot"), hitting nearly every point in between. Some of the advice is, shall we say, idiosyncratic enough that it might not prove so useful to anyone but its purveyor; other advice is solid.

One thing I noticed about the advice this group has offered to future generations of 280 students is its general practicality: it's very focused on the basic "mechanics" of homework completion and class survival. For instance, the several students emphasize things like starting the homework early, unfailingly attending class, and asking questions of the professor as the keys to academic success; surely this is good advice, but it's hardly different from that one would offer to a student about to begin any other class.

What is it about 280 in particular that makes it such a difficult class? And what specific advice might one offer to a new 280 student, as opposed to one ready to begin Language 120 (our first-year composition course) or Humanities 124?

The students had a few words to say about this. I'll be posting the full text of the students' advice on the website for the Fall 2009 280 course in due time.

For now, below, I've compiled a laundry list of things I want to be sure to tell next semester's students, early and often; admittedly the list betrays my own personal bias, but I think every item is a worthwhile bit of wisdom:

1. Write. Write to communicate, write to learn. Write knowing that every jot and tittle of every bit of notation means something precise, something definite. Write clearly, and keep an eye on your composition. A proof, even a correct proof, is meaningless if it's not also clear and well-composed. But don't forget that writing is an iterative process, and that rough drafts are meant to be rough. In all likelihood, your first draft will be shit, but it's important to get it out in front of you so that you can work on cleaning it up.

2. When faced with a new problem, write down what you know and what you need. Often 50% or more of the solution of the problem consists of formulating a clear statement of the problem's hypothesis and a clear statement of its conclusion. Once those statements are on paper (literally) in front of you, often the path you must take to connect the two becomes evident.

3. Trace out that path in baby steps, applying a single definition at a time, a single logical inference at a time. Don't combine steps or take more than one at a time until you are fully confident that you've not misstepped. Most of the mistakes you make will be made when you attempt to take big steps or to skip them altogether; the smaller the steps you take, the likelier you'll be to stay on course. If you're not sure about something you've written, read it out loud.

4. When in doubt return to the definition. As noted above, every symbol, every term, every penstroke means something, and something definite: if you're not sure what that something is, look it up.

5. Work together. Very few are the problems in mathematics for which a single solution is known. Moreover, there are manifold viewpoints on any single solution to a given problem, and it's likely your friends' viewpoints will differ dramatically from your own. In working together you can more easily combine your viewpoints to create a richer picture of the problem with which you're all faced.

I'll leave it at that, as the best lists of advice are short lists of advice. For now, it's bedtime.

Coming soon: the follow-up to Newton v. Leibniz, further reflections on the current graduating class. and more!