Text: Mathematical Experimentation: A Laboratory Bridge Course available from the Mathematics Department at cost.
General Plan
We will work on five of the units in the text, spending roughly two weeks on each of them. I'll give a brief introduction to each unit, and we'll go around the class at the start of each day for a brief report on where you are in the investigation. Most of the time you can be working in groups or alone, as you choose, but talking with others (including me) in any case. At the end of each unit, you'll turn in a written report (this has to be your own writing, of course) in your best mathematical style. Expect to rewrite that report at least once, since good, clear, logical exposition is one of the chief goals of this course. Once it is good enough and clear enough, I'll check it off, but not until! In addition, in the course of the semester, work on a sixth unit of your own choice, and instead of a written report, give a 15 minute talk to the class. We'll schedule the talks in the last two weeks.
A very good practice is to keep a bound notebook, like a logbook, in which you enter, as it happens, a record of all the things you do, including especially computer experiments. It need not be nice and neat -- in fact, it is far more likely to be a mess, with false starts, returns to original ideas, etc. The point is that it is all there, in chronological order, and bound, so that loose sheets do not get lost. You can impose order on it later. And you will be glad to have everything in one place! You aren't keeping the notebook for anyone else -- you're keeping it for yourself.
The purpose of this class is not so much that I teach you something as that you learn by your own inventive efforts. I see myself more as a kind of "coach," suggesting where you should put your efforts, and even "pushing" a little.
Grading
If you check off all 5 written papers and give an adequate talk, you will get at least a B+. For any kind of A you should also work on interesting content. For example, you should address the major questions raised in the text on that unit, and show that you have been inventive yourself in raising your own questions.
Style
Good mathematical style is clear, not too stiff, and not verbose. Above all, it should be logical and correct. Here is where I imagine you may find yourself rewriting, and striving to say things more precisely -- it is not so easy! This is where I think I can help you most, and where you may ultimately find this course especially valuable, at least I hope so. Plan to use LATEX to do your reports. The program WINEDT is an excellent text editor and toolkit for doing this, and I think you'll be very pleased to see how professional your mathematical writing looks. Don't refer explicitly to the questions in the unit, even if you organized your investigation around these questions. Write an essay-like paper in which all the motivation comes from within. For the final talks, we'll schedule a rehearsal and I'll go over your talk with you before you give it to the whole class. Here too it's only natural to expect that you'll find yourself making changes, polishing, improving in the course of getting it ready.