Prepping for a Math Final

It's taken seven semesters, but I think I've finally figured it out. While it's a great thing, I wish I knew a while ago what I know now.

The basic process is like this:

1. Find during the semester another textbook in the area. Classic books in the area are usually a good choice.
2. The prof (or experience) should indicate what the spread of material is for the test.
3. Go through the other book, identify each relevant section, and work as many problems as possible from that book, using its examples and exposition.

If done right, this should result in you having retaught yourself the entire course in a week or two from a different but similar perspective.

The remaining problem is textbook selection. This is tougher. For my compex analysis course, we used Saff and Snieder's book and I prepped out of Churchill. It turns out Churchill is so cannonical that Saff and Snieder is in some sense equivilent to it. This turned out really well since the prof followed the book very closely and specified the problem areas in a fairly granular fashion. Ergo, Churchill became a source of problems more than alternative viewpoint.

On the other hand, for a course where the prof is more prone to do somewhere a bit off the beaten path with tests, it would probably be better to find a book which approaches the area in a different way than the origional so as to be more or less orthogonal in both approach and problems. Then working the other book is very much like relearning the entire course and may expose one to an additional perspective that may come in handy come test time. Having worked out of Royden for my second semester or reals, I would probably use Baby Rudin as my "orthogonal" text.