I am struggling to get caught up on my Calculus III homework. The first exam is 12 days away. I'm deep in the section of the book about which the instructor said, "This is the longest homework section in the semester and it will be the majority of the first exam. Those are the problems to stress about." (I am obedient in all things, sir.) He recommends ten hours of homework a week for a five-hour-a-week class.
When I started the term, it was taking me an average of 30 minutes per problem — something I can't imagine the other students are experiencing. I spent four hours on actual problem-solving today, plus perhaps another hour or so of flash-card making and other sorts of review. It hardly seems very much time. But I am pleased to find that my average speed is now down to 20 minutes/problem. That's cause for optimism, even if it still feels as though my brain is a corroded mass of old gears. Come to think of it, I've had that sensation every time I've taken math recently, but somehow the immediacy of the sensation is replaced by a feeling of accomplishment after the stress of the moment has passed. It has been 25 years since I took Calculus II, but I think the gear-box is getting back to functioning condition.
Initially, I studied by taking careful notes on the ideas of each section in the text book, and only doing problems afterwards. But now I think that's for the birds. Doing problems and groping my way through the ideas as I need to has proven a more effective way to get comfortable with the material. The notion that theoretical understanding, gained from reading the chapter, is a useful guide to problem-solving, is nonsense here just as it is in every other field I know of.
By far the most common cause of error in my work is sloppy arithmetic errors — half the time, it is just the result of getting plus and minus signs wrong. This in spite of considerable effort to avoid such mistakes. I have had this problem since my childhood. Using LaTeX to do my problems makes it easier to find them, since I can now actually read and even search mechanically through what I've written.