My advanced calculus class this semester (part II of the sequence), despite being taught by the same (great) professor, has so far been vastly harder than the first semester. It has been hard enough that I got an 83% on the first exam, which is lower than any of my exam grades (including the one I dropped, and knew ahead of time I would be dropping) from last semester.
We started with sequences of functions, then moved on to series (of numbers), and then to series of functions. I basically skipped this material entirely when I took Calc II in 1991, but I have since reviewed that entire chapter of a regular calculus textbook. I am keeping up with (and doing well on) the homework, but every assignment is difficult-to-impossible and the situation doesn't seem to be improving.
Assuming I go to grad school next year, I'll be taking graduate-level analysis, so the difficulty of this material only makes it more beneficial to be seeing now, rather than for the first time next year. But it's been very hard for me to persevere with it when it often seems as though I'm not improving [note: this is objectively false as best I can determine]. The assignments often frustrate me to the point of tears or rage.
I decided on Saturday night to try to take a humbler approach to the material, to not let it be about whether I am smart or not (a real weakness of mine), but to see myself as a servant (if you will) of the math. I'm not sure it's having any effect yet, but I'm going to keep trying it.
I know that if I'm going to get anywhere in math, I have to learn to work without the promise of success - to work on problems that are hard enough that I may feel stupid and hopeless for quite some time. I guess this is good practice for that.
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2 comments:
The servant approach is interesting - I hope you tell us how it works out.
I'm not sure what you mean by "servant of the math" - but I might adopt that quote anyway...even if I don't manage to share your meaning.
I wouldn't let the difficulty bother you. At some point, the questions you are asked for homework get beyond routine manipulations; even if they're tedious and lengthy bits of calculus and algebra with a cleverly chosen estimate thrown in here-or-there. You might have to think it over for some time; maybe a couple of days, or weeks, etc...
Personally, I think one of the main goals of going to school is to train yourself mentally and emotionally to put up with that sort of work: sustained, concentrated thought. It's no easier than going out for a 10-mile jog. You have to work up to it.
Just my two cents...it sounds like you're on the right track.
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