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Advice for calculus students *November 3, 2010*

*Posted by Sarah in Uncategorized.*

Tags: grad life, teaching

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Tags: grad life, teaching

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I am now a TA holding office hours for some calculus classes, and I actually enjoy it a lot. I’m generally impressed with the students. General advice that ought to hold if you’re taking an intro calc class:

1. Don’t freak out because a problem is taking a long time and seems unfairly hard. You’ll say “There must be some mistake!” No, there isn’t. This isn’t high school; you’re being taught by professors, who don’t always know how to gauge the right difficulty level. They do tend to underestimate how long it takes to finish your homework. Also, calculus is actually harder than high school math. If you have to go through a lot of computations and false steps — don’t worry! That’s what math is actually like!

2. I do not have magical TA superpowers of *Mathematica*. Most of the time, if you ask me for help, I’m going to look at the example on your worksheet and look in the help documentation. You could do that too! The xkcd Tech Support Cheat Sheet is relevant here.

3. L’Hopital’s rule is your friend. Seriously. So is big-O notation. These will save your bacon.

4. 90% of mistakes in multivariable calc result from not drawing pictures. Draw a picture. You are never too cool to draw a picture.

Strongly second the drawing pictures. I always tell my students that when they see a weird function, graph it!

Ooh, this is really good. I’m TAing first semester calc this semester so it isn’t as relevant. But I’ll definitely need to remember this when I’m back to multivariable. Although 1 and 4 seem to be relevant for single variable as well. 3 would be relevant if we taught big-O notation in intro calc. I suspect that it would simply be too abstract for many for of them.

It’s not too abstract if your kids compute limits. What’s the best way to take the limit of (x^3 + x + 1)/(2 x^3 -4x^2)?

But do you have advice for students who enjoy Abstract algebra but get lost in Analysis and topology?

Hm … that doesn’t seem like the worst problem in the world. Everybody specializes sooner or later.

The thing about analysis is that you have to get very basic and look at examples to understand what’s going on. There’s no substitute for concreteness.

As for topology — a lot of it is algebraic machinery anyhow, except when you actually need visualization, which I’m really not sure how to improve upon.

Always consider the possibility that the reason you’re lost is a bad teacher or a bad book, not a problem with the subject. Try a different book if you’re stuck.