MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

## Best Practices for Learning Mathematics (especially in the classroom) [closed]

I am an undergraduate CS major with strong interests in applied math and theoretical computer science. In the past, I've done reasonably well grade-wise in all math-related (that is, pure math, applied or theoretical CS) classes, but I feel that I still haven't taken away as much as i could have from most.

As people who have often taught math courses and had to deal with the inevitable fact that no lecture will be universally effective, what are your suggestions for how I (as a student) can best learn in these classes.

A few problems I've experienced regularly:

When professors try to present long and difficult proofs on the blackboard. I always find it ridiculously hard to understand proofs in real time or to understand verbal and visual explication of the proof simultaneously. I have to look the proof up in a textbook, and the comprehensibility of textbook proofs varies widely.

More generally, accessing the "kernel" of the proof that really makes it comprehensible is sometimes difficult, especially when it's presented more formally. I tend to think of proofs in terms of algorithms, and proofs that don't fit this well tend often evade me.

Definitions, even, (especially in pure math) tend to blend together and become obscure. I've re-learned the basic definitions of probability waaaay too many times.

-
Why would you expect that "long and difficult proofs" be easy to understand in real time, and why do you think you should not have to look the proofs up in textbooks? In any case, I am not quite sure your question is a good match for this site. – Mariano Suárez-Alvarez Jan 21 2011 at 19:36
You might consider asking this question on math.stackexchange.com (although a version of it may have already been asked there). – Qiaochu Yuan Jan 21 2011 at 19:41
I would disagree that it's off-topic. Many topics here are professors asking how they should teach; why not a student asking how he should learn? – DoubleJay Jan 21 2011 at 20:53
@DoubleJay: this site is geared towards research mathematicians and graduate students and their interests. Research mathematicians have to teach, but they do not have to learn (in classrooms, anyway). So I can understand the argument that this is off-topic. – Qiaochu Yuan Jan 21 2011 at 21:26
I agree with Qioachu, but +1 to DoubleJay for making a symmetry argument. This tends to work out better in mathematics than in rhetoric. :) – Pete L. Clark Jan 22 2011 at 10:31

## closed as off topic by Mark Sapir, Andres Caicedo, coudy, Andy Putman, Harry GindiJan 21 2011 at 22:00

This is not a universal recipee for anything, rather a few random points.

1) Make sure your background matches the course expectations. If not, work on it before even thinking of taking an advanced class.

2) Read ahead, not behind. Most teachers will tell you what's coming next and if you come to the class knowing half the story already, you can concentrate on the other half and gain double time for absorbing it.