Conversation started Nov 25, 2011 at 0:49.
Potato
Potato
Nov 25, 2011 00:49
If you want to chat, perhaps we could talk about study tips for math. I'm at the point where my terrible study habits and focus are starting to hurt me.
t.b.
t.b.
Oh, I was just looking around...
Can you expand on "terrible study habits and focus"? Do you mean you're jumping around too much?
Meaning: topic-wise.
Potato
Potato
No, not topic wise. I'm not too good at concentrating for long periods of time, I guess. My mind wanders.
t.b.
t.b.
I see. What does a long period mean? More than 15 minutes, more than an hour, more than two hours?
Potato
Potato
After maybe 10 minutes I start fiddling with music, chatting in here, that kind of thing. Distracting myself.
t.b.
t.b.
I understand. Why do you need a computer nearby in order to learn? I mean your notes, maybe a book and some sheets of paper should be enough, no?
Potato
Potato
Nov 25, 2011 00:56
That is a good point.
t.b.
t.b.
I mean: try to reduce the possibilities for distraction: (I'm absolutely the wrong one to say that, but a clean desk works wonders). Where do you work, at home, in a library in your room?
Potato
Potato
In my room.
A college dorm room.
t.b.
t.b.
Here's something that helped for me when I was having similar issues: different places for different things: library for reading books, my desk for reviewing my course notes, a desk in the hallway for writing stuff and a coffee shop for discussing things with my friends. In some sense, different surroundings helped me get into the right mindset for these different activities.
Potato
Potato
Ok, that sounds good. Here's another question: how do you deal with reading dense books? I've gotten through Ahlfors ok by just reading normally, but I'm also reading Miranda's book on algebraic curves and Riemann surfaces, and it definitely isn't something I can totally comprehend on a first reading.
Definitely it's a good idea to always complete the verifications "left to the reader" and to do the problems, but what else? I'm finding it hard to learn all the new definitions and theorems.
Although perhaps it's just an issue of volume, and I need to go slower?
t.b.
t.b.
Going slower certainly helps. I tend to write a lot when a book or a paper is going too fast for me. I try to summarize the page I just read, formulate things in my own words. I try to work out some examples, come up with my own, and so on. It is hard to say, what exactly I do.
Potato
Potato
Nov 25, 2011 01:11
Yeah, I think it's a matter of just being a more active reader.
t.b.
t.b.
Probably. Always ask: what are the hypotheses used for? How does this assumption enter the argument? What is the crucial point of the proof, what do I need to remember in order to re-prove that result? What is just standard technique, what is new to me?
Try to think of examples that illustrate the statement of a theorem: can you see what is going on in an easy special case?
Potato
Potato
Ok, yet another question. How does one study for advanced exams (say, quals)? Specifically, I know the ideal is knowing the statement and proof of every theorem by heart, but there are certain proofs I feel I just can't commit to memory (or simply that they are unimportant.) Two examples: Ahlfors's 6-ish page proof of Sterling's formula, and his proof of Hadamard's factorization theorem.
Of course it goes without saying that once one knows the material by heart that the only way to prepare is to doing problems until you pass out.
t.b.
t.b.
Sterling's formula? Is that Stirling, the asymptotics of the Gamma function?
Potato
Potato
Yes. My apologies for the spelling error.
t.b.
t.b.
Did you have a look at what Remmert does for these two theorems? His two books usually give excellent accounts of various ways of looking at things. Here's volume 1 and here's volume 2. Basically this boils down to: look up the results in other books, think about what points other books emphasize.
If one proof doesn't help me a lot, I need a different angle of looking at things. If I find a place where things are presented the way I like it, I can then go back and see what the other author emphasizes and thus get a more complete picture.
Tim
Tim
Nov 25, 2011 01:25
Lurking here finally pays off. Nice to learn from t.b.
Potato
Potato
@t.b. Well, I guess what I am asking is, is it really necessary to know how to prove those two theorems by heart, especially when it would be ridiculous to ask a student to prove them on an examination?
t.b.
t.b.
Well, one could certainly ask for an outline of the proof, I believe. There are a few main ideas that one can try to isolate. I mean these six pages aren't six pages of pure calculation, they certainly are divided in some natural steps. Try to partition the proof in such a way that it looks natural. This takes a few hours to do, but if for some reason you know that this theorem is considered important for your exam, you probably need to really grasp these ideas.
Hi Tim!
Thanks.
Tim
Tim
Nov 25, 2011 01:40
Hi tb. Thanks! Learning from right person is important.
Learning from right books is also important.
Tim
Tim
Nov 25, 2011 01:58
Asking (dumb) questions helps too.
I agree and also act like this: "I tend to write a lot when a book or a paper is going too fast for me. I try to summarize the page I just read, formulate things in my own words."
I agree but am not able to act like this: "I try to work out some examples, come up with my own, and so on."
 
Conversation ended Nov 25, 2011 at 2:03.