Reading and Taking Notes (or Not)

[Elwin.Martin]

So I'm starting to review Calculus and I was wondering what you guys do for taking notes from textbooks since I don't normally take notes and I would only read the text when necessary. I am debating taking the following options:

Just reading the book (probably least effective)
Reading and taking definitions
Reading and doing the odd problems
Reading, taking definitions and doing odd problems
Reading and taking complete notes
Reading, taking notes and doing problems...
etc.

How do you guys take notes from texts? I know people learn in different ways so I'm just trying to find different study methods and determine what I like best. When I take complete notes, the process is dreadfully slow, though it is the most thorough.

I am taking Analysis next semester and am familiar with Calculus (if mostly from a computational perspective), and the review of Calc. I'm doing is going to come from Apostol, since I've heard it's thorough and well written. I'm trying to cover most of Apostol I & II by mid-March, but that's quite a lot of material, even for review. If anyone has any better suggestions for material, that would be great. I'm honestly considering just working through the problems since I think I have time to do a great deal of them, and possibly not enough to really read it all. My main goal is being able to work hard, hard problems in this material in preparation for an exam I'm taking so I figured Apostol would be a good place to start.

Thanks in advanced for any and all help!
I'm looking forward to hearing how you guys study from texts.

If anyone has a link to some problem sets that accompany this text, or perhaps Spivak and an accompanying multi book (Spivak is single variable only, right?), that would be fantastic.

 

[micromass]

You have to learn the way you feel is best for you. Some people learn well by taking notes, other people are better off doing the problems.

As for me, I always took complete notes. I liked to write the full definitions, theorems, proofs and examples down. I even wrote them down multiple times. The proofs I always tried to do without looking at the book. I found this the best to learn.

I never really did wrote down many problems (except computational ones). I worked them out in my head and I was satisfied with that.

But you have to try some different things and see what fits you the best.

 

[Highway]

would probably be more efficient to make flash cards as you go over important stuff that you will need to know / memorize. i'd probably do that for the important stuff, then work problems until you are 100% with the material, then move on.

 

[Elwin.Martin]

would probably be more efficient to make flash cards as you go over important stuff that you will need to know / memorize. i'd probably do that for the important stuff, then work problems until you are 100% with the material, then move on.

It's a four hour exam of (mostly) Calculus based proofs ^^; so I'm not sure how much flash cards would help since it's not about memorization at all. I do plan on working a lot of problems though.

 

[Highway]

It's a four hour exam of (mostly) Calculus based proofs ^^; so I'm not sure how much flash cards would help since it's not about memorization at all. I do plan on working a lot of problems though.

if you're proving calculus, you should probably know how to study by now :P

 

[Elwin.Martin]

if you're proving calculus, you should probably know how to study by now :P

I winged my way through undergraduate group theory... got a decent grade but I really need a firmer grasp of the material. Same is true for calculus.

I know *one way* to study, it's just not suited for my present needs. I'll fall back on it if a new method fails. I'm looking for different ways to digest material more efficiently so I can make the best of my time, since this is one of the few times I really want to perform at my best.

I do get what you're saying, though.

****
edit for context:
My situation is comparable to someone who has gone through their Undergrad years studying a nice slow, but not super effective way who is preparing for their PhD entrance exam with only a few months...actually, it's exactly like that :) just a transfer program instead of a PhD program, haha fail.

 

[Highway]

if you make flash cards for the important stuff, you can refer back to it if you need it, and use it to go over stuff you don't know too well. from there you work problems non-stop to find and eliminate your weaknesses.

 

[ZenOne]

Never been a fan of flash cards (and note my previous degree--pre-mechanical engineering is in psychology), it just doesn't help IMO. I agree with doing many problems because you start to make the required material routine--that's what landed me an A+ in all my calculus and physics classes thus far.

I also agree with micromass--I do MANY examples in my head just to make the more basic ones part of my fundamental knowledge and only really spend time on more involved problems.

It's just my methodology I guess.

 

[bael]

have you considered writing out the entire chapter?

 

[Elwin.Martin]

have you considered writing out the entire chapter?

No offense, but I can't tell if this is a joke.

 

[Obis]

I'd suggest to try to understand why the theorem is true before reading the proof. Try to understand why it makes sense. I personally see rewriting as wasting time, but drawing schemes that somehow correspond to proofs, definitions is helpful, even though trying to draw them in your head is more valuable.