How can I optimize my learning of advanced math?

[ivan77]

Hi All,

Its been a while since I took a proper math course. I am will be working through Cal 1-3 (Diff Eq) this year, with some other math topics on the side (probability, or lin alg, not decided yet).

Can you please give me ideas on how to ensure that I get the most out of my courses? What is the best way to learn Calc, and advanced math? I am learning the Calc as a basis for my future personal physics learning among other things (finance job).

Thanks,

Ivan

 

[rochfor1]

Do lots of problems. If you just read a book and think you understand, you probably don't. Math is not a spectator sport, you have to practice it a lot.

 

[fourier jr]

Can you please give me ideas on how to ensure that I get the most out of my courses? What is the best way to learn Calc,

i think i agree with rochfor1. calculus isn't very theoretical, so the best way to get good at it is to pound out mass quantities of problems. these books should be easy to get hold of & they're relatively cheap also:
http://www.mhprofessional.com/product.php?isbn=0071635343
https://www.amazon.com/dp/007007979X/?tag=pfamazon01-20

other ones cover similar stuff, but are more difficult to find. maybe your library has copies:
problems in mathematical analysis - demidovich & others (3193 problems)
a problem book in mathematical analysis - berman (4465 problems)
(the titles say analysis but it's really just calculus)

and advanced math?

get a book & go through it cover-to-cover, proving every theorem without looking at the proofs in the book & of course solve every problem

 

[Diffy]

You can't go wrong with a hot cup of coffee + a quiet corner of a library.

 

[rochfor1]

i think i agree with rochfor1. calculus isn't very theoretical, so the best way to get good at it is to pound out mass quantities of problems.

I think my advice applies to any type of math, no matter how theoretical. True, if you're studying something quite abstract, the problems won't be computational, but I maintain that if you can't apply what you're learning to solve problems, you don't actually understand it. I feel that this applies even to research, where even while moving forward you should keep looking back to see what new problems your research can solve or what new approaches it gives to old problems. Otherwise when you present it at a conference and at the end of your talk someone asks (much more politely) why anyone should care, the silence will be awkward. This hasn't happened to me personally, but I've been in the room when it's happened, and I felt bad for the speaker.

 

[ivan77]

thanks for the advice. I appreciate you taking the time to help me out.
Rochfor1, ultimately, I am interested in being able to 'do things' with that which I am learning. I'll focus on doing lots of problems. Practical relevance is as important, if not more so, than the general intellectual exercise of learning this math.

Fourier, thanks for the specific references. I'll look into these books. I have never thought of trying to prove theorems without looking at the proofs. I'll give that a go.