

Ask HN: Tips for learning maths - Willprice94

I've got a pretty heavy maths workload at college this year and I'm finding it difficult to learn everything, has anyone any tips as to how to approach learning new techniques (e.g. I'm learning how to solve systems of differential equations this evening) they're a dime a dozen at the moment and I'm constantly forgetting them, I feel there <i>should</i> be a better way than just drilling questions but currently I've not really thought of any better way. In general I find the techniques easier to understand and remember when I've got a good understanding of what they should be used for, alas my teachers tend to gloss over the why and focus on the how.<p>How did you approach learning maths? Did you find any particular approach to be especially effective?
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hvass
1) Here's a thread on LessWrong on how to learn math:
<http://lesswrong.com/lw/2ub/discuss_how_to_learn_math/>

2) Here's a discussion on learning math on HN:
<http://news.ycombinator.com/item?id=108723>

3) This is Cal Newport's advice on acing technical courses:
[http://calnewport.com/blog/2008/11/14/how-to-ace-calculus-
th...](http://calnewport.com/blog/2008/11/14/how-to-ace-calculus-the-art-of-
doing-well-in-technical-courses/)

His advice to a new MIT student: [http://calnewport.com/blog/2011/04/28/on-
becoming-a-math-whi...](http://calnewport.com/blog/2011/04/28/on-becoming-a-
math-whiz-my-advice-to-a-new-mit-student/)

~~~
Willprice94
These links are, just brilliant, I'd say I have a passion for maths to begin
with, but these really make my mind blaze with possibilities, motivation to
learn is just important (or more so) as learning how to learn!

------
tokenadult
_In general I find the techniques easier to understand and remember when I've
got a good understanding of what they should be used for, alas my teachers
tend to gloss over the why and focus on the how._

Several authors I can recommend who write good expository books on mathematics
to explain the why are

Ian Stewart

John Stillwell

Keith Devlin

William Dunham

Timothy Gowers has a book about mathematics in the Very Short Introduction
series

[http://www.amazon.com/Mathematics-Short-Introduction-
Timothy...](http://www.amazon.com/Mathematics-Short-Introduction-Timothy-
Gowers/dp/0192853619/)

that should be helpful to you.

On the particular subject you are studying right now, see if Hubbard and
Hubbard's book Vector Calculus, Linear Algebra, and Differential Forms: A
Unified Approach

<http://matrixeditions.com/UnifiedApproach4th.html>

helps your understanding.

------
impendia
Math professor here.

It is good if your teachers explain the why, but it is even better if you fill
it in for yourself. Read your lecture notes, or your textbook, with a critical
eye. "Why are they doing it this way? Why would anyone think of this?" etc. If
you think your book or prof is being obtuse, try to figure out why you think
that way. I curse at math books sometimes...

Instead of refreshing the correct technique and then solving the problem, try
solving the problem without first recalling how to do it. Perhaps you will
figure out the solution and invent the solution method yourself. If you are
more like me, you will fall flat on your ass and produce five pages of
calculations that go nowhere. In either case, you should then read the book's
explanation and you are much more likely to remember it.

And that happens to everybody. I am constantly having to relearn stuff. If you
think it's difficult --- good, you're doing it right.

~~~
Willprice94
Thank you, you've given me the confidence/will power to persevere! "Why are
they doing it this way? Why would anyone think of this?" etc. If you think
your book or prof is being obtuse, try to figure out why you think that way. I
curse at math books sometimes..." Excellent advice, I'll stick to this.

------
chris_dcosta
Try a book Adventures in Numberland. It's not a mathematics manual, but
written in plain language explaining pretty much everything to simpletons,
like me. I'm not saying you're one, but the author is a mathematician, so you
might get more out of it.

Amazing stuff. I now understand much about the patterns in numbers that I had
no idea even existed, and how they can be used to simplify complex concepts.

------
wasd
Learning the proof instead of memorizing the equation sometimes helps. What
sort of math courses are you taking?

~~~
Willprice94
I'm doing introductions to Linear Algebra, Vector Geometry. Calculus - things
along those lines, mainly applied maths with some complex numbers thrown in
for good measure!

