4 ms·

Ask HN: Tips for learning maths

10 points by Willprice94 15y ago

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 should 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. How did you approach learning maths? Did you find any particular approach to be especially effective?

hvass 15y ago
1) Here's a thread on LessWrong on how to learn math: http://lesswrong.com/lw/2ub/discuss_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 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-the-art-of-doing-well-in-technical-courses/ http://calnewport.com/blog/2008/11/14/how-to-ace-calculus-th... His advice to a new MIT student: http://calnewport.com/blog/2011/04/28/on-becoming-a-math-whiz-my-advice-to-a-new-mit-student/ http://calnewport.com/blog/2011/04/28/on-becoming-a-math-whi...
- Willprice94 15y ago
  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!
wasd 15y ago
Learning the proof instead of memorizing the equation sometimes helps. What sort of math courses are you taking?
- Willprice94 15y ago
  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!
tokenadult 15y ago
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-Gowers/dp/0192853619/ http://www.amazon.com/Mathematics-Short-Introduction-Timothy... 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 http://matrixeditions.com/UnifiedApproach4th.html helps your understanding.
impendia 15y ago
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 15y ago
  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 15y ago
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.

10 points by Willprice94 15y ago

hvass 15y ago

1) Here's a thread on LessWrong on how to learn math: http://lesswrong.com/lw/2ub/discuss_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 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-the-art-of-doing-well-in-technical-courses/ http://calnewport.com/blog/2008/11/14/how-to-ace-calculus-th... His advice to a new MIT student: http://calnewport.com/blog/2011/04/28/on-becoming-a-math-whiz-my-advice-to-a-new-mit-student/ http://calnewport.com/blog/2011/04/28/on-becoming-a-math-whi...

Willprice94 15y ago
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!

wasd 15y ago

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

Willprice94 15y ago
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!

tokenadult 15y ago

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-Gowers/dp/0192853619/ http://www.amazon.com/Mathematics-Short-Introduction-Timothy... 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 http://matrixeditions.com/UnifiedApproach4th.html helps your understanding.

impendia 15y ago

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 15y ago
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 15y ago

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.