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How to improve at Mathematics?

  1. Mar 6, 2009 #1

    I've been lurking around this forum for a short while; reading questions, responses and other intellectual goodies...

    So far, I have a positive outlook on this community and I hope I recieve insights regarding my trouble in math...

    I'm not 'strong' in mathematics.. yes I did recieve 100% on a math 10 provincial and my current mark is 100% as well.. however, I don't feel I'm necessarily strong at problem solving or applying learned concepts to real life..

    I need some insights as to how to improve at math at a fast rate... I know practice is one of the key elements; but, I don't know how to practice..

    Thanks in advance!
  2. jcsd
  3. Mar 7, 2009 #2
    Hi Sumanyu!

    I think the most important part in learning math is doing the exercises (like those found in a textbook).

    - An exercise test your knowledge, you soon find out if you should go over definitions and theorems again.

    - Applying concepts yourself helps greatly in memorizing them.

    - Creativity and assertiveness are challenged with the more difficult exercises.

    - Problem solving skills are improved as you learn strategies and tools.
  4. Mar 7, 2009 #3


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    Homework Helper

    The short book "How to solve it" by G. Polya would be a good investment. Occasionally come back to it. Summary below already gives a lot.

    http://www.math.utah.edu/~pa/math/polya.htmlbook [Broken]
    Last edited by a moderator: May 4, 2017
  5. Mar 7, 2009 #4
    Thank you yyat...

    I haven't had luck at finding difficult exercises... I can do all questions in the textbook...

    The issue is, I'm not good at solving contest questions... Moreover, I'm quite slow at those type of questions...

    Thank you epenguin as well..

    I've already read the book by G. Polya =)

    I try to use the strategies he has listed... so far they've helped me improve; however, I just need access to material for practice or specifically 'how to practice'
  6. Mar 8, 2009 #5
    Terry Tao wrote an interesting book on the subject, base around problems for you to solve. You can download the pdf from his site if I recall.
  7. Mar 8, 2009 #6
    As far as I know you can only view sample chapters, here is the link:
    http://terrytao.wordpress.com/books/solving-mathematical-problems/" [Broken]
    Last edited by a moderator: May 4, 2017
  8. Mar 8, 2009 #7
    hmm, looks like he took down the full pdf off the site.
  9. Mar 8, 2009 #8
    ok. you got lot of advice already. here i will tell you few points which made change in my maths interest.
    --> Try to solve the same problem in different ways even though you got correct answer.
    --> try to substitute known and simple values in order to solve the equations.
  10. Mar 8, 2009 #9
    I recommend Thinking Mathematically by John Mason. It really trains your problem solving skills.
  11. Mar 8, 2009 #10
    Try doing problems which are higher level than you actually know how to solve, and then give a serious try to solve them. Learning real math is not about learning to solve every problem but learning to think in the correct ways.

    When you do operations you should not think "I do it like this since this is how I have always done it before and it always gave me points", you should think "I do it like this since according to the given axioms it is the truth and the only truth".

    Don't learn to derive things by reading the derivations in a book, learn to derive things by deriving them yourself, most formulas are quite easy actually. Sometimes you need a few pointers but you can almost always do 90% of the work yourself and actually deriving things yourself gives you incomparably more understanding of math.

    For example start out with the basic operations +- and maybe */, then sit down and derive every theorem and formula you have learned in math without using any book. Add axioms as you see fit and so on. And by deriving I mean that you should do a proof that makes you certain that it is true, not to make certain that you get points on a test. Then when you are done, get a book and validify everything to make sure it was all correct, and understand which thinking process went wrong at the points you errored and then correct that process.

    Imo the schools teach math in the wrong way, they try to get as many to pass as possible but they don't care at all about the kids understanding so roughly everybody coming to the higher maths got a really bad foundation to stand on.

    Anyway to get good enough to do the really hard things you just need really good understanding of the fundamentals.
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