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Where can I learn advanced Mathematics?

  1. Feb 17, 2012 #1
    Hi, I'm 13 and wondering where I can learn this more advance Mathematics.
    Before you start thinking to your self "Well this little blighter must not pay attention at school!", I should probably explain why that statement would be invalid.
    You see, the Mathematical curriculum for my educational year group (Year 9) is rather controversial for a cynical being, such as my self. All they care about is getting you through exams and that's it. I'm a Computer Scientist, but Maths is my weak point and lets me down when it comes to programming games etc.
    I'm looking for Math skills above the Pythagorean Theorem as that is the sort of stage I'm at now and I want to expand my learning by studying more advanced Maths out of school to help me with the Math required in my computer programming and I also want to make Maths a bit of a hobby of mine.
    Any help is appreciated but sarcastic comments are not.
    Thank you for reading.

    Josh, 13.
     
  2. jcsd
  3. Feb 17, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    You're only 13, which is fine, but it means that your math options tend to be quite limited. Basically, the only thing which you can do now is to study the standard curriculum in your free time.

    This entails:
    - Basic algebra: This is extremely boring, but very important. If you feel only a little bit uneasy when asked to solve

    [tex]
    \left\{
    \begin{array}{c}
    2x+4y=5\\ 3x+y=0
    \end{array}
    \right.
    [/tex]

    or

    [tex]x^2-3x+5=0[/tex]

    then you need to practice more. Such things are the very basics and you have to be very comfortable with them (even though it's boring).

    If you know algebra, then you can go to geometry. Geometry will definitely help you program games. You'll learn about equations of lines, slopes, intersection of lines. These are all essential when drawing something on a computer screen.

    If you know geometry, then you can do trig. This will also help you in programming games. Basically, everything that involves circles and triangles will involve trig. So being able to work with it is quite important.

    It would also be wise if you could study some physics (kinematics in particular). If you wish to simulate things like an apple dropping or a car moving or a cannonball launching in the air, then kinematics will be very helpful.

    You should also check out things like projective geometry and linear algebra (matrices). You can learn these things after you taught yourself geometry. They are extremely helpful in programming, but perhaps a little difficult.

    Just report these comments, please.
     
  4. Feb 17, 2012 #3
    Hi, I think its great your taking an interest in learning and trying to find new things to learn.

    Have you tried asking at your school to see if they can provide you with more material? Or perhaps the public library has some books on maths, or even better, game development (I have an interest in that mayself)

    If you enjoy having short lectures, try Khan Academy : http://www.khanacademy.org/ - Some of it is pretty advanced but if you work hard eventually you will get there and your brain will thank you for it.

    Good luck!
     
  5. Feb 17, 2012 #4

    jedishrfu

    Staff: Mentor

    I like the book Math 1001 by Prof Elwes. It introduces many current math topics in bitesize chunks far beyond simple algebra. Ideas to play with.

    https://www.amazon.com/Mathematics-...7192/ref=sr_1_1?ie=UTF8&qid=1329508590&sr=8-1

    There's also the math behind origami paper folding that pretty interesting. Some people have discovered that origami can solve many of the ancient conundrums like trisecting an angle or doubling a cube... Its also very geometrical and has a lot of application in engineering.

    There are also books on game physics and graphics that may be of interest:

    https://www.amazon.com/s/ref=nb_sb_...tripbooks&field-keywords=game+physics&x=0&y=0

    and then there's my favorite: Open Source Physics at www.compadre.org/osp with many examples of doing
    simple physics simulations. You might learn some things that you could apply to your games in the sample java code.
     
    Last edited by a moderator: May 5, 2017
  6. Feb 17, 2012 #5
    Do you know any set theory or formal logics? If not, then you could start studying the basics of those subjects; they're relevant to computer science and amazing tools for every subject in which precision is necessary. Material is available on the web, so all you need is will and patience.
     
  7. Feb 17, 2012 #6
    Thank you for all the help and suggestions given, I hope that if I need help my posts (regardless of the apparent simplicity of the question in context) are welcome in the Math section of these forums.

    Josh
     
  8. Feb 17, 2012 #7
    Here's something you can investigate. What happens if none of the angles in a triangle are 90 degrees? You get something known as the Law of Cosines, of which the Pythagorean Theorem is just a special case. Learn things like that. Connect what you have to what will come and you'll not only solidify your foundations, but have a head start in future subjects. Functions like the cosine are very easy to understand, but are also very important to know.

    Others have given good advice already, but I want to stress connections to higher techniques. For instance, when you start learning about slopes of lines, start thinking about how the slopes of lines will behave as the change in x approaches zero. Then start thinking about what happens when those lines become curves.. yet can still be considered lines if you look at them at a small enough change in x! At your stage of the game, there's all kinds of things you can investigate that are generalizations of "easy" things. Geometry, trigonometry, and calculus (in that order) are great things to motivate such investigations.
     
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