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I am a Software Engineer. With interest on computers I have chosen this path. But I don't know anything about great maths. I want to learn from basic to some level(which would help me in my field..like identifying solution to a problem, designing algorithms, designing shapes and some animation on them). So, please suggest me where do I need to start. Please suggest me/list out the concepts that I need to go through.

Thank you very much

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Maybe you should make a short summary of what you already know. Since you are a programmer, you must already have a basis, no? –  Raskolnikov Dec 19 '10 at 17:24

3 Answers 3

Perhaps what you mean is that you want a book like Polya's "How to solve it".

http://www.amazon.com/How-Solve-Aspect-Mathematical-Method/dp/0691023565

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The most useful mathematical areas for a programmer are

  • trigonometry and linear algebra, especially to draw and recognise shapes, ray tracing, animations and so on,
  • combinatorics, particularly to cleverly enumerate sets, estimate running times of simple loops and recursions etc.,
  • some elementary group theory and particularly permutation groups, for algorithms that involve tracing out graphs (particularly trees) and also for clever enumeration, as above.

There are lots of introductory books on each of the above subjects, although maybe other people can comment on which ones are best suited for non-mathematicians. Note that the three areas are fairly independent, at least at the beginning, and you can learn them in any order or in parallel.

Edit: I forgot the possibly best way to get started: once you know the definition and some basic facts about groups, you should read the book Indra's Pearls. It is a very beautiful book that explains how to draw certain types of fractals with the computer. It introduces all the relevant mathematics pretty much from zero and it provides the actual programs in pseudo-code, ready for you to implement in your favourite language. The mathematics and the algorithms it introduces are very relevant to other situations, but since you are particularly interested in graphics, you will hardly find a better way to get started! There is even a computer graphics artist who bases some of his work on that book.

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I've never heard of Jos Leys before; thank you Alex! Sadly, I can't give another +1... –  J. M. Dec 20 '10 at 14:11

The program ``sage'' helped me a lot. You can experiment with math objects in a programming environment. It is free software - GPL2. You can try it online in a browser. The site is http://sagemath.org/. More information: http://en.wikipedia.org/wiki/Sage_%28mathematics_software%29

EDIT: This will not teach you math, but may help you.

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