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I did well at Mathematics at school (top 0.1% in the country, approximately), however I stopped studying it when I was 16. Since then I've studied a couple of highly specific mathematics modules in university (primarily matrix manipulation) however these weren't taught very clearly.

In all honesty, my current mathematical knowledge only really amounts to addition, subtraction, multiplication, division (not long division), fractions, decimals, percentages, and a bit of algebra. And the odd things about angles, but just the basics. I have certainly studied further than that, but I need a serious refresher! I generally have no problem at all learning new concepts, so long as they are explained clearly.

I'd like to progress from this fairly basic level to having a very solid mathematical understanding, with a view to both improve myself as a programmer and to meet the requirements to start a Masters degree in Computer Vision/Imaging in two years. (While this is my specific goal, I'd also enjoy learning mathematics in general for myself.)

I'd ideally like to learn from a textbook or other written resource (I find it much easier to read than to listen to an explanation) and I'd ideally like some problems to solve to ensure I understand the material. I'm happy to buy a textbook (or several) - I just have no real clue where to start!

Summary -

Progress from basic high school level -> Computer Vision/Imaging related mathematics.

Written resources rather than video. Happy to buy a textbook.

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(I saw Foundation Mathematics as a possible textbook option.) –  ShimmerGeek Aug 13 '11 at 23:26
    
Should be converted to community wiki. –  sxd Aug 13 '11 at 23:44
    
Do you have any subjects of interest? Because if you already know about linear algebra a little bit perhaps calculus could be interesting in terms of optimization (for a programmer, or just for the fun of it). If you are simply willing to get really better, I suggest you find a good textbook on calculus or analysis to begin with. If you have access to a library at a university close to you that would be the best. The only textbooks I know for those things are in French though =( P.S. : Computer-Vision/Imaging related mathematics are AWESOME. You definitely want to get there. –  Patrick Da Silva Aug 14 '11 at 0:37
    
I would like to recommend Paul Garret’s advice, given here on MSE, at this link: math.stackexchange.com/questions/9230/… –  Mike Jones Aug 14 '11 at 6:09
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Aso, here are a couple links you might want to use: Math Reference Project mathreference.com/main.html and a long list of (standard? / famous?) problems: mathproblems.info –  Mike Jones Aug 14 '11 at 6:19
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5 Answers

I know you said that you rather have written resources, but http://www.khanacademy.org/ contains loads of video lectures about high school mathematics.

Once you worked your way up the basics you should check the undergrad math section on MIT open courseware, which contains video lectures but most of the time the syllabus is included!

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Khan Academy also has an interesting online "homework" system available for free. –  Austin Mohr Aug 14 '11 at 0:47
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Thanks, I have heard of (and used) Khan Academy, and the tests are great - but I really can't watch the videos, they're horrible for learning. –  ShimmerGeek Aug 16 '11 at 10:55
    
I really liked the videos on MIT open courseware, but those are already university undergrad courses. –  sxd Aug 16 '11 at 13:24
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I can relate to what you probably instinctively know. That is to be fluent in mathematics requires a knowledge on the basics. I would suggest you take some time out and throughly go through a pre calculus book. In particular one that relates the fundamentals of algebra to calculus concepts. Whilst tedious, the varied ways of solving problems, should become like touch typing. Thus allowing you to be creative when it gets to things like complex numerical analysis.

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"Whilst tedious, the varied ways of solving problems, should become like touch typing." I like this phrasing so much I'm up-voting your answer just because of it! –  Mike Jones Aug 14 '11 at 5:47
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Specific to your professional goals, I would consider buying a book on matrix algebra or linear algebra. For an auto-dydact, learning the fundamentals of linear algebra from the point of view of matrices will be a bit easier. Also, you'll see it grounded in traditional arithmetic first. Probably, Schaum's outline of matrix algebra will work nicely. In general, Schaum's are well-written, but they can be replete with typos, be aware.

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I don't have any book recommendations but I can tell you what subjects you will eventually need to learn:

  • Calculus
  • Linear algebra
  • Probability
  • Machine learning
  • Differential geometry

The first three you definitely should know before you start; the last two you can learn once you get your foot in the door. I also suggest consulting the syllabi of good schools.

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I suggest you look at "Math Overboard" written by a former mathematics professor (me). There are 2 volumes, covering all school math, kindergarten to 12th grade and beyond. The website http://www.mathoverboard.com gives details.

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