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I am 21 years old now. I have been studying Mathematics in school, college and now in university but I simply feel that I don't practically understand it. For example, I can solve complex questions on paper but in real life I can't even add up things properly. Its really embarrassing situation sometimes. I would be very thankful if you all can guide me with some tips what should I do to make my mathematics good. I don't know if this question really suits here but I did not find a better place for it.
Thanks in advance.

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What exactly are you worried about? "Making your mathematics good" is a very vague question. Are you worried that the things you have learned still make you... "useless" in some sense? I think what you mean is that you can answer things in a course context, i.e. when you are somehow guided towards a solution by the teacher, but not outside of this context. Am I right? –  Patrick Da Silva Dec 19 '11 at 6:20
    
@PatrickDaSilva: I simply cant apply it in practical even if it is from course. –  Fahad Uddin Dec 19 '11 at 6:25
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Unless you were following fixed procedures and just blindly plugging in numbers into formulas, you should have a decent understanding of mathematical concepts.

Finding practical uses for what you know is the best way to build up your intuition. For example, a got a good feel for linear algebra by writing OpenGL programs which require use of interpolation and matrices to transform objects.

I suggest that you write down situations where you've felt your math application was inadequate, and then work on practising the math that's applicable to that situation.

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I think that education should be about what you want to do. If you'd like my opinion, I think it would be good to ask yourself why you're studying mathematics in the first place and then decide a course of action from there.

To illustrate my point, I'm a mathematics major at a university. In high school I hated math so much. I swore I'd never sit through a math class, or for that matter, crack another textbook. So I joined the army. Five and a half years later, I hungered for knowledge and wanted to challenge myself. Hence, I got out and went to college.

When I first started school, I took math because it was required and I had to "check the box." But since my mind was open to the pursuit of knowledge -- my GOAL was to learn, not to get A's -- I found math beautiful.

I started off at the university as a double-major in biochemistry and neurobiology. It was interesting for a while, until I realized that the upper-level courses were purely focused on application and the theory was, I guess, missing for me. I decided to switch in my senior year to math. The reason is because I want to learn for the sake of learning. I want to pursue math because I find it beautiful.

So, back to your question. In my opinion, I think you should ask yourself what you want out of mathematics. If you want to be able to apply it to "real-life" situations and you feel that you're somehow lacking in that field, take it from me, all you need to do is practice. I failed high school algebra twice then I went on to the army for five and a half years where the only "math" I did was count how many rounds I had left after a firefight. I came to college, busted my ass, forced myself to get better at it and kept a 4.0 GPA for three and a half years in math. My point is that you can do whatever you put your mind to. All you need to do is work at it.

I'd like to say one more thing. You wrote that you feel you understand complex questions on paper, but in "real life" can't even add properly. To me, mathematics is not about arithmetic or modeling physical phenomena with equations. If that's what you want to use it for, then you can improve with hard work. (Again, trust me on this.) However, if you can solve those "complex questions" on paper and you take satisfaction in that, if you can find beauty in it, then love it for what it is.

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I think one thing you really want to be able to do is quick arithmetic, which can be fun, confidence building (and reduce embarrassment), and is most likely the easiest of your goals to achieve.

There's a lot of books on how to do quick arithmetic, but the most fundamental skill is rote memorization using flash cards before using fancy tricks. Just make yourself flash cards for multiplication tables 1..12 X 1..12 and addition tables 1..10 + 1..10. The key is that you have to get to the point where you know the answer right away. Practice every day and don't stop until the answer is instantaneous. There has to be no thought and no counting in your head. Keep practicing to keep this up, and extend the range to 1..10 + 11..20. Focus on the ones you have trouble with until they are automatic.

Be patient... it may take several months of daily practice to get good. That's because when you are training your brain for "fast knowledge skill" you are actually growing new neural networks in your brain, and that takes biological time.

You can do it! It's how the brain works. You can get good at fast arithmetic! It just takes time, effort, and repetition.

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