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I was always branded weak at mathematics back at school though i loved it. The reason was that I lacked basics in maths. Due to this problem I stopped learning maths after my 10th grade. But I always feel that I can do better.

I want to learn maths again, from Addition to Everything. I want to start afresh from techniques of division to multiplication. Is there any comprehensive book that can teach me the basics?

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migrated from mathematica.stackexchange.com Sep 26 '12 at 13:36

This question came from our site for users of Wolfram Mathematica.

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    $\begingroup$ You don't want a "complete guide". Today's mathematics covers so many areas that the complete guide wouldn't fit on your bookshelf, let alone that you would have the means to absorb all of it: that's time, and mental capacity. No offense: nobody understands everything in mathematics. It would be a good idea if you would indicate what application of your maths you have in mind. $\endgroup$ – stevenvh Sep 26 '12 at 13:51
  • $\begingroup$ I have updated the question. $\endgroup$ – esafwan Sep 26 '12 at 14:49
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The first thing you need to do is to figure out how much you know. You need to know which level you are at.

I recommend going to someplace like khanacademy and try some of the exercises.

Another thing I like to do is to find something that I want to learn, that at the moment is over my head. Then I figure out, what do I need to know to understand this? Then I can make a list for myself of concepts/techniques I need to learn.

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There are lots of good books about math. Here's one such list:

http://www.amazon.com/Books-about-Math-Numbers-More/lm/R3T29ZJGFBT60N

These tend to be more about the ideas in math than the techniques of mathematics, but they might be good motivation. Personally, I liked "Shape of Space" (number of 24 on the list) which helped fill some holes in my background on topology, and also "Fooled by Randomness" (number of 21 on the list) which gives an accessible intro to the ideas of probability.

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I am sure you will get many useful tips for material, however I have one suggestion. Math deals first and foremost with abstract ideas that often have very simple definitions. People that are not experienced in math may sometimes confuse the fact that something is easy to define with it being easy to understand. However, one of the interesting things in math is that something can be very easy to define or write down but challenging to understand deeply and intuitively.

In my experience, one of the most important things you need to do in order to really understand math is to get your hands dirty. That means solving, calculating, proving and playing around to see what happens. This takes time and discipline, but that is the only way to go.

Good luck!

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  • $\begingroup$ I have updated the question. $\endgroup$ – esafwan Sep 26 '12 at 15:19
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Try this:

http://www.artofproblemsolving.com/Store/curriculum.php

Do not think of yourself as an inferior.Just imagine that you are starting fresh.

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I recommend the book

Lang, Serge., Basic Mathematics, Springer, 1971.

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I second using something like khanacademny.com to get a refresher on Math. Their World of Math track starts at the beginning.

I started doing it because I'm preparing to go back to graduate school after a few years out of undergrad. I took up to Calculus (I and II) in college, but now that I've been out of school for a few years some of the specifics have gotten really shaky.

Like in many other areas, a rock solid understanding of the basics will help immensely as you get into the more advanced math.

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