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That's pretty advanced for someone who claims to know absolutely nothing about math.
mmm... depends what country you grew up in. But I'll say if you can do derivatives, you know some math, up to that, you know of math.
What is your specific goal? What are you trying to achieve with math? I would start there first. If your goal is to get a math major level of understanding of math, then I would look at what the standard curriculum is in universities.
Math that can help me to be a good programmer.
Discrete math is the branch that is most likely to make you a better programmer. Not Kahn academy, etc.
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Math that can help me to be a good programmer.
That in itself is quite an interesting question - there are bits of (quite simple) maths that are useful in general programming (logic etc.), maths that can be used in particular domain areas (simulation, crypto etc.), maths that models computation itself and can underlie the design of languages (Turing Machines, Lambda Calculus etc.)...