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Can anybody please show me main branches and subbranches of mathematics and statistic sciences in a hierarchical form? I am not a mathematician and I often in my research see a lot of new mathematical terms and theories. I need a way to find proper path to learn that specific terms (so I first study its prerequisites and focus on just necessary parts).

(Algebra,linear algebra, calculus, Arithmetic, Analysis,...)

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The thing looks more like a tangled web than a neat-looking tree... –  J. M. May 10 '12 at 14:40
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Asking for a hierarchial list of the main branches of math seems like an overly broad request. Why not tell us why you need such a list in the first place. Wanting one to be able to find a specific subject doesn't seem realistic. If you come across a new area of math in your research and you want to find out roughly what it is about, you can just Google it. –  KCd May 10 '12 at 14:41
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possible duplicate of this closed question: math.stackexchange.com/q/82660/1543 The closest thing to some sort of hierarchical classification is ams.org/mathscinet/msc/msc2010.html –  Willie Wong May 10 '12 at 14:47
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Have you even looked at Wikipedia? en.wikipedia.org/wiki/Areas_of_mathematics –  Neal May 10 '12 at 15:01
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There is no such thing. –  AD. May 10 '12 at 15:01

3 Answers 3

up vote 8 down vote accepted

The Mathematical Atlas might be useful. Quote from the front page:

Welcome! This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions. The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages").

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Thanks a lot for your excellent answer. The site is exactly what I was searching for. –  PHPst May 14 '12 at 17:43

A somewhat flawed but possibly useful classification can be found at here. This is the American Mathematical Society's mathematics subject classification.

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Thanks, it is so detailed, I need just main relations between main branch and a short explanation of the special view port of the branches that make it another segment, I mean pure math no applied math –  PHPst May 10 '12 at 14:56
    
The AMS classification includes probability and stochastic process and statistics as categories. I think I can say that probability and stochastic processes could be considered a branch of mathematics. But like many statisticians I do not see the field of statistics as a branch of methematics. While mathematics is used in statistical theory to for example determine properties of estimators, get asymptotic distributions and derive distributions for functions of a random variable it is methodology for data analysis –  Michael Chernick May 10 '12 at 15:10
    
As such it has principles of inference that are used to evaluate patterns in data that can be separated from random noise. That activity is different from mathematics I think. –  Michael Chernick May 10 '12 at 15:12

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Source: EPRS, where it is available an A-Z list of all research areas within the EPSRC portfolio and all research areas within this theme.

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