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

Examples of branches include, but are not limited to, algebra, linear algebra, calculus, arithmetic and analysis.

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    Maybe the Princeton Companion would be a good investment.2012-05-12

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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").

EDIT: It seems that the website no longer available. However, you can still browse it through the internet archive: link.

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    @paulpaul1076: Seems like it's no longer hosted. However, I think most of the content can still be found through the internet archive.2016-04-21
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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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    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.2012-05-10
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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.