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I am looking for diagrams which relate/compare various fields in mathematics or mathematical structures/spaces. My objective is to find out which area of mathematics I should study in order to answer a research question. In other words, I am looking for a hierarchy of mathematical structures and how they are related.s

I found a few such diagrams but looking for more definitive ones. Thank you very much for your help.

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I am not sure it's a good idea to mix two different questions (relations between fields vs. relations between concepts in one field). Wouldn't it be better to consider asking them separately? By the way, since your question (as it stands) asks for quite general relations, would diagrams at johndcook.com/modes_of_convergence.html also satisfy you? –  Marek Sep 10 '12 at 12:42
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