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I'm trying to make a big picture of mathematics as a concept so that I get a better understanding of it and can connect different parts of it and understand the relationship between them. In the picture below mathematics is divide into four fields of study namely Quantity, Structure, Space and Change and each field is subdivided into sub-fields. Wikipedia also names some possible structures such as measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories.

Where are these structures to be placed in the map? I know for example that algebraic structures go under abstract algebra but what about the rest? Are they all sub categories of linear algebra or abstract algebra or do some of them go directly under Structure?

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    $\begingroup$ Please remember that such taxonomies should not be taken too seriously. The divides between the areas is mostly artificial. $\endgroup$ Oct 21 '15 at 7:51
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    $\begingroup$ What Ittay said, I'd also say you'll end up more with a web than a tree. $\endgroup$ Oct 21 '15 at 7:52
  • $\begingroup$ @MorganRodgers Well the map is not flawed because it does not say anaything about algebraic structures or vector spaces. It simply does not go that much into details. $\endgroup$
    – Infinity
    Oct 21 '15 at 8:00

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