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<p>The three main branches of Math are Analysis, Algebra and Topology (as explained recently by a TA). Probability is a branch of Analysis. Statistics is an application of Probability, in the same way different areas of Physics are applications of various mathematical areas.</p>
<p>This is somewhat simplified though, as there are areas like Geometry and Number Theory that don’t really fit neatly in anywhere. And I think he may have completely forgotten Discrete Math and Logic.</p>