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Some time ago, I was searching for a detailed diagram with mathematical fields of study the nearest one I could find is in this file, second page.

I want something that shows information like: "Geometry leads to I topic, Geometry and Algebra leads do J topic and so on.

Can you help me?

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This question was cross-posted at MO. –  Alex Becker Jul 5 '12 at 4:43
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@Gustavo: Look at the following meta.math.SE questions: here, here, here, and here. –  Zev Chonoles Jul 5 '12 at 4:48
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I think this has been asked before here. –  Dylan Moreland Jul 5 '12 at 5:07
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Something that doesn't do what you want, but is quite fine-grained, is the Mathematical Reviews Subject Classification –  André Nicolas Jul 5 '12 at 5:15
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@DylanMoreland Peharps you mean this question: Main branches of mathematics –  Martin Sleziak Jul 5 '12 at 7:50

3 Answers 3

up vote 6 down vote accepted
+100

Saunders Mac Lane's book Mathematics, Form and Function (Springer, 1986) has a number of illuminating diagrams showing linkages between various fields of mathematics (and also to some related areas.)

For example, p149: Functions & related ideas of image and composition;
p184: Concepts of calculus;
p306: Interconnections of mathematics and mechanics;
p408: Sets, functions and categories;
p416: Ideas arising within mathematics;
p422-3: various ideas and subdivisions;
p425: Interconnections for group theory;
p426: Connections of analysis with classical applied mathematics;
p427: Probability and related ideas;
p428: Foundations.

Mac Lane summarises on p428: "We have thus illustrated many subjects and branches of mathematics, together with diagrams of the partial networks in which they appear. The full network of mathematics is suggested thereby, but it is far too extensive and entangled with connections to be captured on any one page of this book."

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Great answer.$ $$ $$ $$ $ –  Vÿska Jul 14 '12 at 1:11

A diagram relating different areas of mathematics can be found at a blog post entitled An Attempt at Mapping Mathematics. It's by far the most comprehensive one I am aware of.

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Someone pointed me this one too.

enter image description here

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