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May 19th, 2014, 10:27 PM   #1
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A "tree of life" of mathematical knowledge?

Hello everyone,

I have a question that I hope I will be able to explain clearly...

I was thinking earlier: Most of my mathematical knowledge is like a branching "tree", in the sense that: You need algebra to understand calculus, and you need arithmetic to understand algebra. Also, you need caulcus to understand statistics. Similarly, you need algebra to understand matrix/linear algebra (but you don't necessarily need calculus for that), and you need matrix algebra to understand dynamical systems theory.

My point is probably clear.

Now I want to develop my knowledge and skills of mathematics further, and for that reason, I'm wondering what the "tree of knowledge" looks like for mathematics.
For example, if I want to learn group theory (which I do), then what would I have to learn first?

I know this is a kind of weird and general question, but: Is there some kind of website/book that gives an overview of all mathematical knowledge in a casual way?

The reason I'm asking this, is that right now, I don't have a clear picture at all of what we know about mathematics, and what I would need to learn first in order to learn about mathematical theory X or Y.

I'm not sure if my question is clear, so if itisn't, I'll be glad to clarify.

Thanks!
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May 20th, 2014, 06:02 AM   #2
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Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
The MSC
MSC2010 database
is a good starting point for what the fields are and how they're connected, though unfortunately it's a graph rather than a digraph so it doesn't quite answer your question.
Thanks from Evgeny.Makarov and raul21
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May 28th, 2014, 03:15 AM   #3
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Function Space is a good resource that satisfies all your purposes!
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