Is the study of differential equations/dynamical systems etc algebraic or analytic?

Question

I'm also wondering whether functional analysis, fourier analysis, lie theory, combinatorics, numerical analysis, order theory, category theory, representation theory are algebraic or analytic? respectively.

By analytic I mean analysis like.

Does set theory belong to algebra or analysis?

score 1 · Accepted Answer · edited Oct 26 '17 at 20:06

1

Functional Analysis is "analytic". Differential equations and dynamical systems are more "analytic" than algebraic. Representation theory and Lie theory are more algebraic. Numerical analysis is more "analytic". Category theory, combinatorics and order theory are more algebraic.

Nevertheless, mathematics doesn't "split" into analysis and algebra. Remember, all the branches of mathematics are somehow connected.

edited Oct 26 '17 at 20:06

Moo

11,311

answered Oct 26 '17 at 18:44

James Garrett

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I would say that combinatorics and geometry are two further categories. – Rene Schipperus Oct 26 '17 at 18:45
I agree on Geometry, but (for me), combinatorics is algebraic, kinda... – James Garrett Oct 26 '17 at 19:03
No, I dont see that at all, combinatorics is very different. – Rene Schipperus Oct 26 '17 at 19:10

score 1 · Answer 2 · answered Oct 30 '17 at 20:48

I would say this isn't the best way to organize branches of mathematics. I think a better way to look at is that set theory and category theory sort of make up two approaches to math. Set theory is bottom up, and category theory is top down. Set theory is concerned with stuff, category theory with structure. Then I would say analysts often like to stay pretty close to the bottom and algebraists pretty close to the top, but most branches generally benefit from both perspectives to varying degrees.

Is the study of differential equations/dynamical systems etc algebraic or analytic?

2 Answers2