## Branches of Mathematics

Hello,

I am just curious, what are the branches of Mathematics, and what does each branch concern of?

Regards
 Recognitions: Gold Member Science Advisor Staff Emeritus You could get as many answers to that as there are mathematicians! Here is a pretty good list: http://en.wikipedia.org/wiki/Lists_o...ematics_topics
 There is also this http://www.math.niu.edu/~rusin/known-math/welcome.html

## Branches of Mathematics

When I first studied mathematics decades ago, was taught the major branches of mathematics were:
• Analysis (e.g. functions, sequences, series, limits, derivatives, integrals, real analysis, complex analysis, complex number theory, functional analysis, measure theory)
• Algebra (e.g. linear algebra, group theory, ring theory, Galois Theory, number theory, algebraic number theory, combinatorics)
• Topology (e.g. point set topology, combinatorial topology, algebraic topology)
• Logic and Set Theory (e.g. propositional calculus, predicate calculus, metamathematics, recursion theory, category theory, von Neumann-Bernays-Gödel (NBG) set theory, Zermelo-Fraenkel (ZF) set theory, model theory, fuzzy logic)
• Applied Mathematics (e.g. ordinary differential equations (ODE), partial differential equations (PDE), Fourier series, Fourier transforms, game theory)
Yet my anachronistic list isn't the end-all and be-all of lists. Some colleges and universities include statistics and numerical analysis as separate branches of mathematics. Some include geometry as a separate branch. There many other variations as well.

There also variations within the branches. Is algebraic topology, algebra or topology? Is complex number theory, analysis or algebra? Opinions vary.