What are the Different Branches of Mathematics?

[EngWiPy]

Hello,

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

Regards

 

[HallsofIvy]

You could get as many answers to that as there are mathematicians!
Here is a pretty good list:
http://en.wikipedia.org/wiki/Lists_of_mathematics_topics

 

[g_edgar]

There is also this
http://www.math.niu.edu/~rusin/known-math/welcome.html

 

[kstahmer]

Interesting question, asked the same question. Did a Google search and got a multitude of answers.

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.