Branches of Mathematics

S_David

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_o...ematics_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.