a.. History of Mathematics
b.. Mathematical logic and mathematical basis
  a.. Deductive logic Also known as symbolic logic  
  b.. Theory of proof Also known as metamathematics
  c.. Recursion theory
  d.. Model theory
  e.. Axiomatic set theory
  f.. Fundamentals of Mathematics
  g.. Mathematical logic and basic mathematics

c.. number theory
  a.. Elementary number theory
  b.. Analytic number theory
  c.. Algebraic number theory
  d.. Beyond number theory
  e.. Diophantine approximation
  f.. The geometry of numbers
  g.. Probability number theory
  h.. Computational number theory
  i.. Other subjects of number theory

d.. Algebra
  a.. linear algebra
  b.. group theory
  c.. Domain theory
  d.. Li Qun
  e.. Lie algebra
  f.. Kac-Moody Algebra
  g.. Ring theory Including commutative rings and commutative algebras , Associative rings and associative algebras , Non associative rings and non associative algebras, etc
  h.. Model theory
  i.. Case theory
  j.. Pan algebra theory
  k.. Category theory
  l.. Homology algebra
  m.. Algebra K theory
  n.. Differential algebra
  o.. Algebraic coding theory
  p.. Other subjects of algebra

e.. Algebraic geometry

f.. geometry
  a.. foundations of geometry
  b.. Euclidean geometry
  c.. Non Euclidean geometry Including Riemannian geometry, etc
  d.. Spherical geometry
  e.. Vector and tensor analysis
  f.. Affine geometry
  g.. Projective geometry
  h.. Differential geometry
  i.. Fractal geometry
  j.. Computational geometry
  k.. Geometry other disciplines

g.. topology
  a.. Point set topology
  b.. Algebraic topology
  c.. Homotopy
  d.. Low-dimensional topology
  e.. Homology theory
  f.. Dimension theory
  g.. Lattice topology
  h.. Fiber bundle theory
  i.. geometric topology
  j.. Singularity theory
  k.. Differential Topology
  l.. Other disciplines of topology

h.. mathematical analysis
  a.. Differential calculus
  b.. Integral calculus
  c.. Series theory
  d.. Other subjects of mathematical analysis

i.. Nonstandard analysis

j.. Function theory
  a.. On functions of real variables
  b.. On functions of simple and complex variables
  c.. On functions of multiple complex variables
  d.. Function approximation theory
  e.. harmonic analysis
  f.. Complex manifold
  g.. Special function theory
  h.. Other disciplines of function theory

k.. ordinary differential equation
  a.. Qualitative theory
  b.. Stability theory
  c.. Analytic theory
  d.. Ordinary differential equations other disciplines

l.. partial differential equation
  a.. Elliptic partial differential equation
  b.. Hyperbolic partial differential equation
  c.. Parabolic partial differential equation
  d.. Nonlinear partial differential equations
  e.. Partial differential equations other disciplines

m.. dynamic system
  a.. Differential dynamical system
  b.. Topological dynamical system
  c.. Complex dynamic system
  d.. Power systems other disciplines

n.. integral equation

o.. functional analysis
  a.. Linear operator theory
  b.. Variational method
  c.. Topological linear space
  d.. Hilbert space
  e.. function space
  f.. Banach space
  g.. Operator algebra
  h.. Measure and integration
  i.. Generalized function theory
  j.. Nonlinear functional analysis
  k.. Other disciplines of functional analysis

p.. Computational Mathematics
  a.. Interpolation and approximation theory
  b.. Numerical solution of ordinary differential equation
  c.. Numerical solutions of differential equations
  d.. Numerical solution of integral equation
  e.. Numerical algebra
  f.. Discretization method for continuous problems
  g.. Random numerical experiment
  h.. error analysis
  i.. Other subjects of Computational Mathematics

q.. probability theory
  a.. Geometric probability
  b.. probability distribution
  c.. Limit theory
  d.. random process It includes normal process and stationary process , Point process, etc
  e.. markov process
  f.. stochastic analysis
  g.. martingale
  h.. Applied probability theory Specific application into relevant disciplines
  i.. Probability theory other disciplines

r.. Mathematical statistics
  a.. Sampling theory Including sampling distribution , Sampling survey, etc
  b.. hypothesis test
  c.. Nonparametric statistics
  d.. variance analysis
  e.. Correlation regression analysis
  f.. statistical inference
  g.. Bayesian statistics Including parameter estimation, etc
  h.. experimental design
  i.. multivariate analysis
  j.. Statistical decision theory
  k.. Time series analysis
  l.. Other subjects of mathematical statistics

s.. Applied Statistical Mathematics
  a.. Statistical quality control
  b.. Reliability mathematics
  c.. Insurance mathematics
  d.. Statistical simulation

t..   Other subjects of Applied Statistical Mathematics

u.. Operations research
  a.. linear programming
  b.. nonlinear programming
  c.. dynamic programming
  d.. Combinatorial optimization
  e.. Parametric programming
  f.. integer programming
  g.. stochastic programming
  h.. queuing theory
  i.. Game theory Also known as game theory
  j.. Inventory theory
  k.. Decision theory
  l.. Search theory
  m.. graph theory
  n.. On overall planning
  o.. optimization
  p.. Other disciplines of operational research

v.. Combinatorics

w.. discrete mathematics

x.. fuzzy mathematics

y.. applied mathematics Specific application into relevant disciplines

z.. Other subjects of Mathematics

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