List of mathematics lists: Encyclopedia II - List of mathematics lists - Fields of mathematics

List of mathematics lists - Fields of mathematics

List of mathematics lists - Basic mathematics

These lists cover topics typically taught in secondary education or in the first year of university.

• List of basic discrete mathematics topics
• List of calculus topics
• List of geometry topics
• List of topics in logic
• List of trigonometry topics

List of mathematics lists - Advanced mathematics

Algebra includes the study of algebraic structures, which are sets and operations defined on these sets satisfying certain axioms. The field of algebra is further divided according to which structure is studied; for instance, group theory concerns an algebraic structure called group.

• List of abstract algebra topics
• List of Boolean algebra topics
• List of category theory topics
• List of commutative algebra topics
• List of homological algebra topics
• List of group theory topics
• List of linear algebra topics
• Glossary of field theory
• Glossary of group theory
• Glossary of linear algebra
• Glossary of ring theory
• List of cohomology theories

Calculus studies the computation of limits, derivatives, and integrals of functions of real numbers, and in particular studies instantaneous rates of change. Analysis studies the same subjects, but on a more rigorous level, and also topics that evolved from calculus.

• List of complex analysis topics
• List of functional analysis topics
• List of integration and measure theory topics
• List of harmonic analysis and representation theory topics
  • List of Fourier analysis topics
• List of multivariable calculus topics
• List of real analysis topics
• List of variational topics
• Glossary of tensor theory

Geometry is initially the study of spatial figures like circles and cubes, though it has been generalized considerably. Topology developed from geometry; it looks at those properties that do not change even when the figures are deformed by stretching and bending, like dimension.

• List of geometry topics
• List of geometric shapes
• List of curve topics
• List of circle topics
  • List of topics related to pi
• List of general topology topics
• List of differential geometry topics
• List of algebraic geometry topics
  • List of algebraic surfaces
• List of algebraic topology topics
  • List of cohomology theories
• List of geometric topology topics
• List of knot theory topics
• List of Lie group topics
• Glossary of differential geometry and topology
• Glossary of general topology
• Glossary of Riemannian and metric geometry
• Glossary of scheme theory

Discrete mathematics concerns itself with the study of finite sets. This is in contrast with analysis and geometry, which study continua: between every two distinct points, however close together, one can always find another point.

• List of combinatorics topics
• List of graph theory topics
• Glossary of graph theory

Logic is the foundation which underlies mathematical logic and the rest of mathematics. It tries to formalize valid reasoning. In particular, it attempts to define what constitutes a proof.

• List of Boolean algebra topics
• List of computability and complexity topics
• List of large cardinal properties
• List of mathematical logic topics
• Glossary of order theory
• List of set theory topics

Number theory studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number, and there are many questions about primes that appear simple but whose resolution continues to elude mathematicians.

• List of algebraic number theory topics
• List of number theory topics
• List of recreational number theory topics
• Glossary of arithmetic and Diophantine geometry

List of mathematics lists - Applied mathematics

The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures, and in scientific computing, the study of algorithmic methods for solving problems in mathematics, science and engineering.

• List of algorithm general topics
• List of algebraic coding theory topics
• List of cryptography topics
• Lists for computational topics in geometry and graphics
  • List of combinatorial computational geometry topics
  • List of computer graphics and descriptive geometry topics
  • List of numerical computational geometry topics
• List of formal language and literal string topics
• List of network theory topics
• List of numerical analysis topics
• List of terms relating to algorithms and data structures

In a dynamical system, a fixed rule describes the time dependence of a point in a geometrical space. The mathematical models used to describe the swinging of a clock pendulum, the flow of water in a pipe, or the number of fish each spring in a lake are examples of dynamical systems.

• List of dynamical systems and differential equations topics
• List of partial differential equation topics

Mathematical physics is concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories"¹.

• List of mathematical topics in classical mechanics
• List of mathematical topics in quantum theory
• List of mathematical topics in relativity
• List of string theory topics
• List of wave topics

Probability theory is the formalization and study of the mathematics of uncertain events or knowledge. The related field of statistics concerns the mathematics and science of collecting and analyzing data.

• List of probability distributions
• List of probability topics
• List of information theory topics
• List of statistical topics
• List of stochastic processes topics

Operations research is the study and use of mathematical models, statistics and algorithms to aid in decision-making, typically with the goal of improving or optimizing performance of real-world systems.

• Glossary of game theory

Adapted from the Wikipedia article "Fields of mathematics", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki