mathematics banner 4Mathematics, abbreviated MATH, is the study of properties, quantities and their relationships using numbers and symbols.

Mathematics Index


Major Branches of Mathematics

  • Applied Mathematics  -  Applies programs that typically involve a wider range of study to problems that arise in various areas.
  • Pure Mathematics  -  The study of mathematical concepts independently of any application outside matnematics.
  • Foundations Mathematics  -  The study of philosophical and logical.


Science Branches

Formal Science
Applied Mathematics Pure Mathematics Foundation Mathematics
  • Approximation Theory
  • Mathematical Statistics
    • Actuarial Science
    • Demography
    • Econometrics
    • Probability
  • Numerical Analysis
  • Optimization
    • Linear Programming
    • Operations Research
  • Dynamical Systems
    • Chaos Theory
    • Fractal Geometry
  • Mathematical Physics
    • Quantum Field Theory
    • Statistical Mechanics
  • Information Theory
  • Combinatorics
    • Coding Theory
  • Computational Statistics
  • Cryptography
  • Statistics
    • Computational Statistics
  • Algebra
    • Abstract Algebra
    • Associative Algebra
    • Category Theory
    • Differential Algebra
    • Elementary Algebra
    • Group Theory
    • Homological Algebra
    • Field Theory
    • Lattice Theory
      • Order Theory
    • Lie Algebra
    • Linear Algebra
    • Multilinear Algebra
    • Non-associative Algebra
    • Ring Theory
    • Universal Algebra
  • Analysis
    • Complex Analysis
    • Functional Analysis
      • Operator Theory
    • Harmonic Analysis
    • Non-standard Analysis
    • Ordinary Differential Equation
    • p-adic Analysis
    • Real Analysis
      • Calculus
  • Probability Theory
    • Ergodic Theory
    • Measure Theory
    • Stochastic Process
  • Arithmetic
  • Geometry
    • Affine Geometry
    • Algebraic Geometry
    • Algebraic Topology
    • Analytic Geometry
    • Convex Geometry
    • Differential Geometry
    • Differential Topology
    • Discrete Geometry
    • Euclidean Geometry
    • General Topology
    • Geometric Topology
    • Non-Euclidean Geometry
    • Projective Geometry
    • Topology
  • Number Theory
    • Algebraic Number Theory
    • Analytic Number Theory
    • Computational Number Theory
    • Geometric Number Theory
  • Trigonometry
  • Intuitionistic Logic
  • Modal Logic
  • Model Theory
  • Proof Theory
  • Recursion Theory
  • Set Theory
Applied Mathematics Pure Mathematics Foundation Mathematics


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Nomenclature & Symbols

Mathematics Glossary


  • Algebra  -  Uses letters or symbols as a place holder for unknown values or numbers.  These variables are used to represent relationships and to solve equations.
  • Analysis  -  The approximation of certain mathematical objects, like numbers or fractions.
  • Applied Mathematics  -  Applies programs that typically involve a wider range of study to problems that arise in various areas.
  • Arithmetic  -  The study of numbers and the properties of their operations.


  • Biomathematics  -  The mathematical way to study biology and medicine.


  • Calculate  -  Determines the amount or number of something using mathematical methods.
  • Calculus  -  The study of how things change.
  • Chaos Theory  -  Deals with complex systems whose behavior is highly sensitive to slight change in conditions.
  • Combinatorics  -  Concerned with the number of ways of choosing some objects out of a collection.
  • Computation  -  A calculation that includes borh arithmetical and non-arithmetical steps and follows a defined method.
  • Computational Statistics  -  The interface between statistics and computer science.
  • Constant  -  Something continuing forever or for an indefinitely long time.
  • Continuous  -  Deals with connected objects.  Connected objects are those which are not seperated from each other, such as set of real numbers. 
  • Cryptography  -  The secret writing with the intention fo keeping the data secret.
  • Counting  -  The action of finding the number of elements of a finite set of objects.


  • Derivative  -  A derivative is a basic tool of calculus.  It is a variable that measures the rate of change of the function value (output value) with respect to a change in its argument (input value).  Example: acceleration is the rate of change of velocity, therefore, acceleration is the derivative of velocity.
  • Discrete Mathematics  -  Deals with discrete objects.  Discrete objects are those which are seperated from each other, such as set of integers.
  • Dynamical Systems  -  How the state of a system changes with time.


  • Elementary Algebra  -  Performs basic concepts of algebra operations.
  • Equation  -  A statement containing one or more variables that are either added, subtracted, divided, or multiplied to get an answer or a value.
  • Estimate  -  An approximate calculation of a quantity.
  • Estimation  -  The process of finding an approximation.
  • Euclidean Geometry  -  The study of plane and solid figures.


  • Finite  -  Something that is bounded or limited in magnitude or special or temporal extent.
  • Formula  -  A rule expressed in symbols or a concise way of expressing information.


  • Game Theory  -  The social interactions, which attempts to explain the mathematical conflicts, cooperation, and interactions people have with one another.
  • Geo-statistics  -  The study of spiral or spatiotemporal datasets.
  • Geometry  - Deals with shapes and their properties or relationships to circles, lines, points, etc.  These relationships can be expressed in plane geometry, two-dimensional figures and solid geometry, three-dimensional figures.
  • Group Theory  -  The study of a set of elements present in a group.






  • Linear Algebra  -  Concerned with vector spaces and linear mapping between such spaces.
  • Logic  -  The principles of reasoning or arriving at some conclusion, though it is not logical, based on statements or propositions.


  • Mathematical Analysis  -  Deals with limits and related theories, such as differential, integral , measure, infinite series, and analytic functions.
  • Mathematical Constant  -  A special number that is significantly interesting in some way.
  • Mathematical Optimization  -  The selection of the best element from some set of available alternatives.
  • Mathematical Proof  -  Demonstrates that a statement is always true.
  • Mathematical Statistics  -  The study of statistics from the standpoint of mathematics of analysis, collection, interpretation, presentation, and organization of data.


  • Number  -  A mathematical object used to count.
  • Number Theory  -  Deals with the properties of numbers and the relationships between them, primarily integers.
  • Numeral System  -  A mathematical notification of a given set, using digits or other symbols in a consistent manner.


  • Operation  -  A calculation from zero or more input values to an output value.
  • Optimization  -  The process of maximizing or minimizing an objects function by finding the best avaliable values across a set of inputs.
  • Order Theory  -  Deals with order using bionary relations.


  • Plane Geometry  -  A two dimensional figure, also called planar geometry, with edges.
  • Planck Constant  -  A physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency.
  • Probability  -  The study of change or the likelihood of an event happening.
  • Proposition  -  A statement that is either true or false.
  • Propositional Logic  -  A tool for reasoning about how various statements affect one another.
  • Pure Mathematics  -  The study of mathematical concepts independently of any application outside matnematics.




  • Set Theory  -  Studies sets, which informally are collections of objects.
  • Solid Geometry  -  A three-dimensional figure with connecting edges on multiple planes.
  • Standard Deviation  -  A measure that is used to quantify the amount of variation or dispersion of a set of data values.
  • Statistics  -  The study of analysis, collection, interpretation, presentation, and organization of data.
  • Symmetry  -  An agreement in dimensions and arrangement.
  • Symmetry Number  -  The number of different but indistinguishable or equivalent arrangements or views of the object.


  • Topology  -  The spaces and their properties while under any continuous deformation.
  • Trigonometry  -  The relations between the sides and angles of plane or spherical triangles.








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