mathematics banner 4Mathematics is a discipline that deals with the study of numbers, quantities, and shapes.  It involves using logical reasoning and critical thinking to solve problems and develop theories.  Mathematics can be divided into many different areas, including algebra, arithmetic, calculus, geometry, statistics, trigonometry, and number theory.  Each of these areas has its own concepts and techniques, and they can be applied in a wide range of fields, from physics and engineering to economics and computer science.

Mathematics plays a fundamental role in many aspects of modern society, from finance and business to medicine and technology.  It provides the tools and techniques needed to analyze and understand complex systems, and to develop solutions to real-world problems.

Mathematics is also a highly abstract and creative field, with a rich history of exploration and discovery.  Mathematicians are constantly pushing the boundaries of knowledge, developing new theories and concepts that deepen our understanding of the natural world.  Overall, mathematics is a fascinating and essential discipline that plays a critical role in advancing our understanding of the world and in developing new technologies that improve our lives.  It is a field that requires curiosity, creativity, and analytical thinking, and it offers endless opportunities for exploration and discovery.


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.




  • Scalar  -  A quantity that is fully described by its magnitude or size and is independent of any specific direction.
  • 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.



  • Vector  -  A mathematical entity that has both magnitude and direction. 






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