Mathematics
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 realworld 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 

Science  
Formal Science  
Mathematics  
Applied Mathematics  Pure Mathematics  Foundation Mathematics 



Applied Mathematics  Pure Mathematics  Foundation Mathematics 
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Nomenclature & Symbols 
Mathematics Glossary
A
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 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.
B
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 Biomathematics  The mathematical way to study biology and medicine.
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 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 nonarithmetical 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.
D
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 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.
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 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.
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 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.
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 Game Theory  The social interactions, which attempts to explain the mathematical conflicts, cooperation, and interactions people have with one another.
 Geostatistics  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, twodimensional figures and solid geometry, threedimensional figures.
 Group Theory  The study of a set of elements present in a group.
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 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.
M
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 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.
N
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 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.
O
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 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.
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 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.
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 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 threedimensional 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.
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 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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 Vector  A mathematical entity that has both magnitude and direction.
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Tags: Mathematics