Equation and Mathematics

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Difference between Equation and Mathematics

Equation vs. Mathematics

In mathematics, an equation is a statement of an equality containing one or more variables. Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

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Addition

Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.

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Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

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Approximation

An approximation is anything that is similar but not exactly equal to something else.

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Biology

Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.

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Chemistry

Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Diophantus

Diophantus of Alexandria (Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299) was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost.

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Division (mathematics)

Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.

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Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined, and behave as when they are applied to rational and real numbers.

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Fluid dynamics

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.

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Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

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Functional analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.

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Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Multiplication

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Numerical linear algebra

Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.

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Operation (mathematics)

In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.

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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

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Pure mathematics

Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.

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Quantum mechanics

Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Subtraction

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.

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Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

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Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

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