163 relations: Abel–Ruffini theorem, Abstract algebra, Addition, Alexandria, Algebra, Algebraic curve, Algebraic equation, Algebraic expression, Algebraic geometry, Algebraic number, Algebraic solution, Algebraic surface, Algebraic variety, Algorithm, Almost all, Analytic geometry, Antiderivative, Approximation, Biology, Cancelling out, Cartesian coordinate system, Cassini oval, Chemistry, Circle, Classical electromagnetism, Clearing denominators, Commutative algebra, Complex number, Computer science, Computer simulation, Cone, Conic section, Coordinate system, Cubic function, Cubic plane curve, Curve, Degree of a polynomial, Dependent and independent variables, Derivative, Difference of two squares, Differential equation, Dimension, Diophantine equation, Diophantus, Division (mathematics), Dynamical system, Economics, Elasticity (physics), Electrostatics, Elementary function, ..., Ellipse, Elliptic curve, Engineering, Equality (mathematics), Equals sign, Equation solving, Euclidean geometry, Expression (mathematics), Extraneous and missing solutions, Factorization of polynomials, Field (mathematics), Five Equations That Changed the World, Fluid dynamics, Formula, Formula editor, Function (mathematics), Functional analysis, Functional equation, Gaussian elimination, Geometry, Heat, History of algebra, Hyperbola, Identity (mathematics), Implicit function, Inequality (mathematics), Inequation, Inflection point, Integer, Integral equation, Integro-differential equation, Latinisation of names, Lattice (group), Lemniscate of Bernoulli, Line (geometry), Linear algebra, Linear equation, Linearization, List of equations, List of mathematical symbols, List of scientific equations named after people, List of trigonometric identities, Lists of shapes, Manifold, Mathematical analysis, Mathematical model, Mathematics, Monomial, Multidimensional system, Multiplication, Multivariable calculus, Nonlinear system, Number, Number theory, Numerical analysis, Numerical linear algebra, Numerical methods for ordinary differential equations, Octic equation, Operation (mathematics), Ordinary differential equation, Parabola, Parameter, Parametric equation, Partial derivative, Partial differential equation, Periodic function, Perpendicular, Physics, Pi, Plane (geometry), Point (geometry), Point at infinity, Polynomial, Polynomial expansion, Pure mathematics, Quadratic equation, Quantum mechanics, Quartic function, Quintic function, Rational number, Real number, Recurrence relation, René Descartes, Robert Recorde, Root-finding algorithm, Seesaw, Septic equation, Sextic equation, Sides of an equation, Sign (mathematics), Sine, Singular point of a curve, Solution set, Sound, Space (mathematics), Stochastic partial differential equation, Subtraction, Surface (topology), System of equations, System of linear equations, System of polynomial equations, Term (logic), Theory of equations, Topology, Transcendental equation, Transcendental function, Transcendental number, Trigonometric functions, Trigonometry, Unit circle, Unit vector, Variable (mathematics), Weighing scale. Expand index (113 more) » « Shrink index
In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
Addition (often signified by the plus symbol "+") is one of the four basic operations of arithmetic; the others are subtraction, multiplication and division.
Alexandria (or; Arabic: الإسكندرية; Egyptian Arabic: إسكندرية; Ⲁⲗⲉⲝⲁⲛⲇⲣⲓⲁ; Ⲣⲁⲕⲟⲧⲉ) is the second-largest city in Egypt and a major economic centre, extending about along the coast of the Mediterranean Sea in the north central part of the country.
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.
In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.
In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).
An algebraic solution or solution in radicals is a closed-form expression, and more specifically a closed-form algebraic expression, that is the solution of an algebraic equation in terms of the coefficients, relying only on addition, subtraction, multiplication, division, raising to integer powers, and the extraction of nth roots (square roots, cube roots, and other integer roots).
In mathematics, an algebraic surface is an algebraic variety of dimension two.
Algebraic varieties are the central objects of study in algebraic geometry.
In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.
In mathematics, the term "almost all" means "all but a negligible amount".
In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
An approximation is anything that is similar but not exactly equal to something else.
Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.
Cancelling out is a mathematical process used for removing subexpressions from a mathematical expression, when this removal does not change the meaning or the value of the expression because the subexpressions have equal and opposing effects.
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.
A Cassini oval is a quartic plane curve defined as the set (or locus) of points in the plane such that the product of the distances to two fixed points is constant.
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.
A circle is a simple closed shape.
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.
In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
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.
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
Computer simulation is the reproduction of the behavior of a system using a computer to simulate the outcomes of a mathematical model associated with said system.
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
In algebra, a cubic function is a function of the form in which is nonzero.
In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation.
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.
A differential equation is a mathematical equation that relates some function with its derivatives.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
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.
Division is one of the four basic operations of arithmetic, the others being addition, subtraction, and multiplication.
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
Economics is the social science that studies the production, distribution, and consumption of goods and services.
In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.
Electrostatics is a branch of physics that studies electric charges at rest.
In mathematics, an elementary function is a function of one variable which is the composition of a finite number of arithmetic operations, exponentials, logarithms, constants, and solutions of algebraic equations (a generalization of ''n''th roots).
In mathematics, an ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve.
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
The equals sign or equality sign is a mathematical symbol used to indicate equality.
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equality sign.
Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.
In mathematics and computer algebra, factorization of polynomials or polynomial factorization is the process of expressing a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain.
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.
Five Equations That Changed the World: The Power and Poetry of Mathematics is a book by Michael Guillen, published in 1995.
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.
In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.
A formula editor is a name for a computer program that is used to typeset mathematical works or formulae.
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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.
In mathematics, a functional equation is any equation in which the unknown represents a function.
In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.
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.
In thermodynamics, heat is energy transferred from one system to another as a result of thermal interactions.
As a branch of mathematics, algebra emerged at the end of the 16th century in Europe, with the work of François Viète.
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
In mathematics an identity is an equality relation A.
In mathematics, an implicit equation is a relation of the form R(x_1,\ldots, x_n).
In mathematics, an inequality is a relation that holds between two values when they are different (see also: equality).
In mathematics, an inequation is a statement that an inequality holds between two values.
In differential calculus, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function.
Latinisation or Latinization is the practice of rendering a non-Latin name (or word) in a Latin style.
In geometry and group theory, a lattice in \mathbbR^n is a subgroup of the additive group \mathbb^n which is isomorphic to the additive group \mathbbZ^n, and which spans the real vector space \mathbb^n.
In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2a from each other as the locus of points P so that PF1·PF2.
The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.
Linear algebra is the branch of mathematics concerning linear equations such as linear functions such as and their representations through matrices and vector spaces.
In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.
In mathematics, linearization is finding the linear approximation to a function at a given point.
This is a list of equations, by Wikipedia page under appropriate bands of maths, science and engineering.
This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.
This is a list of scientific equations named after people (eponymous equations).
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables where both sides of the equality are defined.
This is an index of lists of geometric shapes and related topics.
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.
A mathematical model is a description of a system using mathematical concepts and language.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term.
In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one dependent variable exists (like time), but there are several independent variables.
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.
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one.
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
A number is a mathematical object used to count, measure and also label.
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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).
Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
In algebra, an octic equation is an equation of the form where.
In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.
In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).
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.
The number is a mathematical constant.
In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.
In modern mathematics, a point refers usually to an element of some set called a space.
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
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.
In mathematics, an expansion of a product of sums expresses it as a sum of products by using the fact that multiplication distributes over addition.
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.
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.
In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
In algebra, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.
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.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.
Robert Recorde (c.1512–1558) was a Welsh physician and mathematician.
In mathematics and computing, a root-finding algorithm is an algorithm for finding roots of continuous functions.
A seesaw (also known as a teeter-totter or teeterboard) is a long, narrow board supported by a single pivot point, most commonly located at the midpoint between both ends; as one end goes up, the other goes down.
In algebra, a septic equation is an equation of the form where.
In algebra, a sextic polynomial is a polynomial of degree six.
In mathematics, LHS is informal shorthand for the left-hand side of an equation.
In mathematics, the concept of sign originates from the property of every non-zero real number of being positive or negative.
In mathematics, the sine is a trigonometric function of an angle.
In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter.
In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.
In mathematics, a space is a set (sometimes called a universe) with some added structure.
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations.
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection.
In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.
In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.
A system of polynomial equations is a set of simultaneous equations f1.
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.
In algebra, the theory of equations is the study of algebraic equations (also called “polynomial equations”), which are equations defined by a polynomial.
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.
A transcendental equation is an equation containing a transcendental function of the variable(s) being solved for.
A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.
In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.
Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.
In mathematics, a unit circle is a circle with a radius of one.
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
Weighing scales (or weigh scales or scales) are devices to measure weight.
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