An article from Science News Jan 2020

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Article

## Algebra

The branch of mathematics dealing with the solution of equations. These equations involve unknowns, or variables, along with fixed numbers from a specified system (Fig. 1). The origins of algebra were based on the need to develop equations that…

Article

## Cardioid

A heart-shaped curve generated by a point of a circle that rolls (without slipping) on a fixed circle of the same diameter. In point-wise construction of the curve, let O be a fixed point of a circle C of diameter a, and Q a variable point of C. Lay…

Article

## Differentiation

A mathematical operation performed on a function to determine the effect of a change in the value of the independent variable. Functions of one variable are considered in this article. For differentiation of functions of several variablesPartial…

Article

## Discriminant

For a polynomial f(x) = an xn + an−1 xn−1 + + a1 x + a0, the discriminant is given by the expression where x1, x2, …, xn are the roots of the equation f(x) = 0. There are n(n − 1)/2 terms (xi − xj)2 in the product corresponding to all possible…

Article

## Dyadic

A mathematical abstraction corresponding to an expression of the type βγ + δ∊ + · · · , in which the elements (dyad symbols) consist of two vector symbols in juxtaposition without the intervention of either the dot (·) or cross (×). Essentially a…

Article

## Finite element method

A numerical analysis technique for obtaining approximate solutions to many types of engineering problems. The need for numerical methods arises from the fact that for most engineering problems analytical solutions do not exist. While the governing…

Article

## Game theory

The theory of games of strategy can briefly be characterized as the application of mathematical analysis to abstract models of conflict situations. The first such models analyzed by the theory were parlor games such as chess, poker, and bridge.…

Article

## Graphic methods

Procedures and techniques for visually representing on paper or a screen information pertaining to data analysis and decision making or relationships between variables by means of diagrams or charts.Structural information is usually depicted by a…

Article

## Helix

Any nonplanar curve all of whose tangents make the same angle with a fixed line. Other characteristic properties are that all principal normals are parallel to a plane and that the ratio of torsion to curvature is constant. If a helix has constant…

Article

## Information theory (biology)

The application to biological systems of the theory of encoding effects on signal transmission and communications efficiency. In everyday language, information is associated with knowledge, meaning (semantics), and the influence of information on…

Article

## Least-squares method

A method, developed originally by A. M. Legendre, of obtaining the best values (the ones with least error) of unknown quantities supposed to satisfy a system of linear equations of the form shown as notation (1),1where n > m. Since there are more…

Article

## Legendre functions

Solutions to the differential equation (1 − x2)y′ − 2xy′ + v(v + 1)y = 0. Legendre polynomials The most elementary of the Legendre functions, the Legendre polynomial Pn(x) can be defined by the generating function in Eq. (1). More explicit…

Article

## Lemniscate of Bernoulli

A curve shaped like the figure eight (see illustration), referred to by Jacques Bernoulli in 1694. Let F1, F2 be points of a plane π, with F1 F2 = 2a, a > 0. The locus of a point P of π which moves so that PF1 · PF2 = b2, where b is a positive…

Article

## Lie group

A topological group with only countably many connected components whose identity component is open and is an analytic group. An analytic group or connected Lie group is a topological group with the additional structure of a smooth manifold such that…

Article

## Linear programming

An area of mathematics concerned with the minimization (or maximization) of a linear function of several variables subject to linear equations and inequalities. Linear programming developed from three main areas: transportation problems, game…

Article

## Logic

The subject that investigates, formulates, and establishes principles of valid reasoning.The first attempt to investigate acceptable modes of reasoning systematically was made by Aristotle, in whose Organon reasoning was recognized as the subject of…

Article

## Matrix theory

The study of matrices and their properties, and of linear transformations on vector spaces, which can be represented by matrices. A matrix is a rectangular array of numbers, with the numbers that appear in the matrix being called entries. For…

Article

## Measure theory

A branch of mathematical analysis connected with the theory of integration. In order to discuss this subject, a formal definition of the term measure must be given. Sigma algebras Let X be an arbitrary set. Let m be a fixed collection of subsets of…

Article

## Monte Carlo method

A technique for estimating the solution, x, of a numerical mathematical problem by means of an artificial sampling experiment. The estimate is usually given as the average value, in a sample, of some statistic whose mathematical expectation is equal…

Article

## Nomograph

A graphical relationship between a set of variables that are related by a mathematical equation or law. The fundamental principle involved in the construction of a nomographic or alignment chart consists of representing an equation containing three…

Article

## Nonlinear programming

The area of applied mathematics and operations research concerned with finding the largest or smallest value of a function subject to constraints or restrictions on the variables of the function. Nonlinear programming is sometimes referred to as…

Article

## Number theory

The study of the properties and relationships between integers and other special types of numbers. There are many sets of positive integers of particular interest, such as the primes and the perfect numbers. Number theory, of ancient and continuing…

Article

## Queueing theory

The mathematical theory of the formation and behavior of queues or waiting lines. The name is also applied loosely to the mathematical study of a wide variety of problems connected with traffic congestion and storage systems. Uneven flow through a…

An article from Science News May 2019