Lagrange's theorem is one of the fundamental theorems of finite group theory. Formally stated, the order of a subgroup of a group divides the order of the original group. This means that the number of elements in any subgroup of a finite g...

Laurent Schwartz has won many prestigious awards for his contributions to mathematics, but his most influential work has been in the areas of functional analysis, integral calculus, and differential calculus. In particular, it was his work...

The Lebesgue integral is one of the most important and powerful tools in mathematical analysis. The Lebesgue integral can be defined in very general settings and the vector space of real or complex valued Lebesgue integrable functions can ...

First examined by Jacob Bernoulli (1654 - 16705) in 1694, the lemniscate of Bernoulli has the general form of a figure eight, or the mathematical symbol for infinity. Bernoulli's conceptualization of the lemniscate followed his earlier res...

Lenore Blum has played an integral role in increasing the participation of girls and women in mathematics. She was one of the founders of the Association for Women in Mathematics (AWM), acting as its president from 1975 to 1978. The AWM ha...

Leonardo da Vinci (1452-1519) was an Italian painter, sculptor, architect, engineer, and scientist. He was one of the greatest minds of the Italian Renaissance, and his influence on the painting of the following generations was enormous. L...

The Swiss mathematician Leonhard Euler (1707-1783) made important original contributions to every branch of mathematics studied in his day. The son of a clergyman, Leonhard Euler, was born in Basel on April 15, 1707. He graduated from the ...

Leopold Kronecker's approach to mathematics can best be described in perhaps his most famous words, spoken in 1886 in Berlin: "The integer numbers were made by God, everything else is the work of man." Kronecker believed that all mathemati...

Procedure of differential calculus for evaluating indeterminate forms such as 0/0 and ∞/∞ when they result from attempting to find a limit. It states that when the limit of &math.f;(&math.x;)/&math.g;(&math.x;) is indeterminate...

Lie groups, named after the Norwegian mathematician Sophus Lie (1842-1899), stand at the intersection of several different branches of mathematics: algebra, analysis, geometry and topology. They are defined as groups that have the addition...

That portion of the electromagnetic spectrum visible to the human eye. It ranges from the red end to the violet end of the spectrum, with wavelengths from 700 to 400 nanometres and frequencies from 4.3 × 1014 to 7.5 &t...

Linda Keen devotes her time and energies to some of the hottest topics of the day. Her work in complex analysis and dynamical systems deals with the mathematics responsible for the vibrant graphics seen in science shows, fractal art, and l...

A linear equation is one which when graphed yields a straight line. This is true if the linear equation has two unknowns or variables. The solution to a linear equation is an ordered pair. The standard form of a linear equation in two vari...

mathematical modeling technique useful for guiding quantitative decisions in business planning, industrial engineering, and—to a lesser extent—in the social and physical sciences. Applications of the method of linear programmi...

When two simple waves are combined, but one is rotated out of phase with respect to the other, the result is no longer a sine wave, but a combination of the frequencies, the rotational phase difference, and any time offset between the two ...

Sometimes it is useful in mathematics to describe the path that a point traces as it moves in a plane to meet certain conditions. For example, what is the path that a point on the end of the second hand of a clock traces in 60 seconds? Thi...

A root is a value (X) that when multiplied by itself (n) number of times provides another value (Y), i.e., Xn=Y. In this exponential equation, X is called a root of Y, n is called the exponent, and Y is called a power of X. For example, if...

A logic gate is an electronic circuit that performs a logical operation on one or more input signals. The logic gate's inputs and outputs are electrical signals (voltages and currents) that represent Boolean values. Boolean values take on ...

Set of equations in relativity physics that relate the space and time coordinates of two systems moving at a constant speed relative to each other, developed in 1904 by Hendrik Antoon Lorentz. Required to describe phenomena approaching the...

A common denominator for a set of fractions is simply the same (common) lower symbol (denominator). In practice the common denominator is chosen to be a number that is divisible by all of the denominators in an addition or subtraction prob...

The lasting fame of the Austrian physicist Ludwig Boltzmann (1844-1906) rests on the statistical interpretation which he gave to classical thermodynamics. Ludwig Boltzmann was born on Feb. 20, 1844, in Vienna, the son of Ludwig and Kathari...

Lusin's theorem is an important technical result in measure theory. Let [,] be a closed, nonempty interval of real numbers. Then let ƒ: [,] ℜ be a Lebesgue measurable, real valued function defined at each point of the interval, ...