Any mathematical object that, when applied by an operation, such as addition or multiplication, to another mathematical object, such as a number, leaves the other object unchanged is called an identity element. The two most familiar exampl...

Any number of the form &math.b;&math.i; where &math.b; is a real number, &math.i; is the square root of −1, and &math.b; is not zero. &Seealso; complex number....

An improper integral is an integral of one of two types: either the interval over which the interval is taken is unbounded, or the integrand becomes unbounded in a neighborhood of one or more points in the interval (including the endpoints...

Indeterminate limits are mathematical expressions that cannot be assigned a unique value. Although these expressions have no meaning per se, they frequently arise in limit problems in calculus. For example, to compute the derivative (slope...

in logic, derivation of conclusions from given information or premises by any acceptable form of reasoning. Inferences are commonly drawn (1) by deduction, which, by analyzing valid argument forms, draws out the conclusions implicit in the...

An infinitesimal is a numerical quantity small enough that its limit in some condition is zero. Infinitesimals are widely used in calculus, where the formal, limit-based definition of a derivative depends upon an arbitrary additive quantit...

Information is the fundamental concept of information theory, the mathematical study of symbolic communication. Information theory was founded in 1948 by one seminal paper, Claude Shannon's "The Mathematical Theory of Communication," and h...

Ingrid Daubechies was born August 17, 1954, in Houthalen, Belgium. Her father, Marcel Daubechies, is a retired civil engineer and her mother, Simone, is a retired criminologist. Daubechies credits her parents with giving her a love of lear...

Branch of calculus concerned with the theory and applications of integrals. While differential calculus focuses on rates of change, such as slopes of tangent lines and velocities, integral calculus deals with total size or value, such as l...

In mathematics, estimation of a value between two known data points. A simple example is calculating the mean (&see; mean, median, and mode) of two population counts made 10 years apart to estimate the population in the fifth year. Estimat...

School of mathematical thought introduced by the Dutch mathematician Luitzen Egbertus Jan Brouwer (1881–1966). In contrast with mathematical Platonism, which holds that mathematical concepts exist independent of any human realization...

Mathematical function that undoes the effect of another function. For example, the inverse function of the formula that converts Celsius temperature to Fahrenheit temperature is the formula that converts Fahrenheit to Celsius. Applying one...

Among the real numbers, any of those that cannot be represented as quotients of integers. In decimal form, irrational numbers are represented by nonterminating, nonrepeating decimals. Examples include square roots of prime numbers and such...

Sir Isaac Newton (1642-1727) was an English scientist and mathematician. He made major contributions in mathematics and theoretical and experimental physics and achieved a remarkable synthesis of the work of his predecessors on the laws of...

Iteration is a tool used in a procedural language, such as Basic, Pascal, C or Modula-2, whereby a repetition of a sequence of instructions is carried out that yield results successively closer to a desired result, the termination conditio...