The Swiss mathematician and physicist Daniel Bernoulli (1700-1782) is best known for his work on hydrodynamics, but he also did pioneering work on the kinetic theory of gases. Daniel Bernoulli was born on Jan. 29, 1700, in Gröningen, ...

Augustus DeMorgan (1806-1871), the British mathematician and logician, contributed what we now call DeMorgan's Laws to the science of logic. These laws allow the substitution of one statement for another logically equivalent statement. The...

The number system most commonly used today is based on the Hindu-Arabic number system, which was developed in what is now India around 300 B.C.E. The Arab mathematicians adopted this system and brought it to Spain, where it slowly spread t...

Real analysis, which studies the theoretical foundations of the calculus of real-valued functions, depends upon an accurately defined real number concept. Such a precise definition eluded mathematicians from the time ofPythagoras (c.560-c....

In philosophy, the specification of the meaning of an expression relative to a language. Definitions may be classified as lexical, ostensive, and stipulative. Lexical definition specifies the meaning of an expression by stating it in terms...

A dependent variable is the variable which expresses the results of a function. In a normal algebraic function such as y = 3x or y = x2 + 6, "y" is the dependent variable. In the usual method of graphing a function, the dependent variable ...

Descartes' rule of signs, first published by Renée Descartes in 1637, is a method for determining the largest number of positive or negative roots that a polynomial equation may have. If the terms of the polynomial p(x) are written ...

A diameter is a straight-line segment that passes through the center of a circle or sphere and whose two end points lie on the circumference of the surface. The center is a point of symmetry within a circle or sphere, with any diameter pas...

In calculus, an expression based on the derivative of a function, useful for approximating certain values of the function. The differential of an independent variable &math.x;, written Δ&math.x;, is an infinitesimal change in its val...

Branch of mathematical analysis, devised by Isaac Newton and G.W. Leibniz, and concerned with the problem of finding the rate of change of a function with respect to the variable on which it depends. Thus it involves calculating derivative...

A Diophantine Equation is characterized not by the shape of the equation but by the fact that one is interested only in solutions in integers (whole numbers) or rational numbers. Typically, it will have more than one variable. For example,...

A discriminant is a number, usually invariant under suitable transformations, which characterizes some properties of the roots of a certain quantity. For instance, the most common application of the concept of discriminant is in the second...

One of the laws relating to number operations. In symbols, it is stated: &math.a;(&math.b; + &math.c;) = &math.a;&math.b; + &math.a;&math.c;. The monomial factor &math.a; is distributed, or separately applied, to each term of the polynomia...

The domain of a relation is the set that contains all the first elements, x, from the ordered pairs (x,y) that make up the relation. In mathematics, a relation is defined as a set of ordered pairs (x,y) for which each y depends on x in a p...

The duodecimal system is a mathematical plan that uses a base of twelve rather than the standard base ten. Under base twelve, the place value changes from 10 to 12. Quantities are explained in terms of twelves, such as dozens, grosses, and...