Although the abacus, the first tool of calculation, has existed since ancient times, advanced calculating machines did not appear until the early 1600s. Scientists and mathematicians were determined to simplify complex astronomical and nav...

Field of mathematics that analyzes aspects of change in processes or systems that can be modeled by functions. Through its two primary tools—the derivative and the integral—it allows precise calculation of rates of change and o...

any system for dividing time over extended periods, such as days, months, or years, and arranging such divisions in a definite order. A calendar is convenient for regulating civil life and religious observances and for historical and scien...

Cantor set—an infinite set of numbers between 0 and 1, defined by an inductive process. To define this set, start with the closed interval [0,1]. Remove the middle third--the open interval (1/3,2/3). (That is, remove all the points b...

Bernhard Bolzano defined cardinality in his book Paradoxes of the Infinite (1851). The cardinality of a set is, roughly speaking, its size. Precisely, the cardinality of X is said to be less than or equal to that of Y if there is a functio...

As the impact of the American and French Revolutions was felt across Europe, a social atmosphere arose that encouraged ground breaking work in mathematics. Karl Gustav Jacob Jacobi, who attracted early attention from luminaries such as Adr...

Casper Wesselmade a significant contribution to mathematics, but his legacy is to be a footnote in histories of other great mathematicians. Karl Friedrich Gauss and Jean Robert Argand are most often given credit for expressing complex numb...

A catenary is the shape assumed by a hanging chain. More precisely, it is the solution of the following mathematical problem: of all plane curves of a fixed length joining two fixed points, which has the least potential energy in a uniform...

Cauchy's integral theorem allows for integration over a complex variable. It deals only with analytic functions, that is, those functions which have only a single value at each point in the region of interest. These functions have the same...

In statistics, any of several fundamental theorems in probability. Originally known as the law of errors, in its classic form it states that the sum of a set of independent random variables will approach a normal distribution regardless of...

The chain rule is a method of differentiating a function which is composed of two nested functions. That is, the chain rule provides a general case for taking the x derivative of a function f(g(x)). The chain rule states that the derivativ...

Charles Babbage (1791-1871) was an English inventor and mathematician whose mathematical machines foreshadowed the modern computer. He was a pioneer in the scientific analysis of production systems. Charles Babbage was born on Dec. 26, 179...

Charles Jean Gustave Nicolas de la Vallée-Poussin was responsible for proving the prime number theorem. A prime number is a number that can be divided by only one and itself without producing a remainder, and de la Vallée-Pou...

Along with Simeon-Denis Poisson, Charles Emile Picard was the most important and distinguished French mathematician of his day. Not only was he an avid supporter of other mathematicians and a gifted teacher, he made many contributions of h...

Charles Sanders Peirce (1839-1914) was one of America's most important philosophers. Many of his writings were not published until after his death, but he made important contributions in both philosophy and science. His work in logic helpe...

The French physicist Charles Augustin de Coulomb (1736-1806) was famous for establishing the relation for computing the force between electrical charges. He also did pioneering work on sliding and fluid friction. Charles Augustin de Coulom...

A chi-square model is a statistical method used to analyze the results of certain types of experiments. It involves a comparison of the deviation of real observations from expected values, and helps determine whether a result is significan...

Christian Goldbach was a Russian mathematician born in Königsberg, Prussia in 1690. Not much is known about his early life and education in Russia, but he was appointed to the position of mathematics professor and historian at the St....

Gabrielle-Émilie Châtelet had a major role in the scientific revolution of the eighteenth century. By popularizing the theories of Isaac Newton she brought them more widespread acceptance in Europe where most people still foll...

Geometrical curve, one of the conic sections, consisting of the set of all points the same distance (the radius) from a given point (the centre). A line connecting any two points on a circle is called a chord, and a chord passing through t...

"Closure" is a property which a set either has or lacks with respect to a given operation. A set is closed with respect to that operation if the operation can always be completed with elements in the set. For example, the set of even natur...

Branch of mathematics concerned with the selection, arrangement, and combination of objects chosen from a finite set. The number of possible bridge hands is a simple example; more complex problems include scheduling classes in classrooms a...

Completing the square is a technique used in algebra to create an expression which is a perfect square where none existed before. The presence of a perfect square form in an expression can often simplify the steps in an algebraic process. ...

Any number consisting of both real numbers and imaginary numbers. It has the form &math.a; + &math.b;&math.i;, where &math.a; and &math.b; are real numbers and &math.i; = −1; &math.a; is called the real part and &math.b;&math.i; the ...

in logic, a stipulation, or provision, that needs to be satisfied; also, something that must exist or be the case or happen in order for something else to do so (as in “the will to live is a condition for survival”). In logic, ...