In mathematics, Archimedes used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of pi.

Numerical analysis is the study of algorithms that use numerical approximation ( as opposed to general symbolic manipulations ) for the problems of mathematical analysis ( as distinguished from discrete mathematics ).

For discrete time, where payments are separated by large time periods, the transform reduces to a sum, but when payments are ongoing on an almost continual basis, the mathematics of continuous functions can be used as an approximation.

This discovery proves that Hipparchus mathematics were much more advanced than Ptolemy describes in his books, as it is evident that he developed a good approximation of Kepler ΄ s second law.

In mathematics, Stirling's approximation ( or Stirling's formula ) is an approximation for large factorials.

The approximation is extremely accurate for many such flows, and makes the mathematics and physics simpler.

The mathematics of the flow is therefore simpler because the density ratio (, a dimensionless number ) does not affect the flow ; the Boussinesq approximation states that it may be assumed to be exactly one.

In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be ( by a slight deformation ) approximated by ones that are piecewise of the simplest kind.

In mathematics, the Littlewood conjecture is an open problem () in Diophantine approximation, proposed by John Edensor Littlewood around 1930.

In mathematics, a Banach space is said to have the approximation property ( AP ), if every compact operator is a limit of finite-rank operators.

In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion ( after Henri Poincaré ) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point.

In mathematics, the Thue – Siegel – Roth theorem, also known simply as Roth's theorem, is a foundational result in diophantine approximation to algebraic numbers.

Perhaps paradoxically, technical mathematics applied to financial markets is often simpler if infinitely divisible time is used as an approximation.

William George Horner ( 1786 – 22 September 1837 ) was a British mathematician ; he was a schoolmaster, headmaster and schoolkeeper, proficient in classics as well as mathematics, who wrote extensively on functional equations, number theory and approximation theory, but also on optics.

In mathematics, specifically in integral calculus, the rectangle method ( also called the midpoint or mid-ordinate rule ) computes an approximation to a definite integral, made by finding the area of a collection of rectangles whose heights are determined by the values of the function.

In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

In mathematics, a linear approximation is an approximation of a general function using a linear function ( more precisely, an affine function ).

In mathematics and its applications, linearization refers to finding the linear approximation to a function at a given point.

In mathematics, the stationary phase approximation is a basic principle of asymptotic analysis, applying to oscillatory integrals

In mathematics, approximation theory is concerned with how functions can be approximated with other, simpler, functions, and with characterizing in a quantitative way the errors introduced thereby.

* Weyl's criterion, used in mathematics in the theory of diophantine approximation

In mathematics, in the theory of Diophantine approximation, Weyl's criterion states that a sequence of real numbers is equidistributed mod 1 if and only if for any non-zero integer

This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.

Next September, after receiving a degree from Yale's Master of Arts in Teaching Program, I will be teaching somewhere -- that much is guaranteed by the present shortage of mathematics teachers.

But because science is based on mathematics doesn't mean that a hot rodder must necessarily be a mathematician.

Like primitive numbers in mathematics, the entire axiological framework is taken to rest upon its operational worth.

In the new situation, philosophy is able to provide the social sciences with the same guidance that mathematics offers the physical sciences, a reservoir of logical relations that can be used in framing hypotheses having explanatory and predictive value.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

The principal of the school announced that -- despite the help of private tutors in Hollywood and Philadelphia -- Fabian is a 10-o'clock scholar in English and mathematics.

In mathematics and statistics, the arithmetic mean, or simply the mean or average when the context is clear, is the central tendency of a collection of numbers taken as the sum of the numbers divided by the size of the collection.

The term " arithmetic mean " is preferred in mathematics and statistics because it helps distinguish it from other means such as the geometric and harmonic mean.

In addition to mathematics and statistics, the arithmetic mean is used frequently in fields such as economics, sociology, and history, though it is used in almost every academic field to some extent.

The use of the soroban is still taught in Japanese primary schools as part of mathematics, primarily as an aid to faster mental calculation.

In mathematics and computer science, an algorithm ( originating from al-Khwārizmī, the famous Persian mathematician Muḥammad ibn Mūsā al-Khwārizmī ) is a step-by-step procedure for calculations.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that " the product of a collection of non-empty sets is non-empty ".

The axiom of choice is avoided in some varieties of constructive mathematics, although there are varieties of constructive mathematics in which the axiom of choice is embraced.

The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed.

:" A choice function exists in constructive mathematics, because a choice is implied by the very meaning of existence.

Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up.

There is no prize awarded for mathematics, but see Abel Prize.