In mathematics, the sieve of Eratosthenes (), one of a number of prime number sieves, is a simple, ancient algorithm for finding all prime numbers up to any given limit.

In number theory, a branch of mathematics, the special number field sieve ( SNFS ) is a special-purpose integer factorization algorithm.

In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory.

In mathematics, the large sieve is a method ( or family of methods and related ideas ) in analytic number theory.

In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain.

In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors.

Rosser was well known for his research in pure mathematics, known for research in logic ( Rosser's trick, the Kleene – Rosser paradox, and the Church-Rosser theorem ) and in number theory ( Rosser sieve ).

They were named for Edith Irene Atkin, Illinois State Normal University mathematics professor from 1909 – 1940 and June Rose Colby, English professor from 1892 – 1932.

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.

Thomas Alleyne's is the only high school in Staffordshire that offers an accelerated mathematics course, RAF fast track scheme and a farm.

In mathematics, the irrational base discrete weighted transform ( IBDWT ) is a variant of the fast Fourier transform using an irrational base ; it was developed by Richard Crandall ( Reed College ), Barry Fagin ( Dartmouth College ) and Joshua Doenias ( NeXT Software ) in the early 1990s using Mathematica.

Area plays an important role in modern mathematics.

It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory.

While the roots of formalised logic go back to Aristotele, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics.

Sets are of great importance in mathematics ; in fact, in modern formal treatments, most mathematical objects ( numbers, relations, functions, etc.

This subject constitutes a major part of modern mathematics education.

The contributions of Kurt Gödel in 1940 and Paul Cohen in 1963 showed that the hypothesis can neither be disproved nor be proved using the axioms of Zermelo – Fraenkel set theory, the standard foundation of modern mathematics, provided ZF set theory is consistent.

Methods for breaking modern cryptosystems often involve solving carefully constructed problems in pure mathematics, the best-known being integer factorization.

In the early modern age, Victorian schools were reformed to teach commercially useful topics, such as modern languages and mathematics, rather than classical subjects, such as Latin and Greek.

In modern mathematics, it is more common to define Euclidean space using Cartesian coordinates and the ideas of analytic geometry.

In modern mathematics, Euclidean spaces form the prototypes for other, more complicated geometric objects.

In modern mathematics, the theory of fields ( or field theory ) plays an essential role in number theory and algebraic geometry.

Nowadays, functors are used throughout modern mathematics to relate various categories.

Set theory has come to play the role of a foundational theory in modern mathematics, in the sense that it interprets propositions about mathematical objects ( for example, numbers and functions ) from all the traditional areas of mathematics ( such as algebra, analysis and topology ) in a single theory, and provides a standard set of axioms to prove or disprove them.

In mathematics, more specifically in the area of modern algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.

It inaugurated a new Western-based education system for all young people, sent thousands of students to the United States and Europe, and hired more than 3, 000 Westerners to teach modern science, mathematics, technology, and foreign languages in Japan ( O-yatoi gaikokujin ).

During the Meiji period ( 1868 – 1912 ), leaders inaugurated a new Western-based education system for all young people, sent thousands of students to the United States and Europe, and hired more than 3, 000 Westerners to teach modern science, mathematics, technology, and foreign languages in Japan ( Oyatoi gaikokujin ).

From Robertson, Madison learned mathematics, geography, and modern and ancient languages.

Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics.

A guided tour through the various branches of modern mathematics.

An online mathematics encyclopedia under construction, focusing on modern mathematics.

The development of algebraic geometry from its classical to modern forms is a particularly striking example of the way an area of mathematics can change radically in its viewpoint, without making what was correctly proved before in any way incorrect ; of course mathematical progress clarifies gaps in previous proofs, often by exposing hidden assumptions, which progress has revealed worth conceptualizing.

Intuitionistic logic substitutes constructability for abstract truth and is associated with a transition from the proof to model theory of abstract truth in modern mathematics.