* In mathematics, D < sub > 6 </ sub >, the dihedral group of order 6

In mathematics a combination is a way of selecting several things out of a larger group, where ( unlike permutations ) order does not matter.

The mathematics of crystal structures developed by Bravais, Federov and others was used to classify crystals by their symmetry group, and tables of crystal structures were the basis for the series International Tables of Crystallography, first published in 1935.

In mathematics, particularly in the area of abstract algebra known as group theory, a characteristic subgroup is a subgroup that is invariant under all automorphisms of the parent group.

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four categories described below.

Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory, and more.

A statistical analysis of the effect of dianetic therapy as measured by group tests of intelligence, mathematics and personality.

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.

In mathematics and abstract algebra, a group is the algebraic structure, where is a non-empty set and denotes a binary operation called the group operation.

He was the first to use the word " group " () as a technical term in mathematics to represent a group of permutations.

* E2 or E < sub > 2 </ sub > is an old name for the exceptional group G2 ( mathematics )

In mathematics, more specifically algebraic topology, the fundamental group ( defined by Henri Poincaré in his article Analysis Situs, published in 1895 ) is a group associated to any given pointed topological space that provides a way of determining when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.

There are many distinct FFT algorithms involving a wide range of mathematics, from simple complex-number arithmetic to group theory and number theory ; this article gives an overview of the available techniques and some of their general properties, while the specific algorithms are described in subsidiary articles linked below.

In mathematics, specifically group theory, a quotient group ( or factor group ) is a group obtained by identifying together elements of a larger group using an equivalence relation.

# REDIRECT group ( mathematics )

He gathered a group of students around him to study mathematics, music, and philosophy, and together they discovered most of what high school students learn today in their geometry courses.

In mathematics, given two groups ( G, *) and ( H, ·), a group homomorphism from ( G, *) to ( H, ·) is a function h: G → H such that for all u and v in G it holds that

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.

The application of a permutation group to the elements being permuted is called its group action ; it has applications in both the study of symmetries, combinatorics and many other branches of mathematics, physics and chemistry.

One way mathematics appears in art is through symmetries.

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act ( that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces ).

André-Marie Ampère took his first regular job in 1799 as a mathematics teacher, which gave him the financial security to marry Carron and father his first child, Jean-Jacques, the next year.

In the 1490s he studied mathematics under Luca Pacioli and prepared a series of drawings of regular solids in a skeletal form to be engraved as plates for Pacioli's book De Divina Proportione, published in 1509.

In topology and related branches of mathematics, Tychonoff spaces and completely regular spaces are kinds of topological spaces.

In mathematics, several specific infinite sequences of bits have been studied for their mathematical properties ; these include the Baum – Sweet sequence, Ehrenfeucht – Mycielski sequence, Fibonacci word, Kolakoski sequence, regular paperfolding sequence, Rudin – Shapiro sequence, and Thue – Morse sequence.

In topology and related fields of mathematics, a topological space X is called a regular space if every non-empty closed subset C of X and a point p not contained in C admit non-overlapping open neighborhoods.

Most examples of regular and nonregular spaces studied in mathematics may be found in those two articles.

Most interesting spaces in mathematics that are regular also satisfy some stronger condition.

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods.

* Axiom T3 or T3 space, regular space in topology and related fields of mathematics

In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon.

In 1862, he began to attend lectures in mathematics, physics and astronomy at the University in his city of birth, although he was not qualified to be enrolled as a regular student in part because of his lack of education in classical languages.

In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i. e., has a group law that can be defined by regular functions.

Such questions are usually more difficult to solve than regular mathematical exercises like " 5 − 3 ", even if one knows the mathematics required to solve the problem.

In mathematics, and in particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself by translation.

* Science ( mathematics, physics, astronomy, life sciences, and engineering sciences ) with 110 regular members ;

Examples of domain-specific languages include HTML, Logo for children, Verilog and VHDL hardware description languages, Mata for matrix programming, Mathematica and Maxima for symbolic mathematics, spreadsheet formulas and macros, SQL for relational database queries, YACC grammars for creating parsers, regular expressions for specifying lexers, the Generic Eclipse Modeling System for creating diagramming languages, Csound for sound and music synthesis, and the input languages of GraphViz and GrGen, software packages used for graph layout and graph rewriting.

In mathematics ( specifically, measure theory ), a Radon measure, named after Johann Radon, is a measure on the σ-algebra of Borel sets of a Hausdorff topological space X that is locally finite and inner regular.

In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge.

In mathematics, an outer measure μ on n-dimensional Euclidean space R < sup > n </ sup > is called Borel regular if the following two conditions hold:

In mathematics, a K3 surface is a complex or algebraic smooth minimal complete surface that is regular and has trivial canonical bundle.

Incoming freshmen entering the Baccalaureate programs must have a minimum high school average of 80 with at least 17 academic units such as four units of English, four units of social studies, three units of mathematics, two units of a foreign language, two units of sciences, and two units of regular academic subjects, and a minimum SAT score of 960 ( 480 Verbal 480 Math ) or ACT composite score of 20 or above.

In mathematics, bilinear interpolation is an extension of linear interpolation for interpolating functions of two variables ( e. g., and ) on a regular 2D grid.

In recreational mathematics, a polyhex is a polyform with a regular hexagon ( or ' hex ' for short ) as the base form.

The Russian language and mathematics championships were very prestigious and competitive as well as regular championships in sport, called Spartakiade the word Spartacus.