The fusion of the ideas coming from mathematics with those coming from chemistry is at the origin of a part of the standard terminology of graph theory.

In the abstract, a coordinate system as used in mathematics and geodesy is, e. g., in ISO terminology, referred to as a coordinate system.

Tegmark writes that " abstract mathematics is so general that any Theory Of Everything ( TOE ) that is definable in purely formal terms ( independent of vague human terminology ) is also a mathematical structure.

With the goal of founding all of mathematics on set theory, the group strove for utmost rigour and generality, creating some new terminology and concepts along the way.

Like any other profession, mathematics also has its own brand of technical terminology.

's 1986 paper that introduced hygienic macro expansion, inspired by the terminology used in mathematics.

( 2002 ) " What kind of mathematics and terminology was transmitted into 18th-century Japan from China?

In addition, the 27 elementaries textbooks and manuals published by the commission laid the foundations for Polish language terminology in chemistry, physics, logics, grammar and mathematics.

In the following summary ( as yet incomplete and unchecked ), modern notation and terminology are used, from both chemistry and mathematics, in order to prevent confusion.

# REDIRECT Element ( mathematics )# Notation and terminology

In mathematics, an associative algebra A is an associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satisfying a number of axioms, including associativity of multiplication and distributivity, as well as compatible multiplication by the elements of the field K or the ring R.

Other examples are readily found in different areas of mathematics, for example, vector addition, matrix multiplication and conjugation in groups.

In mathematics, more specifically in functional analysis, a Banach space ( pronounced ) is a complete normed vector space.

In mathematics, a bilinear operator is a function combining elements of two vector spaces to yield an element of a third vector space that is linear in each of its arguments.

Categories now appear in most branches of mathematics, some areas of theoretical computer science where they correspond to types, and mathematical physics where they can be used to describe vector spaces.

In mathematics, any vector space, V, has a corresponding dual vector space ( or just dual space for short ) consisting of all linear functionals on V. Dual vector spaces defined on finite-dimensional vector spaces can be used for defining tensors.

In mathematics, an inner product space is a vector space with an additional structure called an inner product.

In mathematics, a linear map, linear mapping, linear transformation, or linear operator ( in some contexts also called linear function ) is a function between two modules ( including vector spaces ) that preserves the operations of module ( or vector ) addition and scalar multiplication.

The three-dimensional Euclidean space R < sup > 3 </ sup > is a vector space, and lines and planes passing through the origin ( mathematics ) | origin are vector subspaces in R < sup > 3 </ sup >.

Linear algebra is the branch of mathematics concerning vector spaces, often finite or countably infinite dimensional, as well as linear mappings between such spaces.

* Module ( mathematics ) over a ring, a generalization of vector spaces

In mathematics, with 2-or 3-dimensional vectors with real-valued entries, the idea of the " length " of a vector is intuitive and can easily be extended to any real vector space R < sup > n </ sup >.

In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from one to the other.

In mathematics, the tensor product, denoted by ⊗, may be applied in different contexts to vectors, matrices, tensors, vector spaces, algebras, topological vector spaces, and modules, among many other structures or objects.

In mathematics, physics, and engineering, a Euclidean vector ( sometimes called a geometric or spatial vector, or — as here — simply a vector ) is a geometric object that has a magnitude ( or length ) and direction and can be added to other vectors according to vector algebra.

In mathematics, specifically in measure theory, a Borel measure is defined as follows: let X be a locally compact Hausdorff space, and let be the smallest σ-algebra that contains the open sets of X ; this is known as the σ-algebra of Borel sets.

In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers which at the same time is also a Banach space.

In mathematics, specifically general topology and metric topology, a compact space is a mathematical space in which any infinite collection of points sampled from the space must — as a set — be arbitrarily close to some point of the space.

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

In mathematics, compactification is the process or result of making a topological space compact.

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it.

High-dimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics ; these are abstract spaces, independent of the physical space we live in.

In mathematics, the dimension of an object is an intrinsic property independent of the space in which the object is embedded.

A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space.

In mathematics, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry, as well as the generalizations of these notions to higher dimensions.

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

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.