# Mathematics

Area of knowledge that includes such topics as numbers , formulas and related structures (algebra), shapes and the spaces in which they are contained (geometry), and quantities and their changes (calculus and analysis).

- Mathematics171 related topics

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## Logic

Study of correct reasoning or good arguments.

Study of correct reasoning or good arguments.

Logic is studied in and applied to various fields, such as philosophy, mathematics, computer science, and linguistics.

## Topological space

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.

## Vector space

[[File: Vector add scale.svg|200px|thumb|right|Vector addition and scalar multiplication: a vector

[[File: Vector add scale.svg|200px|thumb|right|Vector addition and scalar multiplication: a vector

In mathematics, physics, and engineering, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars.

## Function (mathematics)

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

## Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line (or alternatively, a quantity that can be represented as an infinite decimal expansion).

## Equation

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign.

## Topology

In mathematics, topology (from the Greek words, and λόγος) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

## Arithmetic

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.