# 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).

- Mathematics 171 related topics ## Differential geometry  Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. ## Euclidean space

Fundamental space of geometry, intended to represent physical space.

Fundamental space of geometry, intended to represent physical space.   Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension, including the three-dimensional space and the Euclidean plane (dimension two). ## Field (mathematics)      In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. ## Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: ## Polynomial        In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. ## Theorem    In mathematics, a theorem is a statement that has been proved, or can be proved. One of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.

One of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.                Addition belongs to arithmetic, a branch of mathematics. ## Algorithm        In mathematics and computer science, an algorithm is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. ## Bertrand Russell

Welsh philosopher, logician, and social critic.

Welsh philosopher, logician, and social critic.          As an academic, he worked in philosophy, mathematics, and logic. ## Computer science

Study of computation, automation, and information.

Study of computation, automation, and information.  Computer science research also often intersects other disciplines, such as cognitive science, linguistics, mathematics, physics, biology, Earth science, statistics, philosophy, and logic.