Sum most commonly means the total of two or more numbers added together; see

addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol, +) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication, and Division (mathematics), divis ...

. Sum can also refer to:

Mathematics

* Sum (category theory), the generic concept of summation in mathematics * Sum, the result of

summation In mathematics, summation is the addition of a sequence of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, pol ...

, the addition of a sequence of numbers * 3SUM, a term from computational complexity theory * Band sum, a way of connecting mathematical knots * Connected sum, a way of gluing manifolds *

Digit sum In mathematics, the digit sum of a natural number in a given radix, number base is the sum of all its numerical digit, digits. For example, the digit sum of the decimal number 9045 would be 9 + 0 + 4 + 5 = 18. Definition Let n be a natural number. ...

, in number theory *

Direct sum The direct sum is an operation between structures in abstract algebra, a branch of mathematics. It is defined differently but analogously for different kinds of structures. As an example, the direct sum of two abelian groups A and B is anothe ...

, a combination of algebraic objects **

Direct sum of groups In mathematics, a group ''G'' is called the direct sumHomology. Saunders MacLane. Springer, Berlin; Academic Press, New York, 1963.László Fuchs. Infinite Abelian Groups of two normal subgroups with trivial intersection if it is generated ...

Direct sum of modules In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, m ...

** Direct sum of permutations ** Direct sum of topological groups *

Einstein summation In mathematics, especially the usage of linear algebra in mathematical physics and differential geometry, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies s ...

, a way of contracting tensor indices *

Empty sum In mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero. The natural way to extend non-empty sums is to let the empty sum be the additive identity. Let a_1, a_2, a_3, ... be a sequence of numbers, and let ...

, a sum with no terms * Indefinite sum, the inverse of a finite difference * Kronecker sum, an operation considered a kind of addition for matrices *

Matrix addition In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. For a vector, \vec\!, adding two matrices would have the geometric effect of applying each matrix transformation separately ...

, in linear algebra *

Minkowski addition In geometry, the Minkowski sum of two set (mathematics), sets of position vectors ''A'' and ''B'' in Euclidean space is formed by vector addition, adding each vector in ''A'' to each vector in ''B'': A + B = \ The Minkowski difference (also ''M ...

, a sum of two subsets of a

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

* Power sum symmetric polynomial, in commutative algebra * Prefix sum, in computing *

Pushout (category theory) In category theory, a branch of mathematics, a pushout (also called a fibered coproduct or fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms ''f'' : ''Z'' → ''X'' and ''g'' : ''Z'' & ...

(also called an amalgamated sum or a cocartesian square, fibered coproduct, or fibered sum), the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domainor pushout, leading to a fibered sum in category theory *

QCD sum rules In quantum chromodynamics, the color confinement, confining and strong coupling nature of the theory means that conventional perturbative techniques often fail to apply. The QCD sum rules (or Mikhail Shifman, Shifman–Arkady Vainshtein, Vainshtei ...

, in quantum field theory *

Riemann sum In mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is in numerical integration, i.e., approxima ...

, in calculus * Rule of sum, in combinatorics *

Subset sum problem The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S of integers and a target-sum T, and the question is to decide whether any subset of the integers sum to precisely T''.'' ...

, in cryptography * Sum rule in differentiation, in calculus * Sum rule in integration, in calculus * Sum rule in quantum mechanics *

Wedge sum In topology, the wedge sum is a "one-point union" of a family of topological spaces. Specifically, if ''X'' and ''Y'' are pointed spaces (i.e. topological spaces with distinguished basepoints x_0 and y_0) the wedge sum of ''X'' and ''Y'' is the ...

, a one-point union of topological spaces *

Whitney sum In mathematics, a vector bundle is a topological construction that makes precise the idea of a Family of sets, family of vector spaces parameterized by another space (mathematics), space X (for example X could be a topological space, a manifold, ...

, of fiber bundles * Zero-sum problem in combinatorics

Computing and technology

* Sum (Unix), a program for generating checksums * StartUp-Manager, a program to configure GRUB, GRUB2, Usplash and Splashy * Sum type, a computer science term

Art and entertainment

* Sum, the first beat (pronounced like "some") in any rhythmic cycle of

Hindustani classical music Hindustani classical music is the Indian classical music, classical music of the Indian subcontinent's northern regions. It may also be called North Indian classical music or ''Uttar Bhartiya shastriya sangeet''. The term ''shastriya sangeet'' ...

* "Sum", a song by Pink Floyd from '' The Endless River'' * '' Sum: Forty Tales from the Afterlives'', a 2009 collection of short stories by David Eagleman *

Sum 41 Sum 41 was a Canadian rock band formed in Ajax, Ontario, in 1996. The band's final lineup consisted of Deryck Whibley (lead vocals, guitars, keyboards), Dave Baksh (lead guitar, backing vocals), Jason McCaslin (bass, backing vocals), Tom T ...

, a Canadian punk band * SUM, the computer in '' Goat Song (novelette)'' story by Poul Anderson in '' Magazine of Fantasy and Science Fiction'', (1972).

Organizations

* ''Senter for utvikling og miljø'' ( Centre for Development and the Environment), a research institute which is part of the University of Oslo * Soccer United Marketing, the for-profit marketing arm of Major League Soccer * Society for the Establishment of Useful Manufactures, a now-defunct private state-sponsored corporation founded in 1791 to promote industrial development along the Passaic River in New Jersey in the United States * The State University of Management, a Russian university * Save Uganda Movement, a Ugandan militant opposition group * Ukrainian Youth Association (''Спілка української молоді'', Spilka Ukraïns'koï Molodi), a youth organization in Ukraine and countries with a Ukrainian diaspora

Places

* Sum (administrative division), an administrative division in Mongolia, China, and some areas of Russia ** Sum (Mongolia), an administrative division of Mongolia * SUM, the IATA airport code for the Sumter Airport in Sumter County, South Carolina, U.S.

Other uses

* Sum, an old name for the

Finns Finns or Finnish people (, ) are a Baltic Finns, Baltic Finnic ethnic group native to Finland. Finns are traditionally divided into smaller regional groups that span several countries adjacent to Finland, both those who are native to these cou ...

in East Slavic languages, derived from the word Suomi, "Finland" * Soum (currency) (also spelled "sum"), a unit of currency used in some Turkic-speaking countries of Central Asia *

SUM (interbank network) SUM is an interbank network in forty-two U.S. states (all except Alaska, Alabama, Delaware, Montana, Nebraska, North Dakota, South Dakota, Wyoming), the District of Columbia and Puerto Rico. It is largely made up of smaller local banks and cre ...

, an interbank network in 42 U.S. states * SUM, the ISO 639-3 code for the Sumo language * Cen (surname) 岑, a Chinese surname sometimes romanized as Sum * Shěn (surname) 沈, a Chinese surname sometimes romanized as Sum * ''

Cogito, ergo sum The Latin , usually translated into English as "I think, therefore I am", is the "first principle" of René Descartes's philosophy. He originally published it in French language, French as , in his 1637 ''Discourse on the Method'', so as to re ...