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), division. ...

. 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 any kind 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, mat ...

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

Connected sum In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds. Its effect is to join two given manifolds together near a chosen point on each. This construction plays a key role in the classifi ...

, a way of gluing manifolds *

Digit sum In mathematics, the digit sum of a natural number in a given number base is the sum of all its 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. We define the digit ...

, 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. To see how the direct sum is used in abstract algebra, consider a more ...

, 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 b ...

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, ma ...

Direct sum of permutations In combinatorics, the skew sum and direct sum of permutations are two operations to combine shorter permutations into longer ones. Given a permutation ''π'' of length ''m'' and the permutation ''σ'' of length ''n'', the skew sum of ''π'' and '' ...

Direct sum of topological groups In mathematics, a topological group G is called the topological direct sum of two subgroups H_1 and H_2 if the map \begin H_1\times H_2 &\longrightarrow G \\ (h_1,h_2) &\longmapsto h_1 h_2 \end is a topological isomorphism, meaning that ...

Einstein summation In mathematics, especially the usage of linear algebra in Mathematical physics, Einstein notation (also known as the Einstein summation convention or Einstein summation notation) is a notational convention that implies summation over a set of ...

, 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 In discrete calculus the indefinite sum operator (also known as the antidifference operator), denoted by \sum _x or \Delta^ , is the linear operator, inverse of the forward difference operator \Delta . It relates to the forward difference operator ...

, 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. However, there are other operations which could also be considered addition for matrices, such as the direct sum and the Kronec ...

, in linear algebra *

Minkowski addition In geometry, the Minkowski sum (also known as dilation) of two sets of position vectors ''A'' and ''B'' in Euclidean space is formed by adding each vector in ''A'' to each vector in ''B'', i.e., the set : A + B = \. Analogously, the Minkowski ...

, a sum of two subsets of a

vector space In mathematics and physics, 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''. Scalars are often real numbers, but can ...

Power sum symmetric polynomial In mathematics, specifically in commutative algebra, the power sum symmetric polynomials are a type of basic building block for symmetric polynomials, in the sense that every symmetric polynomial with rational coefficients can be expressed as a sum ...

, in commutative algebra *

Prefix sum In computer science, the prefix sum, cumulative sum, inclusive scan, or simply scan of a sequence of numbers is a second sequence of numbers , the sums of prefixes ( running totals) of the input sequence: : : : :... For instance, the prefix sums ...

, 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'' &r ...

(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 confining and strong coupling nature of the theory means that conventional perturbative techniques often fail to apply. The QCD sum rules (or Shifman– Vainshtein–Zakharov sum rules) are a way of dealing with t ...

, 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 approximating the area of functions or lin ...

, in calculus *

Rule of sum In combinatorics, the addition principle or rule of sum is a basic counting principle. Stated simply, it is the intuitive idea that if we have ''A'' number of ways of doing something and ''B'' number of ways of doing another thing and we can not ...

, 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''.'' T ...

, in cryptography *

Sum rule in differentiation This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Elementary rules of differentiation Unless otherwise stated, all functions are functions of real numbers (R) that return real ...

, in calculus *

Sum rule in integration In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...

, in calculus *

Sum rule in quantum mechanics In quantum mechanics, a sum rule is a formula for transitions between energy levels, in which the sum of the transition strengths is expressed in a simple form. Sum rules are used to describe the properties of many physical systems, including soli ...

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 qu ...

, 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 vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every po ...

, of fiber bundles *

Zero-sum problem In number theory, zero-sum problems are certain kinds of combinatorial problems about the structure of a finite abelian group. Concretely, given a finite abelian group ''G'' and a positive integer ''n'', one asks for the smallest value of ''k'' suc ...

in combinatorics

Computing and technology

Sum (Unix) is a legacy utility available on some Unix and Unix-like operating systems. This utility outputs a 16-bit checksum of each argument file, as well as the number of blocks they take on disk. — manual pages from GNU coreutils Two different check ...

, a program for generating checksums *

StartUp-Manager GNU GRUB (short for GNU GRand Unified Bootloader, commonly referred to as GRUB) is a boot loader package from the GNU Project. GRUB is the reference implementation of the Free Software Foundation's Multiboot Specification, which provides a us ...

, a program to configure GRUB, GRUB2, Usplash and Splashy *

Sum type In computer science, a tagged union, also called a variant, variant record, choice type, discriminated union, disjoint union, sum type or coproduct, is a data structure used to hold a value that could take on several different, but fixed, types. ...

, 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 classical music of northern regions of the Indian subcontinent. It may also be called North Indian classical music or, in Hindustani, ''shastriya sangeet'' (). It is played in instruments like the violin, sita ...

* "Sum", a song by Pink Floyd from ''

The Endless River ''The Endless River'' is the fifteenth studio album by the English rock band Pink Floyd, released in November 2014 by Parlophone Records in Europe and Columbia Records in the rest of the world. It was the third Pink Floyd album recorded under ...

'' * '' Sum: Forty Tales from the Afterlives'', a 2009 collection of short stories by David Eagleman *

Sum 41 Sum 41 is a Canadian rock band from Ajax, Ontario. Originally called Kaspir, the band was formed in 1996 and currently consists of Deryck Whibley (lead vocals, guitars, keyboards), Dave Baksh (lead guitar, backing vocals), Jason "Cone" McCas ...

, a Canadian punk band * SUM, the computer in ''

Goat Song (novelette) "Goat Song" is a science fiction novelette by American writer Poul Anderson. Originally published in ''The Magazine of Fantasy and Science Fiction'' issue of February 1972, it was later included in the anthologies '' Nebula Award Stories Eight'' ...

'' story by Poul Anderson in ''

Magazine of Fantasy and Science Fiction ''The Magazine of Fantasy & Science Fiction'' (usually referred to as ''F&SF'') is a U.S. fantasy fiction magazine, fantasy and science fiction magazine first published in 1949 by Mystery House, a subsidiary of Lawrence E. Spivak, Lawrence Spiva ...

'', (1972).

Organizations

* ''Senter for utvikling og miljø'' (

Centre for Development and the Environment The Centre for Development and the Environment ( no, Senter for utvikling og miljø, SUM) is a research institute which is part of the University of Oslo. Its focus areas are international development and environmental studies. History The Centre ...

), a research institute which is part of the University of Oslo *

Soccer United Marketing Soccer United Marketing is the for-profit marketing arm of Major League Soccer which primarily deals in the promotion and sanctioning of professional soccer in the United States. In 2016, Soccer United Marketing was also chosen as the exclusive w ...

, the for-profit marketing arm of Major League Soccer and the exclusive marketing partner of the United States Soccer Federation *

Society for the Establishment of Useful Manufactures The Society for Establishing Useful Manufactures (S.U.M.) or Society for the Establishment of Useful Manufactures was a private state-sponsored corporation founded in 1791 to promote industrial development along the Passaic River in New Jersey i ...

, 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 The Save Uganda Movement (abbreviated SUM) was a militant Ugandan opposition group which fought against the Second Republic of Uganda, government of President of Uganda, President Idi Amin from 1973 to 1979. Described as "specialists in sabotage" ...

, a Ugandan militant opposition group

Places

Sum (administrative division) A sum is the lowest level of administrative division used in China, Mongolia, and Russia. The word ''sum'' is a direct translation of the Manchu word ''niru'', meaning ‘arrow’. Countries such as China and Mongolia have employed the sum as admini ...

, an administrative division in Mongolia, China and some areas of Russia **

Sum (Mongolia) A district ( mn, сум, , , ; "arrow"), is a second level administrative subdivision of Mongolia. The 21 Provinces of Mongolia are divided into 331 districts.Montsame News Agency. ''Mongolia''. 2006, Foreign Service office of Montsame News A ...

, , an administrative division in Mongolia * SUM, the IATA airport code for the

Sumter Airport Sumter Airport is a public use airport located four nautical miles (7 km) north of the central business district of Sumter, a city in Sumter County, South Carolina, United States. The airport is owned and operated by the Sumter County unde ...

in Sumter County, South Carolina, USA

Other uses

* Sum, an old name for the

Finns Finns or Finnish people ( fi, suomalaiset, ) are a 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 ...

in East Slavic languages, derived from the word Suomi, "Finland" *

Soum (currency) The som, sum, or soum is a unit of currency used in Turkic-speaking countries in Central Asia. Its name comes from words in the respective languages (including Kazakh, Kyrgyz, Uyghur and Uzbek) for "pure", referring to historical coins of pur ...

(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 credi ...

, an interbank network in forty-two U.S. state * SUM, the ISO 639-3 code for the Sumo language *

Cen (surname) Cen is the Mandarin pinyin romanization of the Chinese surname written in Chinese character. It is romanized Ts'en in Wade–Giles, and variously as Sam, Sum, Sham, Shum in Cantonese, Gim, Khim, Chim in Taiwanese Hokkien and Chen in other pinyin ...

, sometimes Romanized Sum * '' ''Cogito, ergo sum'', Latin for: "I think, therefore I am" *

Sum certain A sum certain is a specified and set amount of money owed by one person to another. It is a legal term of art, having specialized meaning in the law. Some kinds of legal claims can not be brought at all unless the sum certain can be pleaded. A docum ...

, a legal term

Mathematics

Computing and technology

Art and entertainment

Organizations

Places

Other uses

See also