Sum

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

Sum can also refer to:

Mathematics

• Sum (category theory), the generic concept of summation in mathematics
• Sum, the result of summation, 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 number theory
• Direct sum, a combination of algebraic objects
  • Direct sum of groups
  • Direct sum of modules
  • Direct sum of permutations
  • Direct sum of topological groups
• Einstein summation, a way of contracting tensor indices
• Empty sum, 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 linear algebra
• Minkowski addition, a sum of two subsets of a vector space
• Power sum symmetric polynomial, in commutative algebra
• Prefix sum, in computing
• Pushout (category theory) (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 field theory
• Riemann sum, in calculus
• Rule of sum, in combinatorics
• Subset sum problem, in cryptography
• Sum rule in differentiation, in calculus
• Sum rule in integration, in calculus
• Sum rule in quantum mechanics
• Wedge sum, a one-point union of topological spaces
• Whitney sum, 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
• "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, 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 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), 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, Latin for: "I think, therefore I am"
• Sum certain, a legal term

See also

• Addition
• Additive category
• Preadditive category