CivilizationA civilization (British English: civilisation) is any complex society characterized by the development of the state, social stratification, urbanization, and symbolic systems of communication beyond natural spoken language (namely, a writing system). Civilizations are additionally characterized by other features, including agriculture, architecture, infrastructure, technological advancement, taxation, regulation, and specialization of labour.
Cradle of civilizationA cradle of civilization is a location and a culture where civilization was created independent of other civilizations in other locations. The formation of urban settlements (cities) is the primary characteristic of a society that can be characterized as "civilized". Other characteristics of civilization include a sedentary non-nomadic population, monumental architecture, the existence of social classes and inequality, and the creation of a writing system for communication.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Group representationIn the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector space to itself (i.e. vector space automorphisms); in particular, they can be used to represent group elements as invertible matrices so that the group operation can be represented by matrix multiplication. In chemistry, a group representation can relate mathematical group elements to symmetric rotations and reflections of molecules.
Andean civilizationsThe Andean civilizations were South American complex societies of many indigenous people. They stretched down the spine of the Andes for from southern Colombia, to Ecuador and Peru, including the deserts of coastal Peru, to north Chile and northwest Argentina. Archaeologists believe that Andean civilizations first developed on the narrow coastal plain of the Pacific Ocean. The Caral or Norte Chico civilization of coastal Peru is the oldest known civilization in the Americas, dating back to 3500 BCE.
