AfricaAfrica is the world's second-largest and second-most populous continent, after Asia in both aspects. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 20% of Earth's land area and 6% of its total surface area. With billion people as of , it accounts for about of the world's human population. Africa's population is the youngest amongst all the continents; the median age in 2012 was 19.7, when the worldwide median age was 30.4.
Ancient EgyptAncient Egypt was a civilization in Northeast Africa situated in the Nile Valley. Ancient Egyptian civilization followed prehistoric Egypt and coalesced around 3100 BC (according to conventional Egyptian chronology) with the political unification of Upper and Lower Egypt under Menes (often identified with Narmer). The history of ancient Egypt occurred as a series of stable kingdoms, separated by periods of relative instability known as Intermediate Periods: the Old Kingdom of the Early Bronze Age, the Middle Kingdom of the Middle Bronze Age and the New Kingdom of the Late Bronze Age.
Sub-Saharan AfricaSub-Saharan Africa, Subsahara, or Non-Mediterranean Africa, is the area and regions of the continent of Africa that lie south of the Sahara. These include Central Africa, East Africa, Southern Africa, and West Africa. Geopolitically, in addition to the African countries and territories that are situated fully in that specified region, the term may also include polities that only have part of their territory located in that region, per the definition of the United Nations (UN).
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.
Slavery in AfricaSlavery has historically been widespread in Africa. Systems of servitude and slavery were common in parts of Africa in ancient times, as they were in much of the rest of the ancient world. When the trans-Saharan slave trade, Indian Ocean slave trade and Atlantic slave trade (which started in the 16th century) began, many of the pre-existing local African slave systems began supplying captives for slave markets outside Africa. Slavery in contemporary Africa is still practiced despite it being illegal.
EgyptEgypt (مصر ALA mɑsʕr), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and the Sinai Peninsula in the southwest corner of Asia. It is bordered by the Mediterranean Sea to the north, the Gaza Strip of Palestine and Israel to the northeast, the Red Sea to the east, Sudan to the south, and Libya to the west. The Gulf of Aqaba in the northeast separates Egypt from Jordan and Saudi Arabia.
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.
Economy of AfricaThe economy of Africa consists of the trade, industry, agriculture, and human resources of the continent. , approximately 1.3 billion people were living in 54 countries in Africa. Africa is a resource-rich continent. Recent growth has been due to growth in sales, commodities, services, and manufacturing. West Africa, East Africa, Central Africa and Southern Africa in particular, are expected to reach a combined GDP of $29 trillion by 2050.
Irreducible representationIn mathematics, specifically in the representation theory of groups and algebras, an irreducible representation or irrep of an algebraic structure is a nonzero representation that has no proper nontrivial subrepresentation , with closed under the action of . Every finite-dimensional unitary representation on a Hilbert space is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.
Ancient Egyptian medicineThe medicine of the ancient Egyptians is some of the oldest documented. From the beginnings of the civilization in the late fourth millennium BC until the Persian invasion of 525 BC, Egyptian medical practice went largely unchanged and included simple non-invasive surgery, setting of bones, dentistry, and an extensive set of pharmacopoeia. Egyptian medical thought influenced later traditions, including the Greeks. Egyptian medical papyri Until the 19th century, the main sources of information about ancient Egyptian medicine were writings from later in antiquity.
Ancient Egyptian funerary practicesThe ancient Egyptians had an elaborate set of funerary practices that they believed were necessary to ensure their immortality after death. These rituals included mummifying the body, casting magic spells, and burials with specific grave goods thought to be needed in the afterlife. The ancient burial process evolved over time as old customs were discarded and new ones adopted, but several important elements of the process persisted.
HistoryHistory (derived ) is the systematic study and documentation of the human past. The period of events before the invention of writing systems is considered prehistory. "History" is an umbrella term comprising past events as well as the memory, discovery, collection, organization, presentation, and interpretation of these events. Historians seek knowledge of the past using historical sources such as written documents, oral accounts, art and material artifacts, and ecological markers.
History of EgyptThe history of Egypt has been long and wealthy, due to the flow of the Nile River with its fertile banks and delta, as well as the accomplishments of Egypt's native inhabitants and outside influence. Much of Egypt's ancient history was a mystery until Egyptian hieroglyphs were deciphered with the discovery and help of the Rosetta Stone. Among the Seven Wonders of the Ancient World is the Great Pyramid of Giza. Ancient Egyptian civilization coalesced around 3150 BC with the political unification of Upper and Lower Egypt under the first king of the First Dynasty, Narmer.
Ancient Egyptian religionAncient Egyptian religion was a complex system of polytheistic beliefs and rituals that formed an integral part of ancient Egyptian culture. It centered on the Egyptians' interactions with many deities believed to be present in, and in control of the world. About 1500 deities are known. Rituals such as prayer and offerings were provided to the gods to gain their favor. Formal religious practice centered on the pharaohs, the rulers of Egypt, believed to possess divine powers by virtue of their positions.
Lie algebra representationIn the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator. In the language of physics, one looks for a vector space together with a collection of operators on satisfying some fixed set of commutation relations, such as the relations satisfied by the angular momentum operators.
EgyptiansEgyptians (مِصرِيُّون, mɪsʕrɪjˈjuːn; مَصرِيِّين, mɑsʕɾɪjˈjiːn; remenkhēmi) are an ethnic group native to the Nile Valley in Egypt. Egyptian identity is closely tied to geography. The population is concentrated in the Nile Valley, a small strip of cultivable land stretching from the First Cataract to the Mediterranean and enclosed by desert both to the east and to the west. This unique geography has been the basis of the development of Egyptian society since antiquity.
