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This articles introduces “algebra” and its applications.
Algebra (from Arabic al-jebr meaning “reunion of broken parts”) is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. Algebra has numerous usages in daily life and is commonly taught in public schools.
Elementary algebra, often part of the curriculum in secondary education, introduces the concept of variables representing numbers. Statements based on these variables are manipulated using the rules of operations that apply to numbers, such as addition. This can be done for a variety of reasons, including equation solving. Algebra is much broader than elementary algebra and studies what happens when different rules of operations are used and when operations are devised for things other than numbers. Addition and multiplication can be generalized and their precise definitions lead to structures such as groups, rings and fields, studied in the area of mathematics called abstract algebra.
With Babylonian roots, claims for the 3rd century Greek mathematician Diophantus and Muhammad ibn Musa al-Khwarizmi (from whose name “algorithm’ comes) to the title “father of algebra”, algebra expresses fundamental truths of abstraction that would occur in any culture that reached similar levels of mathematical sophistication as these are requisite for further development. Algebra itself becomes an object of study in modern topics such as universal algebra.
Algebra may be divided roughly into the following categories: