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Algebra, which is one of the main branches of Math, is the study of rules of operations, relations, constructions and concepts arising from them including terms, polynomials, equations and algebraic structures. Other branches of math are; geometry, analysis, topology, combinations and number theory.

Linear Algebra which majorly studies what happens when different rules of operations are used and when operations are devised for things other than numbers, is much broader than Elementary Algebra. Addition and Multiplication can be generalized and their accurate definitions give rise to structures like groups, rings and fields. These are studied in the field of Math known as abstract or modern algebra.

Refer to Wikipedia, Algebra.


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