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Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
The scope of algebra thus grew to include the study of algebraic structures. This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether. [36] Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics.
This article brings together the same content organized in a manner better suited for browsing. Lists cover aspects of basic and advanced mathematics, methodology, mathematical statements, integrals, general concepts, mathematical objects, and reference tables.
Algebra is one of the main branches of mathematics, covering the study of structure, relation and quantity. Algebra studies the effects of adding and multiplying numbers , variables , and polynomials , along with their factorization and determining their roots .
The Math Myth describes the approach of the contemporary American education system towards mathematics as a "self-delusion", especially critiquing the Common Core standards and the role of obtuse and abstract mathematics in impeding the mathematical literacy of students, arguing that current methods lead to higher drop out rates.
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.