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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.
1.6 Ring theory and commutative algebra. 1.7 Universal algebra. ... Download as PDF; Printable version; In other projects ... An example of a covering described by ...
[1] Elementary algebra, also known as high school algebra or college algebra, [2] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 3 ] whilst algebra introduces variables (quantities without fixed values).
An algebra is a module, wherein you can also multiply two module elements. (The multiplication in the module is compatible with multiplication-by-scalars from the base ring). *-algebra; Affine Lie algebra; Akivis algebra; Algebra for a monad; Albert algebra; Alternative algebra; AW*-algebra; Azumaya algebra; Banach algebra; Birman–Wenzl ...
In mathematics, an algebraic expression is an expression build up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Rhetorical algebra, in which equations are written in full sentences. For example, the rhetorical form of + = is "The thing plus one equals two" or possibly "The thing plus 1 equals 2". Rhetorical algebra was first developed by the ancient Babylonians and remained dominant up to the 16th century.
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Also called infinitesimal calculus A foundation of calculus, first developed in the 17th century, that makes use of infinitesimal numbers. Calculus of moving surfaces an extension of the theory of tensor calculus to include deforming manifolds. Calculus of variations the field dedicated to maximizing or minimizing functionals. It used to be called functional calculus. Catastrophe theory a ...
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