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Elementary algebra, also known as high school algebra or college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 2 ] whilst algebra introduces variables (quantities without fixed values).
In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots (fractional power). [1] These operations may be performed on numbers, in which case they are often called arithmetic operations.
Over a field, the free algebra on n indeterminates can be constructed as the tensor algebra on an n-dimensional vector space. For a more general coefficient ring, the same construction works if we take the free module on n generators. The construction of the free algebra on E is functorial in nature and satisfies an appropriate universal property.
'4000 Years of Algebra', lecture by Robin Wilson, at Gresham College, 17 October 2007 (available for MP3 and MP4 download, as well as a text file). ExampleProblems.com Example problems and solutions from basic and abstract algebra.
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.
Basic topics in elementary mathematics include polygons, circles, perimeter and areas. A polygon is a shape that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit .
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