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Algebra is the branch of mathematics that studies algebraic structures and the operations they use. [1] An algebraic structure is a non-empty set of mathematical objects, such as the integers, together with algebraic operations defined on that set, like addition and multiplication.
A composition algebra (,,) consists of an algebra over a field, an involution, and a quadratic form = called the "norm". The characteristic feature of composition algebras is the homomorphism property of N {\displaystyle N} : for the product w z {\displaystyle wz} of two elements w {\displaystyle w} and z {\displaystyle z} of the composition ...
A Taxicab number is the smallest positive number that can be expressed as a sum of two positive integer cubes in n distinct ways. The smallest taxicab number after Ta(1) = 1, is Ta(2) = 1729, [4] expressed as
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).
Conditions (1) and (2) together are equivalent to L being a linear subspace of A. It follows from condition (3) that every left or right ideal is a subalgebra. This definition is different from the definition of an ideal of a ring, in that here we require the condition (2). Of course if the algebra is unital, then condition (3) implies ...
A typical sequence of secondary-school (grades 6 to 12) courses in mathematics reads: Pre-Algebra (7th or 8th grade), Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs [ 3 ] while many complete high school without passing Calculus or Statistics.