The history of Algebraic Expressions
The father of algebraic expressions
The Hellenistic mathematician Diophantus has traditionally been known as "the father of algebra but debate now exists as to whether or not Al-Khwarizmi deserves this title instead.] Those who support Diophantus point to the fact that the algebra found in Al-Jabr is more elementary than the algebra found in Arithmetica and that Arithmetica is syncopated while Al-Jabr is fully rhetorical.[77]
Those who support Al-Khwarizmi point to the fact that he gave an exhaustive explanation for the algebraic solution of quadratic equations with positive roots,] and was the first to teach algebra in an elementary form and for its own sake, whereas Diophantus was primarily concerned with the theory of numbers. Al-Khwarizmi also introduced the fundamental concept of "reduction" and "balancing" (which he originally used the term al-jabr to refer to), referring to the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. Other supporters of Al-Khwarizmi point to his algebra no longer being concerned "with a series of problems to be resolved, but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which hence forward explicitly constitute the true object of study. They also point to his treatment of an equation for its own sake and "in a generic manner, in sofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems. Al-Khwarizmi's work established algebra as a mathematical discipline that is independent of geometry and arithmetic
Algebra
Algebra is often referred to as a generalization of arithmetic:
problems and operations are expressed in terms of variables as well as
constants. A constant is some number that always has the same value, such as 3
or 14.89. A variable is a number that may have different values. In algebra,
letters such as a, b, c, x, y, and z are often used to represent variables. In
any given situation, a variable such as x may stand for one, two, or any number
of values. For example, in the expression x + 5 = 7, the only value that x can
have is 2. In the expression x2 = 4, however, x can be either +2 or −2.
And in the expression x + y = 9, x can have an unlimited number of values,
depending on the value of y.
Origins
of algebra
Algebra became popular
as a way of expressing mathematical ideas in the early ninth century. Arab
mathematician Al-Khwarizmi is credited with writing the first algebra book, Al-jabr
waʾl Muqabalah, from which the English word algebra is derived. The title
of the book translates as "restoring and balancing," which refers to
the way in which equations are handled in algebra. Al-Khwarizmi's book was
influential in its day and remained the most important text in algebra for many
years.
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