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Mathematics is a very big subject and is divided into so many branches like geometry, algebra, coordinate geometry, calculus and so on. Mathematics enters in all fields of science and it is essential for the development of science and technology. It is the basis for proving any new scientific theory or making any new discovery. In this article I will speak about algebra. I will consider its definition and history. It is interesting to many people to know how algebra started and evolved. The reason why I chose algebra is because it is an essential element in all fields of mathematics. All these fields require the use and manipulations of equations. As a matter of fact algebra historically started as several subjects scattered in different fields till it became a branch and by the end of the sixteenth century it reached its final stages of evolution. Algebra can be essentially considered as doing arithmetic operations with non numeric mathematical entities or objects. This is a very powerful structure because it allows us to proof properties that are true no matter what are the numbers involved. The non numeric entities can be unknown and we are required to find them or they can be unspecified. That is to say we have an equation and we can plug in different values to get different results. This is why algebra is used to express the relationship between entities. When we deal with algebra we mainly deal with expressions and equations. Equations describe the equity relationship between entities and an expression describes a phrase that contains variables, numbers and arithmetic operators. As algebra developed the non numeric entities were extended to accommodate more complex structure like vectors, matrices, and polynomials. It is now accommodating more complex and abstract new structures. This is what makes algebra useful in modeling mathematical and scientific problems that can not be modeled in any other way. Algebra took a very long evolution period before it became like the way we know it today. Its roots extend to the ancient Egyptian era and even before that. Algebra started at the time of the ancient Babylonians. They created advanced algorithms to solve certain problems. These algorithms are used today to solve quadratic equations and linear equations. The Egyptians of the same era used to model algebraic problems in terms of geometry and solve them geometrically. So they considered algebra as an application of geometry. The ancient Greek mathematicians and ancient Chinese mathematicians followed the same example as the Egyptians. The Egyptians developed geometric methods to solve particular algebraic problems. The Greeks even developed the Egyptian algorithms further to solve more general problems. All this influenced Muhammad Ibn Musa al-Khwarizmi the Arab Islamic scientist who created afterwards much of the algebraic method that we know today. The word algebra is actually an Arabic word and was created after he established algebra as an independent mathematical discipline other than geometry and arithmetic. He established algebra in his book the Compendious Book on Calculation by Completion and Balance. The classical algebraic discipline did not start before the end of the sixteenth century. In the year 1637 the modern algebraic notion was introduced. Then the solution of quadratic and cubic equations was introduced. Then matrices and determinants were used to solve systems of simultaneous equations. Many other new algebraic concepts were introduced later. Today we are fortunate that we have many innovative mathematical calculators and tools that incorporate all these algebraic ideas into a program that allow us to model real life problems just by pressing buttons and in seconds. We can use the outcome of all these algebraic findings from ancient Egyptians till today by the use of these calculators.
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