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Algebra


Algebra is a generalization of arithmetic. Each statement of arithmetic deals with particular numbers. The statement (20+4)2 = JJ02 + 2*20*4 + 42 = 576 explains how the square of the sum of the two numbers 20 and 4 can be computed. To state a general rule we write symbols, ordinary letters, instead of particular numbers. Then the square of the sum of any two numbers a and b can be calculated by the rule (a+b)2 = a2+ 2ab + b2.

This is a general rule which is true no matter what particular numbers may replace the symbols a and b.

So, in arithmetic every number has a single definite value, and in algebra we use symbols, which usually have not a single definite value.

The systematic use of letters of the Latin alphabet was introduced in the 16Ih century by the French mathematicians Viet and Descartes.

An algebraic expression is an expression in which several numbers represented by letters or by letters and figures are connected by means of signs. The signs indicate the operations which the numbers must be subjected to and the order of these operations. Algebra deals with the operations of rational and irrational numbers, equations, logarithms, functions, graphs and complex numbers. Algebra is one of the most rapidly changing areas of mathematics because it is very sensitive to all the trends, which originate in other areas of mathematics.