Conversational Practice

1. Choose one of the words given below and illustrate the concept:

equation;

the pure imaginary numbers;

the real numbers.

2. Discuss the statements given below. Summarize the discussion. Use the following phrases:

There is no point is denying that…

I will start by saying that…

All I mean to say is that…

To begin with, my point is that…

I am all for … but …

That doesn’t sound convincing enough…

I doubt it…

Summarizing the discussion…

1. Algebra is changing constantly and rapidly.

2. Anyone is now free to invent his own algebra.

3. The major stumbling block in the extension of complex number system and its effect on the theory of equations.

Give a short summary of the text.

Text B. The Early Algebra

1. Read and translate the text:

The Early Algebra

Babylonian Algebra – Rhetorical Style

Since algebra might have probably originated in Babylonia, it seems appropriate to credit the country with the origin of the rhetorical style of algebra, illustrated by the problems found in clay tablets dating back to c. 1700 B.C. The problems show the relatively sophisticated level of their algebra. Nowadays, such problems are solved by the method of elimination. The Babylonians also knew how to solve systems by elimination but preferred often to use their parametric method. The Babylonians were able to solve a rather surprising variety of equations, including certain special types of cubics and quartics – all with numerical coefficients, of course.

Algebra in Egypt

Algebra inEgypt must have appeared almost as soon as in Babylonia; but Egyptian algebra lacked the sophistication in method shown by Babylonian algebra, as well as its variety in types of equations solved. For linear equations the Egyptians used a method of solution consisting of an initial estimate followed by a final correction, a method now known as the "rule of false position". The algebra of Egypt, like that of Babylonia, was rhetorical.

The numeration system of the Egyptians, relatively primitive in comparison with that of the Babylonians, helps to explain the lack of sophistication in Egyptian algebra. European mathematicians of the sixteenth century had to extend the Hindu-Arabic notion of number before they could progress significantly beyond the Babylonian results in solving equations.

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