Read the article below and complete it with a word from the task 1 (column B).



Algebra is the 1 _____ of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. 

The word algebra comes from the Arabic language (al-jabr, literally, restoration) and much of its methods from Arabic/Islamic mathematics. Its roots can be traced to ancient Indian mathematics, which had a direct influence on Muhammad ibn M sā al-khwārizmī (c. 780–850). He learned Indian mathematics and introduced it to the Muslim world through his famous arithmetic text, Book on Addition and Subtraction after the method of the Indians. He later wrote The Compendious Book on Calculation by Completion and Balancing, which established algebra as a mathematical discipline that is independent of geometry and arithmetic.

    Algebra in its simplest 2 _____ is a generalized form of arithmetic. Thus algebra usage includes all the definitions and processes of arithmetic.

    In arithmetic all the numbers we use are expressed by means of the digits 0, 1, 2, … 9, each of which has a single definite 3 _____.

    In algebra besides the ordinary arithmetical numbers we use symbols which usually have not a single definitevalue. Letters of the Latin alphabet are generally used to represent numbers. A number represented by algebraic symbols is called an algebraic expression. An algebraic expression is an expression in which several numbers represented by letters (or by letters and figures) are connected by means of signs. These signs indicate the operations to which the number must be subjected and the 4 _____ of these operations.

    Algebra deals with the operations of rational and irrational numbers, algebraic expressions, equations, logarithms, functions, graphs and complex numbers.

    The turning point in the history of algebra was the 16-th century. In the 16-th century the French mathematician Viet and later Descartes introduced the systematic use of the first letters of the alphabet for given quantities and the last letters for the unknown. Just as the discovery of zero created the arithmetic of today so did the literal 5 _____ ushered in a new era in the history of algebra.

The names of many other famous mathematicians are connected with the development of algebra because of their great contributionto this branch of mathematics.

The first Russian book containing a certain information on algebra was ‘Arithmetic’ by Magnitsky. The elementary algebra has been taught as a subject at school in Russia since the XVIII century. Lobachevsky, Bunyakovsky, Chebishev touched the problem of teaching algebra too.

Algebra is one of the most rapidly changing areas of mathematics. It is sensitive to the trends which originate in all other branches of mathematics. The most important new demands in algebra come from topology, analysis and algebraic geometry.

 

Find the words or phrases (1–5) in the text above which are explained / defined (a–e)? The first and the last letter are given to help you.

1 r--t(s) a that from which sth grows (basis, source)
2 be s--------d b to be made to undergo
3 d—l with c be concerned with
4 q------y d amount, sum or number
5 c----------n e act of giving ideas for a purpose, act of contributing sth

Test yourself. Cover the dictionary meanings and look at the words. What are the meanings?

Answer the questions on the text.

a. What branch of Mathematics is Algebra?

b. What does the word ‘algebra’ come from?

c. What ancient civilization had a direct influence on the Arabic mathematician Muhammad ibn M sā al-khwārizmī?

d. What is the difference between Arithmetic and Algebra?

e. What is an algebraic expression?

f. When was the turning point in the history of Algebra?

g. Who contributed much to Algebra?

h. What do the most important new demands in Algebra come from?

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