1 arithmetical A. quantities
2 unknown B spaces
3 abstract C system
4 vector D algebra
Reading
Algebra
Algebra originated in the Middle East. Earlier than 1000 BC, the Babylonians developed an arithmetical system for solving problems that could be written algebraically. This was in advance of other systems, notably that of the Ancient Egyptians, who were able to solve the same problems, but did so by using geometry. The word algebra comes from Arabic and translates into English as reunion. It describes a system of mathematics which performs calculations by firstly rewriting, that is, transposing them, and then reducing them to their simplest form.
Algebra is the branch of mathematics which studies the structure of things, the relationship between things and quantity. It looks different from arithmetic when it is written. Arithmetic uses numbers and the four operators (plus, minus, multiply and divide). Algebra uses symbols, usually letters, and the operators. Actually, it is not very different from arithmetic; what can be done in algebra can be done in arithmetic. There are good mathematical reasons, however, why algebra is used instead of arithmetic.
Firstly, by not using numbers, mathematicians are able to set out arithmetical laws. In this way they
are able to understand the system of numbers more clearly. Secondly, by using algebra,
mathematicians are able to perform calculations where unknown quantities are involved. This
unknown is usually represented by x. Solutions can then be applied not just to the immediate problem,
but to all problems of the same nature by the use of a formula. A common algebraic problem to solve
in school exams would be, for example -.find x where 3x + 8 - 14. A third reason for the use of
algebra rather than arithmetic is that it allows calculations which involve change in the relationship
between what goes into the problem and what comes out of it, that is, between input and output.
It is an algebraic formula which allows a business to calculate its potential profit (or loss) over any
period of time.It is possible to classify algebra by dividing it into four areas. Firstly, there is
elementary algebra in which symbols (such as x and y, or a and b) are used to denote numbers.
In this area, the rules that control the mathematical expressions and equations using these symbols
are studied. Then,there is abstract or modern algebra in which mathematical systems consisting
of a set of elements and several rules (axioms) for the interaction of the elements and the
operations are defined and researched. Thirdly, there is linear algebra (linear equations) in
which linear transformations and vector spaces, including matrices, are studied. Finally,
there is universal algebra in which the ideas common to all algebraic structures are studied.
Like all branches of mathematics, algebra has developed because we need it to solve our problems. By avoiding the use of numbers we are able to generalise both the problem and the solution.
Pronunciation guide
Equation
Linear
Matrices
B Comprehension
Read the text and decide if the following statements are true or false.
1 Algebra is a mathematical system which rewrites a problem making it as simple as T o possible. F o
2 Written down, algebra differs to arithmetic in the operators it uses. T o F o
3 Algebra has some advantages to offer the mathematician. T o
F o
4 Algebraic formulae are primarily of use in businesses. T o
F o
5 Universal algebra combines all the structures from the other three areas. T o
F o
Before yоu read
Discuss these questions with your partner.
-» What is the job of an engineer?
-» Why does an engineer need to know maths?
D Vocabulary
Complete the sentences below with words and phrases from the box.
