4. Express agreement or disagreement with the following:

1. Each statement of arithmetic deals with particular numbers.

2. A formula is a general rule which remains true no matter what particular numbers may replace the symbols a and b.

3. Algebra is the system of rules which don't work with the operations with numbers.

4. The use of letters to represent numbers isn't the characteristic of algebra.

5. Algebraic expressions have much in common with trigonometric functions.

5. Insert the missing words.

1. Algebra is a ... of arithmetic.

2. The characteristic of ... is to use of letters to ... .

3. The operations of ..... are called algebraic expressions.

4. The rules concerning the operations with ... can be stated as ... .

5. The operation of multiplication is denoted by ... as by placing the letters ... to each other.

6. Translate into Russian.

Algebra is used in many spheres of life, from that of the philosopher to that of the manual labour. The skilled worker may use algebra to determine the location of the centre or the size of holes he must drill. Doctors, engineers and scientists use algebra in their research.

By the use of algebra we can reduce complex problems to simple formulas. We can find the answer to problems about the Universe and problems of sewing, building, cooking, measuring, buying, and selling as well.

7. Answer the following questions:

1. What is the relationship between arithmetic and algebra?

2. What do we use in algebra to represent numbers?

3. In what operations in arithmetic do we use numbers?

4. How can the rules of algebra be stated?

5. What operations are called algebraic expressions?

TEXT 2

При работе над текстом “Definitions and notations” формируется компетенция ОК-10: владеет одним из иностранных языков на уровне, позволяющем получать и оценивать информацию в области профессиональной деятельности из зарубежных источников.

В рамках формирования компетенции у студентов вырабатываются следующие умения, навыки:

Уметь

• понимать информацию текстов из учебной литературы в соответствии с конкретной целью;

• выступать с подготовленным сообщением.

Владеть

• навыками оформления речевых высказываний в соответствии с грамматическими и лексическими нормами устной и письменной речи, фонетическими нормами (устная речь) и основными правилами орфографии и пунктуации (письменная речь) иностранного языка, не допуская ошибок, препятствующих речевому общению;

• навыком использования двуязычных словарей при чтении различного типа текстов;

• профессиональными основами речевой коммуникации с использованием терминологии данной дисциплины.

Применяются интерактивные технологии: работа малыми группами, решение ситуационных задач.

Definitions and notations

A unit or an aggregate of units is called a whole number or an integer; a part of a unit is called a frac­tional number.

Such numbers are called arithmetical numbers and represented by symbols called numerals, as the Arabic figures, 1, 2, 3, etc., and the Roman I, V, X, etc.

It is convenient, in solving problems, to use letters for the numbers whose values are sought. Also, in stating rules, letters are used to represent not only the numbers whose values are to be found, but also the numbers that must be given whenever the rule is applied.

For example, the volume of any rectangular prism is equal to the area of the base multiplied by the height. By using V for volume, A for area of base and h for height this rule is stated in symbols, thus: V = A* h, when A = 60 and h = 5, 60x5 = 300, etc.

An equation that states a rule in brief form is called a formula.

A number whose value is to be found is called an unknown number.

In 3x = 21, x is an unknown number; in the formula for volume, V = A x h, V is an unknown number; but when this formula is changed to the formula for height, h = V/A , the V and A are known numbers and h is an unknown number.