Grammar: Gerund: Gerundial Constructions

Objectives: By the end of this unit, students should be able to use active vocabulary of this theme in different forms of speech exercises.

Students should be better at discussing on theme “What is mathematics?”.

Students should know the rule of non-finite form of the verb: Gerund and fulfill grammar exercises.

Methodical instructions: This theme must be worked out during two lessons a week according to timetable.

Lexical material: Introduce and fix new vocabulary on theme “What is mathematics?”. Students should be better at thinking about their future and what they are to do.

Students should know Gerund: Gerundial Constructions till the end of this course.

Grammar:Introduce and practice theGerund and Gerundial Constructions. Revise the use of Infinitive Constructions.

What is mathematics?

The students of mathematics may wonder where the word "mathematics "comes from. Mathematics is a Greek word, and, by origin or etymologically, it means "something that must be learnt or understood", perhaps “acquired knowledge" or "knowledge acquirable by learning" or “general knowledge". The word "mathematics'' is a contraction of all these phrases. The celebrated Pythagorean school in ancient Greece had both regular and incidental members. The incidental members were called "auditors"; the regular members were named "mathematicians" as a general class and not because they specialized in mathematics; for them mathematics was a mental discipline of science of learning. What is ma­thematics in the modern sense of the term, its implications and connota­tions? There is no neat, simple, general and unique answer to this question.

Mathematics as a science, viewed as a whole, is a collection of branches. The largest branch is that which builds on the ordinary whole num­bers, fractions, and irrational numbers, or what, collectively, is called the real number system. Arithmetic, algebra, the study of functions, the cal­culus differential, equations, and various other subjects which follow the calculus in logical order, are all developments of the real number sys­tem. This part of mathematics is termed the mathematics of number. A second branch is geometry consisting of several geometries. Mathematics contains many more divisions. Each branch has the same logical structure: it begins with certain concepts, such as the whole numbers or integers in the mathematics of number, and such as point, line and tri­angle in geometry. These concepts must verify explicitly stated axioms. Some of the axioms of the mathematics of number are the associative, commutative, and distributive properties and the axioms about equalities. Some of the axioms of geometry are that two points determine a line, all right angles are equal, etc. From the concepts and axioms theorems are deduced. Hence, from the standpoint of structure, the concepts, axioms and theorems are the essential components of any compartment of ma­thematics. We must break down mathematics into separately taught sub­jects, but this compartmentalization taken as a necessity, must be com­pensated for as much as possible. Students must see the interrelation­ships of the various areas and the importance of mathematics for other domains. Knowledge is not additive but an organic whole and mathema­tics is an inseparable part of that whole. The full significance of mathe­matics can be seen and taught only in terms of its intimate relationships to other fields of knowledge. If mathematics is isolated-from other provinces, it loses importance.

Ex.1.Match the columns:

А	В
1. fraction 2. whole numbers 3. irrational numbers 4. differential equations 5. concept 6. point 7. line 8. triangle 9. equality 10. axiom	a) аксиома b) иррациональные числа c) дробь d) целые числа e) концепция f) точка g) дифференциальные уравнения h) равенство i) линия j) треугольник

Ex.2. Choose a,b,c or d.

1. Where does the word “mathematics” come from?

a) Greece b) England

c) Russia d) Alexandria

2. What does the word “mathematics” mean by origin or etymologically?

a) “acquired knowledge” b) “logical construction”

c) “scientific knowledge” d)“knowledge about nature”

3. What is mathematics as a science?

a) a real number system b) a collection of branches

c) a calculus in logical order

d) a calculus, differential equations, and functions

4. What is the largest branch of mathematics?

a) geometry b) differential equations

c) the whole number system d) the real number system

5. What is the certain concept of mathematics of number?

a) whole numbers or integers b) points, lines, and triangles

c) differential equations d)fractions and irrational numbers

6. What is deduced from the concepts and axioms?

a) structures b) theorems

c) calculus d) equations

Ex.3. Choose rhe title of the text according to summary.

a. Geometry

b. Mathematics of number

c. Mathematics as a science

d. The Pythagorean school

Ex.4. Translate the highlighted word correctly.

1. The incidental members were called “auditors”.

a) называютb) назывались

c) названный

2. This part of mathematics is termed the mathematics of number.

a) будет определенаb) была определена

c) определяется

3. From the concepts and axioms theorems are deduced.

a) выводятb) выводятся

c) были выведены

4. Mathematics as a science, viewed as a whole, is a collection of branches.

a) рассматриваетсяb) рассмотрела

c) рассматриваемая

5. A second branch is geometry consisting of several geometries.

a) состоящаяb) состояла

c) состоит

6. These concepts must verify explicitly stated axioms.

a) установивb) установленные

c) устанавливающие

Ex.5.Listening

Follow the link: http://www.youtube.com/watch?v=r2HJcWg1Moo (Beauty and Truth in Mathematics and Science)

Grammar: Gerund: Gerundial Constructions

Do exercises from Units 53,p.106-107 ex.:53.1-53.4 and Unit 58 p.116-117 ex.:58.1-58.4 (Raymond Murphy “English Grammar in Use” A self-study reference and practice book for intermediate students of English Third Edition. Cambridge)

БӨЖ тапсырмалар:

Write an essay or be ready to speak about “What is mathematics ?”.

Follow the link and pass the test for grammar:

http://www.study.ru/test/test.php?id=367