Unit 10 Theme:The basic and new concepts.

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 about The basic and new concepts.

Students should know the rule of Conditionals and ‘wish’

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 “The basic and new concepts”.

Define the important aspects of geometry. Discuss in groups.

Grammar: Conditionals and ‘wish’. Introduce and practice Conditionals. Revise the use of Conditionals.

The basic and new concepts.

The basic concepts of the main branches of mathematics are abstractions from experience, implied by their obvious physical counterparts. But it is noteworthy, that many more concepts are introduced which are, in essence, creations of the human mind with or without any help of experience. Irrational numbers, negative numbers and so forth are not wholly abstracted from the physical practice, for the man's mind must create the notion of entirely new types of numbers to which operations such as addition, multiplication, and the like can be applied. The notion of a variable that represents the quantitative values of some changing physical phenomena, such as temperature and time, is also at least one mental step beyond the mere observation of change. The concept of a function, relationship between variables, is almost totally a mental creation.

The more we study mathematics the more we see that the ideas and conceptions involved become more divorced and remote from experience, and the role played by the mind of the mathematician becomes larger and larger. The gradual introduction of new concepts which more and more depart from forms of experience finds its parallel in geometry and many of the specific geometrical terms are mental creations.

As mathematicians nowadays working in any given branch discover new concepts which are less and less drawn from experience and more and more from human mind the development of concepts is progressive and later concepts are built on earlier notions. These facts have unpleasant consequences. Because the more advanced ideas are purely mental creations rather than abstractions from physical experience and because they are defined in terms, of prior concepts it is more difficult to understand them and illustrate their meanings even for a specialist in some other province of mathematics. Nevertheless, the current introduction of new concepts in any field enables mathematics to grow rapidly. Indeed, the growth of modern mathematics is, in part, due to the introduction of new concepts and new systems of axioms.

Ex.1. Choose a,b,c or d.

1. What are the basic concepts of the main branches of mathematics?

a) abstractions from experience b) experience

c) physical abstractions d) quantitative values

2. What does the notion of a variable represent?

a) the quantitative values of some constant physical phenomena.

b) the quantitative values of some changing physical phenomena.

c) mathematical concepts.

d) functions.

3. Where does the gradual introduction of new mathematical concepts find its parallel in?

a) physics b) geometry

c) experience d) physical practice

4. Where are the new concepts remoted from?

a) experience b) human mind

c) geometry d) mathematics

5. Why are the new concepts more difficult to understand?

a) they are not defined in terms.

b) they are defined in terms of prior concepts.

c) they are defined in terms of physical concepts.

d) they involve many difficult notions.

6. What do new concepts enable mathematics to do?

a)to grow rapidly.

b) to grow slowly.

c) to stop the development.

Ex.2. Choose the title of the text according to summary.

a. The basic and new concepts c. Modern mathematicians

b. The basic concepts d. Irrational numbers

Ex.3. Translate the highlighted word correctly.

1. But it is noteworthy, that many more concepts arc introduced which are, in essence, creations of human mind.

a) представленыb) были представлены

c) представляли

2. Irrational numbers, negative numbers, and so forth are not wholly abstracted from the physical practice.

a) не отделяютсяb) не отделяли

c) не были отделены

3. Later concepts are built on earlier notions.

a) строилиb) строятся

c) были построены

4. The basic concepts of the main branches of mathematics are abstractions from experience, implied by their obvious physical counterparts.

a) подразумеваемыеb) подразумевают

c) подразумевали

5. Irrational numbers, negative numbers and so forth are not wholly abstracted from the physical practice, for the man's mind must create the notion of entirely new types of numbers to which operations such as addition, multiplication, and the like can be applied.

a) можно будет применитьb) могли применить

c) могут применяться

6. The more we study mathematics the more we see that the ideas and conceptions involved become more divorced and remote from experience, and the role played by the mind of the mathematician becomes larger and larger.

a) игралаb) играемая

c) играющая

Ex.4.Listening

Follow the link: http://www.youtube.com/watch?v=fZaRCvc9cqY (Mathematics)

Grammar : If and wish

Do exercises from Units 38-41p.76-83 ex.:38.1-41.4 (Raymond Murphy “English Grammar in Use” A self-study reference and practice book for intermediate students of English Third Edition. Cambridge).

БӨЖ тапсырмалар:

Find out information about the great mathematicians in history of the world and make presentation about them.

Follow the link and pass the test for grammar:

http://www.study.ru/test/test.php?id=392