Fill in the gaps with the words from the box.

division knots set up numerals symbols notation tally

 

1. If you keep a _______, you have a system to note how much has been spent.

2. The Roman _______ are still used as numbers nowadays.

3. There is a _______ between science and art subjects.

4. In maths we use _______ to show what kind of problem we are solving.

5. _______ in maths are things like numerals.

6. Some people tie _______ to remember something.

7. She _______ an experiment.

 

Grammar revision

2.7 Put the verb in brackets into the correct form of the Participle .

 

1 Numeral is a system of figures or symbols (to represent) numbers.

2 (to calculate) the distance, he solved the task.

3 There are various ways of recording numbers (to develop) in different countries.

4 You can do some arithmetic sums (to use) computer.

5 (to measure) the angles of triangle, he showed results to the engineer.

6 The results (to receive) were of great importance.

7 He thought about the problem (to discuss) at the conference.

 

2.8 Translate the sentences using Complex Object or Complex Subject.

 

1. Я знаю, что факультет прикладной математики является одним из самых престижных.

2. Считается, что арабские цифры используются по всему миру.

3. Кажется, математика была его любимым предметом в школе.

4. Я слышал, что она проводила эксперимент два года назад.

5. Оказалось, что они использовали новые методы в работе.

6. Так случилось, что эти ученые работают над одной проблемой.

7. Сообщили, что все вычисления являются неверными.

Speaking

What other interesting facts from the history of the maths do you know?

Prepare a short report about at least one and deliver it to your classmates.

 

 

Unit 3

Before you read

Match these words with their definitions.

1. to arise	a. to make better
2. to refine	b. to allow
3.to exclude	c. to occur
4. to simplify	d. to leave out
5. adjustments	e. understandable
6. comprehensible	f. small changes
7.to enable	g. to make something easier to do or understand

Fill in the gaps with the words 1 to 7 in the correct form from 3.1.

 

1. Computerisation should _______ to cut production costs by half.

2. Are there any matters _______ from the last meeting?

3. Could you _______ what you have just said?

4. I don’t think we can _______ the possibility that this prediction is incorrect.

5. She made a few minor __________ to the device.

6. The new computer software is highly ________ and can do much more than the old version.

7. It’s written in clear, __________ English.

 

Read the text. Then put the events (A-F) below in the correct order to show the procedure for using applied mathematics.

 

A The revised model is applied.

B The model is adjusted.

C A mathematical model is created.

D A problem arises.

E A solution is found.

F Approximate solutions are obtained.

 

Applied Mathematics

 

When mathematics is used to solve problems in some related areas of life, it is known as applied mathematics. Applied mathematics provides us with answers and solutions. It is used in numerous ways. A few examples are numerical analysis, engineering and programming. In these and other areas, applied mathematics takes problems from real life, and gives us successful and creative tools for solving them. Often, the first step when using applied mathematics is to create a mathematical model. This is a description of the problem in mathematical terms. This model is then studied to obtain exact or approximate solutions. If the solution is exact, the model is applied to the problem; if it is approximate, the model is refined until it is exact. Then, conclusions are interpreted and explained in comprehensible terms. Often the model is changed to be more realistic. So the modeling process may involve many adjustments. The second stage is the final solution to the problems mathematically formulated in the first stage.

It is often not clear which mathematical tools will be used in the study of a new problem, for example, algebra or differential calculus. For this reason, applied mathematicians need to be well trained in a range of mathematical areas so they will have a wide variety of mathematical tools available to them, They must not only be skilled mathematicians but must also be knowledgeable in the specific area to which mathematics is being applied. For example, in dealing with business and industry, knowledge of economics is necessary.

When it comes to creating models, the mathematician will make choices about which factors to include and which to exclude. The goal is to produce a model that is realistic enough to reflect the main aspects of the problem being studied, but simple enough to be treated mathematically.

Sometimes the mathematician has to either simplify this model so it can be analysed, or devise new mathematical methods that will allow the model to be analysed. Problems sometimes lead to new mathematical methods, and existing mathematical methods often lead to a new understanding of the problem.

Vocabulary development

3.4 Listen to a course director giving some information to a group of potential maths students. Then decide if the following statements are true or false.

 

1. Mathematics is an expanding area with good job prospects.

2.The difference between pure and applied mathematics lies in the content of the studies.

3. An applied mathematician finds answers to questions raised by mathematics.

4. A pure mathematician’s answers take the form of general propositions with exact, formal proof.

5. The two kinds of mathematics can come to the same conclusions.

 

Fill in the table.

 

Verb	Noun	Adjective
exclude
simplify
	adjustment
analyse
		comprehensible
provide
reflect
apply