МЕТ_1к_1ч

integral between limits n and m

a sub one

a sub two

x squared

round brackets opened x minus a

R sub one multiplied by x

a to the -th power

the ratio of the product pl divided by the product ae

cube root (out) of

the square root of four

the n-th root out of a to the m-th (power)

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Appendix 8: MEASUREMENT

UNITS OF MEASUREMENT OF DISTANCE

(LINEAR MEASURES)

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Appendix 9: POSSIBLE PHRASES FOR CONVERSATIONAL PRACTICE

to order a sequence of arguments firstly − secondly − finally

to begin / start with − next − lastly first of all − and also

let me begin by pointing out − and besides in addition to this

furthermore / moreover essentially, the problem is ...

basically besides above all what is more

There is one more point ...

I may as well add that ...

to introduce arguments

Let me come to my first / second /... / next argument

My first /... argument is ...

The first /... reason why we're

Wouldn't you have to agree ...? /

No, thank you, ...

Yes, please. / Go ahead.

Thank you very much, .... ,

I will start by saying (claiming) that ...

To begin with, my point is that ...

to express one's opinion

In my opinion / view …

To my mind …

It seems to me that … (> tentative)

I feel / think / believe that … (> neutral)

I have the feeling / the impression that …

As I see it, …

I rather think that …

I am sure that …

I am convinced that …(> strong)

As for me ...

As concerns ...

As far as I am concerned ...

What I mean to say is ...

My point is that ...

It is a well-known fact that ...

It means ...

I don't mean to say ...

It is too much to say that ...

I am convinced that ...

This is a convincing argument.

The statement is convincing by itself.

It seems reasonable to say ...

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My (own) point is that ...

It's too much to say that ...

It is common knowledge that ...

What is missing (lacking) in the statement is that ...

In view of the idea ...

The statement may be confirmed by ...

One can confirm it by further ...

There is no denying the fact that ...

I hold a similar view ...

I'd like to make it clear ...

It seems reasonable to assume that ...

It will be seen that ...

It's worth considering (appreciating) ...

I'd like to make it clear that ...

What I mean to say is ...

to express one's agreement

I agree.

I agree completely / entirely. I think you're quite right.

I think so, too.

I don't think so, either. That's exactly what I think.

That's just what I was thinking. That's right.

I quite agree to it.

Quite so. Absolutely correct. I think, it is right.

That's right. It's O.K. Exactly. Quite so. It's correct to say.

I quite agree with you. I share this viewpoint. Exactly ... Indeed ...

Exactly. Certainly. This is the case.

I fully agree to it. I accept it fully.

Right you are (it is). I agree to it.

There is no point in disagreeing that ...

There is no point in denying that ...

I see no point at all to disagree that ...

to express one's disagreement or doubt

I don't quite agree here.

I cannot accept your view that …

I cannot share this view. That seems obvious. Do you really think so? I wouldn't say so.

I don't know.

I'm not quite so sure.

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although nevertheless / still even so

yet however

I don't think so.

I don't agree with you. I can't agree, I'm afraid. That's not how I see it. I disagree (completely). I don't agree at all.

I am afraid, you are mistaken here. It is quite the reverse.

On the contrary.

Just the other way round. I am afraid, it is wrong. I don't quite agree to it.

Excuse me, but ... Not at all. On the contrary. Far from it. Quite the contrary (the reverse). You're wrong there, I am afraid. It's unlikely.

Not at all. Not quite so. Just the other way round.

The statement does not imply ...

Scientists do not mean/claim ...

It's not correct / It's not right / It's wrong, I am afraid. Although no conviction serves as a proof ...

I can't but refute it.

The statement must be refuted.

I have a counter-argument that may serve as a refutation. Not quite so, I am afraid.

I don't think this is just the case. I dout it. Far from that.

I deny that this is the case.

I deny that the statement is true. The statement does not imply ...

It can be denied that ...

That doesn't sound convincing enough. I don't think so.

The definition is inappropriate. It's hardly likely that ...

One cannot say that ...

You are free to disagree with me but ...

to give examples

There are many examples for this / for ..., for instance.

In fact, you can find many examples for this in real life. Just think of...

And there are similar cases, such as ..., ...

So in this simple example we can clearly see the effect of ...

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to summarize one's arguments

To conclude… In conclusion… To sum up… so

therefore

Summarizing the discussion ...

In conclusion I must say ...

Summing up the discussion ...

To summarize the topic ...

In conclusion, I may say ...

To sum up, here are the main points our opponents have not addressed … We pointed out that …

Our opponents have claimed that … To recap the main points …

Let’s sum up where we stand in this debate. Let me summarize our position in this debate. In summary, we want to point out that … Let’s see which arguments are still standing. Let’s take stock of where we are in this debate. On the whole ... In the long run ...

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Appendix 10: WRITING HELP

ABSTRACT

A text / an article abstract is a brief summary of the text / article. It provides the key information of the text / article in a short form; gives the reader the idea about the topic of the text / article.

An abstract is characterized by 1) logicality and sequence of information;

2)neutrality of the author; 3) factual information of a text / an article including:

–What the author did;

–How the author did it;

–What the author found;

–What the author concluded.

ABSTRACT REQUIREMENTS

1.It must contain one paragraph (3−4 sentences).

2.It must give both general information and specific information about the text / article.

3.It is characterized by the use of present tenses (for general information), past tense (for results), third person, passive, and the non-use of negatives. It is necessary to avoid subordinate clauses, abbreviation, jargon, symbols, repetition, meaningless expressions, superlatives, illustrations, descriptive details, examples.

4.It must be self-contained and unambiguous.

5.The information of an abstract has to be conveyed in a neutral, logical, coherent, precise and condense way.

USEFUL PHRASES

Example:

ABSTRACT

THE RISE OF THE ENVIRONMENTAL JUSTICE PARADIGM

This article uses social movement theory to analyse environmental justice rhetoric. It argues that the environmental justice frame is a master frame that uses discourses about injustice as an effective mobilizing tool. The article identifies an environmental justice paradigm and compares it with the new environmental paradigm. In addition, the article discusses why the environmental justice movement grew so fast and why its adherents find the environmental justice frame so appealing.

SUMMARY

Summary is a shortened version of the text / article that highlights its key points.

Follow these steps to write summary:

Read the text.

Make notes of the main points of the text.

Start your piece of writing with one sentence that summarizes the idea of the whole text.

Write your summary, including all the main points. Use your own words.

Check if your summary is clear, complete and that it makes sense.

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Example:

Air, water, and land pollution is a result of increasing population and industry. Air pollution, such as acid rain and photochemical smog, can destroy forests and crops, kill animals and cause illness in humans. Water pollution from toxic chemicals, herbicides, pesticides, and waste can cause human tragedy and upset the food chain. Land pollution can cause toxic waste, fires, and explosions. This can affect both humans and their environment.

COMMENTS

To write comments means writing explanatory or critical notes upon a text. When you write comments, try to keep these things in mind:

write only relevant information;

express your ideas logically;

use the correct spelling, punctuation, grammar;

read over your comment to check if it makes sense;

edit your comment if it is necessary.

ESSAY

An essay is a short literary composition on a particular theme or subject, usually in prose and generally analytic, speculative, or interpretative. It must have at least three paragraphs, but a five-paragraph essay is a common length for academic writing.

The structure of an essay includes:

an introduction (state the problem and its consequence(s);

a main body (suggestions);

a conclusion (summarise your opinion).

TRANSITION WORDS AND PHRASES

Appendix 11: PROBLEM-SOLVING

Unit 1

CURIOUS PROBLEMS AND PUZZLES

HOW MANY MILES A DAY?

Harry walked 117 miles, beginning on Sunday morning and finishing on Monday evening of the following week. He walked each day one mile farther than the day before. How many miles did he walk each day?

WHEN WILL HARRY HAVE A BICYCLE?

Harry was 12 years old when his father promised him a bicycle. "I’ll buy a bicycle for you when you are one-third of my age", said his father who was 56 years old then. When will Harry get a bicycle?

HOW MUCH DOES THE MAN WEIGH?

A man weighs 60 kilograms plus one-third of his weight. How much does he weigh?

DIVIDE THE CAMELS

Many years ago an Egyptian died and left 17 camels to his three sons. He left half of the camels to his eldest son, the second son was left a third of the camels and the youngest son was left one-ninth of the camels. The sons couldn’t divide the camels without cutting up one of them. So they went to a judge for advice. The judge listened to the problem, thought for a moment and then announced the solution. What was the solution?

HOW DID THEY CROSS THE RIVER?

Fred and Albert, with their father and village postman, were standing near the river. They had to cross it, because their village was on the other side of the river. Fred and Albert each weighed 112 pounds. Their father and postman each weighed 224 pounds. But the boat could carry only 224 pounds at a time. How did they cross?

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