Find the words or phrases (1–7) in the text above which are explained / defined (a–g)? The first and the last letter are given to help you.

1 r-------g a the process of thinking about something in an intelligent sensible way in order to make a decision or form an opinion
2 p------e b exact in form, detail, time, measurements
3 e-------s c to include or be concerned with
4 d---------h d to recognize the difference between things
5 v------y e in spoken words and not in writing
6 a----------n(s) f shortened form of a word
7 d----------g g making you feel that it is useless to try to do something

Test yourself. Cover the dictionary meanings and look at the words. What are the meanings?

Decide if the statements are true or false.

1. The language of mathematics is mainly made up of words.

2. Symbolism used in maths facilitates efficiency of thought.

3. Symbols help mathematicians to avoid ambiguity of the common language.

4. Symbols are always abbreviations of words.

Find the following information in the text.

a. Characteristics of the mathematical language.

b. The effects of symbolism.

c. The difference between forming the language of maths and common language.



HELP box
Grammar focus: Quantifiers: too, too much/ many, enough, etc.

LARGE quantities SMALL quantities ZERO quantity

●Use a lot of/lots of inpositivesentences, e.g.:

They have a lot of knowledge.

This text has lots of symbols.

Use a lot when there is no noun, e.g.:

He talks a lot.

●Much/many are normally used in negative sentences and in questions, but a lot ofcan also be used e.g.:

Do you know much about the language of Maths?

There aren’t many abbreviations of words in this sentence.

Use plenty of in + sentences to mean as much as we need or more e. g.:

We have plenty of time to

find out what this sign means

●Use little + uncountable nouns, few + plural countable nouns: Little time is left before our exams. ●a little and a few =some, but not a lot: I only need a few minutes to get ready. Nadya drink a little coffee & no alcohol ●little and few = not much/many, very little/ very few: Few discoveries can equal to the discovery of Lobachevsky   ●Use any for zero quantity with a negative verb. Use no with a positive verb: Sorry, I’ve got no time. No tourists came to our museum last year. ●Use none (without a noun) in short answers.
MORE than you need or want LESS than you need
●Use too + adjective, too much + uncountable noun, too many + plural countable nouns, e.g.: I don’t like this letter. It’s too big. There’s too much noise. There’re too many operations in this expression ●Use enough before a noun but after an adjective, e.g.: There aren’t enough numerals in the given example. These equations aren’t difficult enough

A Choose the correct word or phrase for each sentence.

1. How much/many knowledge do you need for solving this problem?

2. He knows a lot of/lot of important symbols in Mathematics.

3. ‘How much exercise do you do?’ – ‘None/Any’

4. You should be friendly, but not too much/too friendly.

5. Could I have a little/a few time to think?

6. She spends too many/too much on doing her tasks.

7. There were too many/too much abbreviations of words in that text.

8. We’re writing a few/ a little ideas to avoid ambiguity of the common language

9. We’re going to give you a little information about common language.

10. He has enough experience/experience enough for this job.

B Complete the sentences. Try to write something positive after ‘But on the other hand,…’. Then compare what you’ve written with a partner. How similar are you?

My lifestyle

L I think I play computer games too much.
L I don’t __________________________________________ enough.
L I’m too _________________________________________________.
J But on the other hand, _____________________________________.


My diet

L I don’t eat enough green vegetables.
L I eat too much _______________________________________.
L I eat too many _______________________________________.
J But on the other hand __________________________________.


My home town/city

L There are too many bars and restaurants in the center of Donetsk.
L There’s too much _____________________________________.
L There aren’t enough ___________________________________.
J But on the other hand, _________________________________.



L There aren’t enough programmes about great mathematicians.
L There’s too much _______________________________________.
L There are too many ______________________________________.
J But on the other hand, ____________________________________.


Describe the main properties of the language of Mathematics.

2. Explain what the phrase ‘there is no royal road to mathematics’ means.

Learn mathematics in English

    As you know the language of mathematics uses signs and symbols. In the table below you can find some of them. Study their wording.






Summation sign (capital sigma)


The sum from (a equals) one to n of x sub a


Product sign  (capital pi [pai])


The product from (a equals) one to n of x sub a



Logarithm (log) sign

log 10 3

The log(arithm) of three to the base ten


Dash, prime

a′ b″

a dash times b double dash = a prime times b double prime


( )


3 (a+b)

Three multiplied by a plus b in parentheses = three times the sum of a and b= three times the quantity, a plus b= three, (initial) parenthesis, a plus b, (final) parenthesis


[ ]


Bracket, a+b, bracket, multiplied by c


{ }


One third times (initial) brace, a, (initial) bracket, b plus k, (initial) parenthesis, c minus d, (final) parenthesis, (final) bracket, (final) brace


Identity sign

a is identical to/with b



Greater than sign

a > b

a is greater than b



Less than sign

a < b

a is less than b


Greater than or equal to sign


a is greater than or equal to b


Less than or equal to sign


a is less than or equal to b


Approximation sign

a is approximately (nearly) equal to b


Infinity sign

→ ∞

x tends to infinity = x approaches infinity


Therefore sign

Therefore a equals b


Differential sign

Differential of x




(The first) derivative of y with respect to x = dy to dx ; the second derivative of y with respect to x


Integral sign

Integral between limits x and y




Sine x



Cosine x




Tan x

Tangent x




Cot x

Cotangent x


In pairs, look at the highlighted words and phrases. Try to guess what they mean from the context. Then check with your dictionary or teacher. Work out the list of the terms involved, make a kind of glossary.

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