Mathematics through English

Министерство образования и науки Российской Федерации
Сибирский федеральный университет

Т. Н. Свиридова

MATHEMATICS THROUGH ENGLISH

Рекомендовано федеральным государственным бюджетным образовательным учреждением высшего профессионального образования 
«Санкт-Петербургский государственный университет» в качестве учебного пособия по дисциплине «Английский язык» для студентов высших 
учебных заведений, обучающихся по направлению подготовки 040400 
«Прикладная математика и информатика», № 3085 от 21.07.2015

Красноярск 
СФУ 
2016

УДК 811.111:51(07)
ББК 81.432.1я73+22.1я73
С247

Свиридова, Т. Н.
С247 
 
Mathematics through English : учеб. пособие / Т. Н. Свиридова. – Красноярск : Сиб. федер. ун-т, 2016. – 138 с.
ISBN 978-5-7638-3415-4

Представлены материалы для совершенствования умений профессионально ориентированного чтения и навыков устной и письменной речи. Приведены 
тексты аутентичного характера. Предложена серия упражнений, способствующих расширению и систематизации словарного запаса, развитию разговорных 
навыков и умений, закреплению грамматического материала.
Предназначено для студентов высших учебных заведений, обучающихся 
по направлению подготовки 040400 «Прикладная математика и информатика».

Электронный вариант издания см.: 
УДК 811.111:51(07)
http://catalog.sfu-kras.ru 
ББК 81.432.1я73+22.1я73

ISBN 978-5-7638-3415-4 
© Сибирский федеральный
университет, 2016

CONTENTS

Введение .......................................................................................................4

To the Student ...............................................................................................5

Module 1. Mathematics and mathematicians ............................................6
UNIT 1 ...................................................................................................6
UNIT 2 ................................................................................................ 11
UNIT 3 ................................................................................................ 16
Module 2. Algebra ..................................................................................... 24
UNIT 1 ................................................................................................ 24
UNIT 2 ................................................................................................ 29
UNIT 3 ................................................................................................ 34
Module 3. Geometry ................................................................................. 42
UNIT 1 ................................................................................................ 42
UNIT 2 ................................................................................................ 47
UNIT 3 ................................................................................................ 54
Module 4. Mechanics ................................................................................ 61
UNIT 1 ................................................................................................ 61
UNIT 2 ................................................................................................ 67
UNIT 3 ................................................................................................ 73
Module 5. Informatics .............................................................................. 80
UNIT 1 ................................................................................................ 80
UNIT 2 ................................................................................................ 88
UNIT 3 ................................................................................................ 91
Module 6. Unsolved problems .................................................................. 99
UNIT 1 ................................................................................................ 99
UNIT 2 .............................................................................................. 105
UNIT 3 .............................................................................................. 111

References ................................................................................................ 117

Appendix 1 ............................................................................................... 119

Appendix 2 ............................................................................................... 131

Appendix 3 ............................................................................................... 134

ВВедение

Основная цель пособия – совершенствование умений профессионально-ориентированного чтения и перевода современной научной 
литературы, а также развитие навыков устной и письменной речи на 
основе изученных текстов. Следует подчеркнуть, что конкретные задачи, решаемые при работе с пособием, определяются конечными целями 
обучения, предусматривающими свободное чтение литературы по специальности, умение вести беседу, дискуссию, выступать с сообщениями, 
докладами, презентациями и т. п.
Пособие состоит из шести модулей, каждый из которых посвящен 
определенной области математики. Тематика текстов включает сведения из истории математики, описание ее основных проблем, современную оценку развития данной области науки и занимательные факты из 
жизни ученых. При отборе текстов учитывалась как их познавательная 
ценность, так и их насыщенность лексико-грамматическими структурами.  Каждому тексту предшествует ряд упражнений разминочного 
характера, в которых студентам предлагается высказать свое мнение по 
ряду проблем, затрагиваемых в тексте – посредством этого достигается большая вовлеченность учащихся в процесс дальнейшей работы над 
текстом и основной лексической темой урока.
Включение в учебный материал текстов с занимательной информацией  и элементами математических игр способствует, по мнению автора, оживлению учебного процесса. 
Каждый модуль состоит из разделов, предусматривающих работу 
над закреплением грамматического материала, расширением потенциального словаря, развитием навыков чтения, говорения и письма.
В каждом модуле учебного пособия представлены упражнения, 
отличающиеся по своему содержанию, целевой направленности и форме выполнения.
Система речевых упражнений построена в соответствии с методикой проблемного обучения: проблемный вопрос, проблемное высказывание, дискуссия по проблеме.
Равномерное чередование различных видов упражнений и использование в них различных моделей помогает более эффективной работе студентов.

TO THE STUdENT

This book is intended for intermediate students of English.
It is designed to improve your professional English.
You will be given a chance to:
• master communicative competence;
• develop thoughts and ideas;
• activate personal opinion;
• stimulate your imagination;
• enrich your vocabulary;
• experience various ways of exploring a language and developing 
your skills: speaking, reading and writing;
• prepare for the examination.
To get the most out of this book, you have to think. Don’t be a passive 
learner. With your group-mates work out the solutions to different activities.
Help in understanding mathematical terms may be obtained from the 
mini-dictionary in Appendix.
The material is taken from the Internet, math textbooks, authentic 
sources – thus they are related to your own experience.
This book is designed so that it can be used sequentially from 
Module 1 to 6.
However, each Module stands on its own, therefore you can use it 
selectively.
Every Module starts with a list of objectives so you always know 
exactly what you are going to do.
Good luck and enjoy using this book!
Author

Module 1

MatheMatics and MatheMaticians

Learning objectives:
In this module you will:
• understand basic mathematical concepts, and acquire vocabulary 
connected with it
• develop the idea
• express agreement, disagreement
• do mental math tricks
• review sentence-structure
• write a composition
• check spelling, punctuation and grammar

Unit 1

Before you read

1. Discuss these questions with your partner.
1. How far do you agree that:
Mathematics is not:
• just doing things with numbers and letters and other symbols;
• just a collection of facts and rote recipes;
• just computational and arithmetic skills;
Mathematics is:
• a way of thinking;
• the language of science;
• a creative discipline;
• a source of pleasure and wonder;
• a means of problem solving.
2. What is mathematics?
3. Where does the word mathematics come from?
4. How many branches of mathematics do there exist nowadays?
5. What field of maths is the most interesting (important, essential, 
significant) to your mind?

Mathematics and mathematicians

Reading

2. Read the text.
The six sentences below have been removed. Decide where they 
should go.
A. It is believed that mathematics is the mother of modern science. 
B. The second reason of the importance of studying mathematics is its 
everyday use in real life by everyone.
C. Mathematics is important; all of it.
D. Finally, mathematics is the only mutual language used by all human 
beings regardless of their origin, gender, religion, or culture.
E. Mathematics is the mother science of the abstract world.
F. Another good example of the use of the importance of mathematics 
in daily life is managing how money grows and how to keep it from shrinking.
The Importance of Mathematics
Mathematics is the tool to 
keep balance in our life. 1) .......... 
Mathematics is the confusing course 
that causes my headaches. These 
are three different definitions of the 
word mathematics according to three 
different people. However mathematics 
is considered as the most important 
science, and its development affects 
the development of science in all of 
its kind medical, physics, biology, 
technology, and more. The importance 
of mathematics is being an essential, creative, and powerful discipline 
recognized globally.
First reason of studying mathematics is its importance for the 
development of modern science. 2) .......... The basics developed in 
mathematics such as equations, laws, algorithms, they are used implicitly 
in other sciences. For instance, the development of algorithms in 
mathematics will affect the future of computer science since ninety percent 
of the computer science theories and programming structures are based on 
abstract algorithms. Another example is related to the medical field where 
according to The Ourant Institute, New York University, “equations that 
describe cardiac mechanics including blood, muscle, and valve mechanics 
and electrophysiology are different, in both cases a realistic treatment 

Module 1

demands the use of methods that account for anisotropy, in homogeneity, 
and complex geometries” which are fields in abstract mathematics. 
Mathematics is the science that develops explicitly other kind of science 
to apply its capacity for speed and precision. 3) .......... Since the early 
ages the basic arithmetic operations have been used by human regarding 
his/her origin, culture, and language. These four operations construct the 
elementary parts of mathematics. Cooking, for instance; is a simple task 
done by anybody; however, the quality of cooking is based on the amount of 
ingredient used; people use mathematics to weigh the quantity used through 
adding and subtracting using balances and units like kilogram and liter. 
4) .......... The simple arithmetic operations are used for the calculation of 
the income from a savings account or the charges accumulated on a credit 
card; these operations could mean big payoffs over time. For thousands 
of years mathematics has been used daily if it is in commerce while 
trading or in kitchens while cooking. 5) .......... One plus one is still equal 
to two despite of what country is used in or what language is expressed 
with. Adding the cost of the shopping items is the same whether it is in 
dollars, euros, or dirham. Few are the people that can speak more than one 
tongue language; however, all of us possess the ability to be literate in 
the mutual language of math. The language of math is what connects the 
world because it is a tool using which we can express the mysteries of the 
universe, paranormal phenomenon, or the secret of curing extreme diseases. 
Mathematics connects people with other cultures in order to communicate 
and transfer the understanding of strange phenomena. Mathematics is more 
than just the science of numbers taught by teachers in schools to students. 
Mathematical theories are used everyday either by expert in applied science 
like physicians or by chefs in cheap restaurants. It needs to be amplified 
in education to provide students with skills required to achieve higher 
education, career aspirations, and reaching personal fulfillment. 6) ..........

(abridged from http://voices.yahoo.com/the-importance-mathematics-5224583.html)

3. Look through the text and find the word that means the same as.
1) common to two or more people;
2) quality of being of the same kind;
3) an ability to hold, contain, learn things/qualities/ideas etc.;
4) made or become greater in number or quantity;
5) made larger or fuller;
6) able to read and write; cultured.

Mathematics and mathematicians

4. Decide if the following statements are true or false, or there is no 
information in the text.
a) true 
b) false 
c) no information
1. Mathematics is a tool for describing the world.
2. Mathematics connects people with other cultures.
3. Mathematics is just the science of numbers.
4. Mathematicians do not deal with applications of mathematics.
5. Like all other sciences maths arose out of the needs of men.
6. Mathematical theories are used everyday.
7. Mathematics as a science is a collection of branches.
5. Divide the text into logical units. Suggest titles for each unit. Find 
the sentences expressing the main ideas of each logical unit in the text. 
Combine the topic sentences using the following connectives.
Because, in case of, besides, still, nevertheless, hence, accordingly, 
therefore, as well as, consequently, either …or.

Speaking

6. Agree or disagree with the following statements. Use the 
introductory phrases.
I quite agree to it. 
I don’t quite agree to it.
I think, it is right. 
On the contrary. Far from it.
I accept it fully. 
Not at all. Quite the reverse.
Exactly. Certainly. 
Just the other way round.
1. Maths is a game, a free creation of the mind divorced from practical 
problems.
2. Maths is a universal tool for describing the world around.
3. Maths is an activity which has as its goal the formulation and 
understanding of a complete model of the universe.
4. Scientists can use maths as a shorthand script to codify relationships.
5. Mental reasoning from obvious truths, i.e., axioms and postulates, 
constitutes applied science.
6. Maths is an inspiration to the artist as well as a tool to scientist.
7. The present role of maths is the same as in previous stages of its 
development.
8. Maths is the technique of discovering and expressing in the most 
economical possible way useful rules of reliable reasoning about calculation, 
shape and measurement.
9. Math language was not developed all of a sudden.

Module 1

10. A sharp dividing line between “pure” and “applied” maths can, in 
fact, be drawn.
7. Discussion
1. Which image of maths do you prefer?
• “Maths is general learnable knowledge” (The Pythagoreans).
• “Maths is great oaktree with deep roots and powerful trunk, and 
from the trunk’s top numerous branches had issued and subdivided into 
smaller branches” (H. Eves, historian of maths).
• “Maths is the whole universe”. (Experts of modern mathematical 
logic.)
2. Most mathematicians object to the separation of pure and applied 
aspects of maths. Why? Do pure and applied maths have common language, 
methods, applications?
3. The requirement of rigour in reasoning is proverbial in maths. Maths 
rigour – who needs it?
4. What is the role of a) experience, b) common sense, c) intuition, 
d) talent, e) genius, f) imagination, g) flashes of insight in maths?
5. What is meant by the phrase “mathematization of science”? What 
are its advantages/disadvantages and implications?
6. It is convenient to keep the old classification of maths as one of the 
sciences, but it is more just to call it an art. If maths is an art with cultural 
bearings it must be a part of the liberal education of a doctor, lawyer or 
average educated person. Agree or disagree.
8. Your friend can’t decide if he should study mathematics or not. 
Work out arguments in favour of studying mathematics. Try to sound 
convincingly.
9. Fill in the gaps with the derivative.
It is said that Mathematics is the gate and key of the Science. According 
to the famous Philosopher Kant, “A Science is exact only in so far as it (1) 
… Mathematics”. 
So, all (2) … education which does not commence with Mathematics 
is said to be defective at its foundation. Neglect of mathematics works injury 
to all knowledge.
One who is (3) … of mathematics cannot know other things of the 
World. Again, what is worse, who are thus ignorant are unable to perceive 
their own ignorance and do not seek any remedy. 
So Kant says, “A natural Science is a Science in so far as it is 
mathematical”. And Mathematics (4) ... a very important role in building up 
modern Civilization by perfecting all Science.