Свиридова Т. Н. Mathematics through English

139 Pages·01.947 MB·Russian

by  Коллектив авторов

Министерство образования и науки Российской Федерации
Сибирский федеральный университет
Т. Н. Свиридова
MATHEMATICS THROUGH ENGLISH
Рекомендовано федеральным государственным бюджетным об-
разовательным учреждением высшего профессионального образования
«Санкт-Петербургский государственный университет» в качестве учеб-
ного 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. Свиридо-
ва. – Красноярск : Сиб. федер. ун-т, 2016. – 138 с.
ISBN 978-5-7638-3415-4
Представлены материалы для совершенствования умений профессиональ-
но ориентированного чтения и навыков устной и письменной речи. Приведены
тексты аутентичного характера. Предложена серия упражнений, способствую-
щих 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
3
ВВедение
Основная цель пособия – совершенствование умений професси-
онально-ориентированного чтения и перевода современной научной
литературы, а также развитие навыков устной и письменной речи на
основе изученных текстов. Следует подчеркнуть, что конкретные зада-
чи, решаемые при работе с пособием, определяются конечными целями
обучения, предусматривающими свободное чтение литературы по специ-
альности, 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 сведе-
ния из истории математики, описание ее основных проблем, современ-
ную 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 структу-
рами. Каждому тексту предшествует ряд упражнений разминочного
характера, в которых студентам предлагается высказать свое мнение по
ряду проблем, затрагиваемых в тексте – посредством этого достигает-
ся большая вовлеченность учащихся в процесс дальнейшей работы над
текстом и основной лексической темой урока.
Включение в учебный материал текстов с занимательной инфор-
мацией и элементами математических игр способствует, по мнению ав-
тора, оживлению учебного процесса.
Каждый модуль состоит из разделов, предусматривающих работу
над закреплением грамматического материала, расширением потенци-
ального словаря, развитием навыков чтения, говорения и письма.
В каждом модуле учебного пособия представлены упражнения,
отличающиеся по своему содержанию, целевой направленности и фор-
ме выполнения.
Система речевых упражнений построена в соответствии с мето-
дикой проблемного обучения: проблемный вопрос, проблемное выска-
зывание, дискуссия по проблеме.
Равномерное чередование различных видов упражнений и ис-
пользование в них различных моделей помогает более эффективной ра-
боте студентов.
4
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
5
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?
6
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
7
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.
8
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.
9