Если у вас возникли сложности с курсовой, контрольной, дипломной, рефератом, отчетом по практике, научно-исследовательской и любой другой работой - мы готовы помочь.
Предоплата всего
Подписываем
|
category – вид, категорія |
boundary – межа |
|
source – джерело |
(sub)division – (під)розділ |
|
theoretical (pure) math – теоретична математика |
applied math – прикладна математика |
Modern mathematics is a vast field of knowledge with many divisions and subdivisions.
Math is divided into two categories – pure and applied. Pure, or theoretical, math is concerned with problems and questions within the world of math itself. The four main branches of pure math are arithmetic, algebra, geometry, and calculus. The main arithmetical operations are addition, subtraction, multiplication, and division.
Applied math is concerned with the practical uses of math in the world around us. It uses the principles of theoretical math to solve problems in such areas as astronomy, business, computer science, economics, navigation, and physics. It is also important in statistics, the science of collecting, organizing, displaying, and analyzing information.
The boundary between pure and applied mathematics is not always clear. Ideas developed in pure mathematics often have practical applications, and work in applied mathematics frequently leads to research in pure mathematics.
Nearly every part of our lives involves mathematics. It has played an essential role in the development of modern technology – the tools, materials, and sources of power that make our lives and work easier.
VOCABULARY
mathematics /‚mæθ(ə)'mætɪks/ the science of numbers and of shapes, including arithmetic, algebra and geometry (математика):
Mathematics is one of the most fascinating divisions of human knowledge.
Математика – це один із самих захоплюючих розділів людського знання.
Her major is mathematics.
Її спеціалізація – математика.
math(s) /mæθ(s) / informal mathematics:
math lessons – уроки математики
a math test – тест з математики
math problems – задачі з математики
Denis is good at math and science.
Денис гарно встигає з математики й природознавста.
mathematical /‚mæθ(ə)'mætɪk(ə)l/ 1) relating to or using mathematics (математичний):
mathematical signs – математичні знаки
mathematical skills – математисні навички
mathematical formula – математична формула
Mathematical operations are (those of) addition, subtraction, multiplication, and division.
Математичні дії – додавання, віднімання, множення і ділення.
2) calculating things in a careful, exact way (математичний, точний):
The whole trip was planned with mathematical precision.
Уся подорож була спланована з математичною точністю.
add / / if you add numbers or amounts together, you calculate their total (додати):
Add 10 and 5 to make 15.
Додайте 10 і 5, щоб отримати 15.
subtract / / to take a number or an amount from a larger number or amount (відняти):
If you subtract 20 from 45, you get 25.
Якщо ви віднімаєте 20 від 45, то отримуєте 25.
multiply / / to do a calculation in which you add a number to itself a particular number of times (помножити):
Multiply the total by 12.
Помножте результат на 12.
divide / / 1) to calculate how many times one number contains a smaller number (поділити):
divide smth by smth – ділити що- небудь на що-небудь
If you divide 6 by 3, you get 2.
Якщо ви ділите 6 на 3, то отримуєте 2.
2) if something divides, it separates into two or more parts (розподілити):
The book is divided into six sections.
Книга поділена на шість розділів.
mathematician /‚mæθ(ə)mə'tɪ∫(ə)n/ someone who studies or teaches mathematics, or is a specialist in mathematics (математик):
In 1614, John Napier, a Scottish mathematician, discovered logarithms.
У 1614 році Джон Непер, шотландський математик, відкрив логарифми.
Computers enable mathematicians to do complicated calculations quickly.
Комп’ютери дають змогу математикам швидко здійснювати складні обчислення.
knowledge /'nɒlɪdʒ/ the information, skills, and understanding that you have gained through learning or experience (знання):
have knowledge – мати знання
acquire/gain knowledge – отримати/здобути знання
scientific knowledge – наукові знання
science /'saɪəns/ knowledge about the world, especially based on examining, testing, and proving facts (наука):
Isaac Newton is the founder of modern science.
Ісаак Ньютон – засновник сучасної науки.
application/ / practical purpose for which a machine, idea can be used, or situation when this is used (застосування):
The research has many practical applications.
Дослідження має багато практичних застосувань.
apply / / to use something as a method, idea, or law in a particular situation, activity, or process (застосовувати, використовувати ):
These ideas are difficult to apply in practice.
Ці ідеї складно застосувати на практиці.
branch/ /one part of a large subject of study or knowledge; field (галузь):
a branch of mathematics (physics, biology) – галузь математики (фізики, біології
Geometry is a branch of mathematics.
Геометрія – це галузь математики.
EXERCISES
Exercise 1. Listen to the text and repeat each sentence after the speaker.
Exercise 2. Read the words paying attention to their pronunciation.
Mathematics, math(s), science, category, concern, algebra, geometry, calculus, branch, applied math, theoretical math, research, boundary, essential, area, frequently, source.
Exercise 3. Find in the text the English equivalents of the following words and word combinations.
a) поділити на дві категорії; b) у світі математики; c) чотири основні галузі; d) практичне застосування; e) принципи теоретичної математики; f) наука про збір, впорядкування, представлення й аналіз інформації; g) головна роль; h) розвиток сучасної технології; i) джерела енергії
Exercise 4. Find international words in the text and give their Ukrainian equivalents.
Mathematics – математика, ... .
Exercise 5. Translate into Ukrainian.
To solve problems, area, questions, main, important, always, develop, development, tools, research, nearly.
Exercise 6. Find in the text the English equivalents of the following sentences.
a) Математика поділяється на два види (розділи) – теоретичну й прикладну. b) Теоретична математика має справу з теоретичними задачами. c) Прикладна математика торкається практичного застосування математики в оточуючому нас світі. d) Межа між теоретичною і прикладною математикою не завжди чітка. e) Майже кожна галузь нашого життя пов’язана з математикою.
Exercise 7. Derive nouns from the verbs given below. Use the productive suffixes – -tion, -sion. Translate the nouns into Ukrainian.
Divide, apply, educate, relate, discuss, add, multiply, subtract, direct, create, calculate, invent, express, decide, explain, present, operate, collect, describe, connect, prepare, construct, conclude, inform, combine, rotate, include, modify, form, introduce.
Exercise 8. Translate into Ukrainian the following words with the non-productive suffix -ment.
Development, government, measurement, requirement, (un)employment, astonishment, statement, entertainment.
Exercise 9. Translate the nouns into English using the productive suffix -er/or.
a) -er:
teach, lecture, interpret, read, lead, manufacture, astronomy, listen, research, win, begin, condense;
b) -or:
educate, protect, direct, translate, accumulate, separate, regulate, accelerate, invent, communicate, act.
Exercise 10. Match the terms with their definitions.
|
Mathematics |
a type pf mathematics that uses letters and other signs to represent numbers and other values______________________ |
|
Subtraction |
the science of numbers and of shapes, including algebra, geometry, and arithmetic____________________ |
|
Algebra |
to take a number or an amount from a larger number or amount ________________ |
|
Addition |
the study in mathematics of the angles and shapes formed by the relationships of lines, surfaces, and solid objects in space ___________________ |
|
Geometry |
the process of adding numbers or amounts to make a total __________________ |
Exercise11. Complete the sentences with words from the box.
Multiply symbols add Algebra subtract numbers formulas Arithmetic divide science
a) ____________________ is calculation with numbers using fundamental operations such as addition, subtraction, multiplication, and division.
b) _________________uses letters to represent some of the numbers.
c) If you __________________ 6 from 9", you get 3.
d) The numbers 1,2,3,4,5,6,7,8,9,10,11,12, and so on are called the natural __________________.
e) If you _______________ 30 by 6, the answer is 5.
f) __________________ 3 by 5, to make 15.
g) Mathematics is the ________________ of size and numbers.
h) If you ____________ 5 to 5, you get 10.
i) What algebraic __________________ do you know?
j) Mathematical ________________ are + , – , ÷ , × etc.
Exercise 12. Make up sentences from the table.
|
Mathematics |
is based on/upon |
the study of functions. |
|
Arithmetic |
logic. |
|
|
Calculus |
relies on/upon |
probability. |
|
Statistics |
four basic operations – addition, subtraction, multiplication, and division. |
Exercise13. Put the words in each sentence in the correct order.
a) Mathematics, logic, based, is, upon. b) major, I, mathematics, in. c) science, Mathematics, is, the, and, shapes, of, numbers. d) studies, at, faculty, the , Physics and Mathematics, He, of. e) in, am, first, my, I, year. f) in, are, We, same, the, for, mathematics, class.
Exercise 14. Answer the following questions.
a) Where do you study? b) What are you majoring in? c) What are the main two categories of the science of mathematics? d) What are the four branches of pure math? e) What arithmetic operations do we use in our daily living? f) What does applied math deal with? g) Is mathematics concerned with the development of modern technology?
Exercise15. Say in English.
a) Математика – це точна наука. b) Математика завжди була моїм улюбленим предметом. c) Ми – студенти першого курсу. d) Я отримувала високі оцінки з математики в школі. e) Я люблю розв’язувати математичні задачі. f) Наші уроки математики дуже цікаві. g) Тест з математики був не складний. h) Ми навчаємося, аби бути хорошими вчителями математики. i) Ми відвідуємо лекції з математичного аналізу й фізики. j) Я хочу отримати хорошу вищу освіту.
Exercise 16. Speak about your studies at the university.
Exercise 17. Translate the text "The science of mathematics" into Ukrainian.
Exercise 18. Read the text for supplementary reading "Kovalevska". Answer the questions. Retell the text in English. While retelling use the following word combinations: "Let me tell you about …"; "It is a well-known fact that …"; "Also, I want to say that …"; "To/in my mind …"; "Of course …"; "For example/For instance …".
Exercise 19. Write a paragraph (5 – 7 sentences) about mathematics as one of your favourite subjects.
TEST YOUR PROGRESS
Read the text.
The importance of mathematics
Mathematics is one of the most useful and interesting divisions of human knowledge. It includes many topics of study. For this reason, the term mathematics is difficult to define. It comes from a Greek word meaning "inclined to learn".
Mathematics is the science of numbers and of shapes, including algebra, geometry, and arithmetic. Most of the basic mathematics taught in school involves the study of number, quantity, form, and relations. Arithmetic, for example, concerns problems with numbers. Algebra involves solving equations in which letters represent unknown quantities. Geometry concerns the properties and relationships of figures in space.
The most important skills in mathematics are careful analysis and clear reasoning. These skills can help us solve some of the deepest puzzles we must face.
Mathematics is based upon logic. Mathematicians use logic to draw conclusions and develop mathematical systems. One of the main aims of math is to solve a problem in a systematic way so that similar problems can be solved more easily in the same way.
Task 1. Match the following terms with their definitions.
|
Mathematician |
an educational institution at the highest level, where you study for a degree ________________ |
|
University |
the process of teaching and learning, usually at school or university ________________ |
|
Education |
someone who is studying at a university, school __________________ |
|
Equation |
a type of mathematics that uses letters and other signs to represent numbers and other values _________________ |
|
Student |
a statement in mathematics that shows that two amounts or totals are equal ________________ |
|
Algebra |
a sign showing that one number is multiplied by another _____________ |
|
Geometry |
the study of the angles and shapes formed by the relationships of lines, surfaces, and solid objects _________________ |
|
Multiplication sign |
someone who studies or teaches mathematics, or is a specialist in mathematics ___________________ |
Task 2. Make complete sentences by filling the gaps with words from the box.
Pedagogical equals teacher numbers minus problems Division equation plus mathematical
a) Math is the language of _______________.
b) Seventeen ____________ five is twelve.
c) Three plus six ___________ nine.
d) _____________ in algebra is opposite of multiplication.
e) He was educated at Kirovograd State ________________ University.
f) In the _____________ 2x+1=7, what is x?
g) The ________ sign is used to show that one number is added to another.
h) The new math _____________ entered the classroom.
i) The development of _____________________ skills is very important at an early age.
j) She gave us twenty mathematical _________________ to solve.
Task 3. Answer the following questions.
a) What is modern mathematics? b) What are the main subdivisions of pure math? c) What does arithmetic deal with? d) What is algebra concerned with? e) What are the most important mathematical skills? f) What is math based on? g) Why do we learn math?
Task 4. Insert articles and the verb "to be" where necessary.
I ______ ________ student.
We ______ first-year students.
I like to relax and watch _____ television.
I study at ____ Volodymyr Vynnychenko University in Kirovograd.
We _____ from ______ Ukraine.
______ Math is one of my favourite subjects at University.
______ children like solving mathematical problems.
I want to ______ _______ good math teacher.
_____ education ______ more important today than ever before.
I’m sure he has _____ university education.
Task 5. Translate into English.
a) Математика має багато галузей. b) Математичні навички допомагають нам розв’язувати багато задач. c) Контрольна робота з математики була дійсно легкою. d) Вона завжди отримує гарні оцінки. e) Ти склав іспит?
Task 6. Translate the text into Ukrainian.
Math in our lives
In everyday life, we use mathematics for such simple tasks as telling time from a clock or counting our change after making a purchase. Cooking, driving, gardening, sewing, and many other common activities involve mathematical calculations. Mathematics is also part of many games, hobbies, and sports.
Mathematics is an essential part of nearly all scientific study. It helps scientists design experiments and analyze data. The physical sciences, such as astronomy, chemistry, and physics, rely heavily on mathematics. Such social sciences as economics, psychology, and sociology also depend greatly on statistics and other kinds of mathematics.
The science of mathematics helps industries design, develop, and test products and manufacturing processes. Mathematics is necessary in designing bridges, buildings, dams, highways, tunnels, and other architectural and engineering projects.
In business, mathematics is used in transactions that involve buying and selling. Bankers use mathematics to handle and invest funds. Mathematicians help insurance companies calculate risks.