- •Contents
- •Передмова
- •We are students at donetsk national university
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •Student Dima Loboda
- •Student Dasha Klimova
- •Student Nastya Savchuk
- •Student profile
- •L earn mathematics in English Cardinal and ordinal numbers
- •1. Read the text about two arithmetical operations and do the exercises that follow it Basic arithmetical operations. (Addition & subtraction)
- •What’s your best friend like?
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •Who’s their ideal partner?
- •L earn mathematics in English
- •1. Read the text and do the exercises below it Basic arithmetical operations (Multiplication & division)
- •A day in the life of a student
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •I. Look through the text and do the tasks
- •Learn mathematics in English
- •I. Read the text and do the exercises below it. Advanced arithmetical operations
- •What’s your university like?
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Donetsk national university
- •The University of Sheffield
- •1. Find a partner from the other group. Tell each other the information you read about one of the universities
- •Fractions
- •The city I live and study in
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Learn mathematics in English
- •Mixed numbers
- •Mathematics is the queen of scienses
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words:
- •“`A mathematician is a machine for converting coffee into theorems”. /Paul Erdos/
- •L earn mathematics in English
- •Equivalent fractions
- •Reciprocals and the "invisible denominator"
- •The language of mathematics
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words
- •L earn mathematics in English
- •Statistics is very serious!
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •Key words:
- •Statistics is very serious!
- •Get to know a typical computer
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words:
- •Get to know a typical computer
- •Computer without a program is just a heap of metal!
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary.
- •2. Key words
- •We can’t imagine modern computing without them
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary
- •2. Key words
- •I. Read the following texts and do the tasks Alan Turing
- •Tim Berners-Lee
- •He has left mathematicians enough to keep them busy for five hundred years
- •Vocabulary
- •1. Guess the meaning of these international words. Check with your teacher or a dictionary.
- •2. Key words
- •I. Read the text and do the tasks niels henric abel
- •Getting to know each other better
- •II. Swap charts with b. Ask a to explain the information in his/her chart. Ask for more information
- •III. Explain your answers to b
- •Mood graph
- •A time for everything
- •Expert opinion
- •Vocabulary
- •Vocabulary
- •What’s your body age?
- •I. Read the questionnaire and answer the questions below, adding or subtracting the numbers after your answer from your actual age
- •How many friends can you share problems with?
- •15. Have you taken antibiotics in the past five years?
- •II. Check your score
- •If you're younger than your years
- •I. Look at your partner’s answers. Ask for more information, for example: What is your worst diet habit? How much time do you have for yourself?
- •II. Some ways to lower our body age are given below. Read it and give your partner some good advice starting with the following words: I think you should…
- •Donetsk national university
- •Inspires students’ enthusiasm for learning
- •An ideal teacher
- •Is a well-educated person has a good sense of humor is a polite and a punctual person delivers interesting lectures
- •Numbers
- •I. Mind–map’ numbers’. When you read this ‘mind-map’, you’ll meet words that are new to you. First try to guess their meaning and then look them up in a dictionary.
- •II. Answering and explaining
- •III. Playing a trick with numbers
- •IV. The ‘Terribly Stressed‘ game
- •I. Use this mind-map ‘Four basic operations in Mathematics’ as a topic activator to speak about the basic operations in Arithmetic
- •III. Reading, writing and saying numerical expressions
- •3. Look at each numerical expression written in symbols and signs. Then say it in words. Your partner will listen to see if you repeat correctly and correct your incorrect answers
- •I. Use this mind-map ‘Algebra’ as a topic activator to speak about Algebra (its origin and some facts from its history)
- •II. Match each numerical expression in the left column with the equivalent expression in the right column
- •Look at the expressions written in words and write them in mathematical notation (in symbols)
- •III. Read the following inequalities aloud. Your partner will check your answers
- •I. Mind-map ‘Geometry’. Use this map to speak about geometry (its meaning, the history of its development, its application). Add more information you know
- •II. Working with geometric terms. Demonstrate your knowledge of geometric terms. Work in pairs (a/b)
- •The language of mathematics
- •Practice set 12
- •III. Draw your mood graph or graph with your marks showing changes during the week or a month (semester). Explain it to your partner
- •Some facts from the history of mathematics education
- •I. Read the article and mark the sentences t (true), f (false) or ng (not given)
- •Do you know that…
- •II. Search for some information about one of these mathematics teachers and share it with other students. Make a table of the most important facts of his/her biography
- •Ancient sources of information
- •I. Choose from (a-j) the one which best fits each of (1-7). There are two choices you do not need to use.
- •II. Tell your partner about these famous papyri
- •III. Find some information about Mathematics of ancient civilizations and share it with other students (e.G. The Maya calendar, the ancient numeration systems)
- •The history of the symbols for plus and minus
- •I. Read the article. Guess the meaning of the highlighted words. Check with the teacher or your dictionary
- •II. Read the article again. Say what events the following years refer to:
- •III. Tick (√) the things the article says
- •IV. Read the facts listed below. In pairs, discuss which one is the most surprising do you know that...
- •V. Find some information on the history of the mathematical symbols. Give a presentation to the students of your group
- •Statistics
- •I. Match the words with their definitions:
- •II. Decide if the given statements are true (t) or false (f) according to the text
- •III. Search for information about one of the scientists listed below and then give a presentation
- •Important contributors to statistics
- •Degrees and diplomas in statistics
- •III. Do you know anything about awards in Statistics in your country or abroad?
- •Why is there no nobel prize in mathematics?
- •I. Read the text. Seven sentences have been removed from it. Choose from the choices (a- I) the one which fits each gap (1-7). There are two choices you do not need to use
- •III. Work in pairs. Tell your partner why Nobel decided against a Nobel Prize in mathematics
- •Major awards in mathematics
- •The obverse of the Fields Medal
- •The reverse of the Fields Medal
- •A. Fields medal
- •III. Look at these words. Why are they important in this text?
- •B. Abel prize
- •IV. Focus on these words. Why are they important in the text?
- •VI. Compare the major awards in Mathematics with the Nobel Prize by using like (similar to) or unlike (different from) in the sentences
- •V. Search for more information on the following topics on the Internet and share it with other students
- •Abel Prize Laureates
- •Fields medalist
- •I. Decide if the given statement is true (t) according to the text, if it is false (f) or if the information is not given (ng) in the text (Work in pairs)
- •II. Number these events in the order they happened. Look at the Reading
- •III. Interview your partner about this great mathematician (Work in pairs)
- •IV. Ask and answer the following questions in pairs
- •II. Match the number with its symbolic meaning:
- •III. Answer the questions below and then ask for more information (Work in pairs)
- •Do you know that…
- •IV. Find information on the Internet and give a presentation of the number you are interested in (brings you good or bad luck)
- •Text 10
- •Reading and Speaking
- •Number and reality
- •I. Match the word with its meaning:
- •II. Work in pairs. Decide if the sentences 1- 7 are t (true) or f (false)
- •A strong mathematical component
- •I. Choose from (a-j) the one which best fits each of (1-6). There is one choice you do not need to use
- •II. Match choices (a-d) to (1-4)
- •III. In pairs, find and then say what events the following years refer to:
- •IV. Do you know an artist (a writer) having a strong mathematical component in his/her creative work? Search for information on the Internet and give a presentation on the subject
- •Reading and Speaking fractal
- •I. Match the words with their meanings:
- •II. Choose from (a-f) the one which best fits each of (1-5). There is one choice you do not need to use
- •III. Work in pairs. Tell your partner about fractal
- •IV. On the Internet search for information about applications of fractals and then share your information with other students
- •Healthy computer work
- •Match the words with their meanings:
- •I I. Read the article once and then decide if the following guidelines are true, false or are not mentioned in the text above
- •III. Team work. Work out the main rules for operating the computer. The winner is to give clear recommendations for young people working on the computer. The first one is given for you
- •IV. Ask and answer the questions (Work in pairs)
- •Computers can do wonders
- •I. Match the words with their meanings
- •II. Decide if the following statements are true or false (t/f) by referring to the information in the text
- •III. Work in pairs. Tell your partner about the most surprising facts from the article
- •IV. Search for information about ‘computer wonders’ on the Internet and give a presentation about new computer developments (e.G. Robots)
- •Watching ‘how did mathematics begin? (a cartoon)
- •I. Answer the following questions:
- •II. Tell the class about the most interesting facts you have learned from the cartoon. Do you agree with the information mentioned in the cartoon? Add more information about the development of numbers
- •Recommendations and some useful phrases for giving presentations
- •Introduction
- •Introducing your subject
- •If you make a mistake, start your sentence again.
- •If you can’t remember a word, use another one.
- •Conclusion
- •Inviting questions
- •Questions
- •Wording mathematical signs, symbols and formulae
- •Answer keys
- •References
Statistics is very serious!
Vocabulary
1. Guess the meaning of these international words. Check with your teacher or a dictionary
Statistics – statistician, organize, summarize, analyze – analysis, official, policies, diagnosis, patient, agriculture, geology, resource, experiment, actuarial, premium, optimize – optimization, produce – production, procedure, basis, phenomenon – phenomena, specialized – specialization, phase.
Key words:
To make up one’s mind |
Вирішувати |
To support |
Підтримувати, підпирати |
Valid |
Вагомий, обґрунтований, правильний |
Reasonable |
Розумний, обґрунтований, раціональний |
Census |
Перепис населення |
Survey |
Опитування, анкетування, дослідження, огляд |
Current |
Поточний, діючий, нинішній |
To evaluate = to assess |
Оцінювати, давати оцінку |
Treatment |
Лікування |
Fertilizer |
Добриво |
Suitable premium |
Прийнятний страховий внесок (премія) |
Advertising |
Реклама |
Inevitable |
Неминучий, постійний |
To set up a model |
Створювати модель |
Random |
Випадковий |
Misconception |
Помилкове уявлення |
To churn out |
Виробляти велику кількість, випускати потоком |
To attempt |
Намагатися, прагнути |
Reading
Task 1. Work in pairs. Make a list of areas where statistics is used today.
Task 2. Read the text and compare your list with statistics applications mentioned in the text
Statistics is very serious!
I am a first-year student at the University of Donetsk. I study at the Faculty of Mathematics and take a course in statistics.
When I made up my mind to be a statistician my friends laughed at me. Some of them quoted Mark Twain: ‘There are three kinds of lies: lies, damn lies and statistics’. Others quoted Andrew Lang, ‘He uses statistics as a drunken man uses lamp-posts - for support rather than illumination’. I’ll try to prove that statistics is used for illumination rather than support.
A lot has changed since the times of Mark Twain. Today statistics is a science, a branch of applied mathematics. It is concerned with scientific methods for collecting, organizing, summarizing, presenting and analyzing data, as well as drawing valid conclusions and making reasonable decisions on the basis of that analysis.
It’s being used more and more in various applications. In government many people are involved in collecting data from censuses and surveys. Such data are often referred to as ‘official statistics’. They are used to evaluate and improve current policies. On a smaller scale, statistics is used in medicine, for example, to assess which of two treatments is better or to aid in the diagnosis of a patient. Statisticians are involved in agriculture, with the comparison of different fertilizers; in geology, with the estimation of oil resources; in the analysis of psychological experiments; in the actuarial profession, with the establishment of suitable premiums; in market research, to discover and interpret trends and frequencies; and in industry, in optimization of production and formation of advertising policies.
Statistical procedure can vary from the drawing and assessment of a few simple graphs to carrying out very complex mathematical analysis. There is clearly an inevitable link between statistics and probability, which provides the mathematical basis for setting up models to describe random phenomena.”
As you see my profession requires profound knowledge of the theory of probability and calculus, and we study those subjects in our first and second year. In our third year specialization begins. We are given specialized courses in sampling theory, statistical estimation theory, statistical decision theory, correlation theory. Some students begin doing their own research under the supervision of their scientific advisers. So, at the end of our study at the university we are prepared to apply our knowledge to practice.
You may ask me what a statistician actually does. The typical view is that you get data and hand it to a statistician. But this is a misconception. A good statistician will be integrated with projects right from the start, not sitting in a back room churning out numbers. Databases and special programming packages are the tools of the trade, but the main part of the job is the modeling phase where you build a model which attempts to describe the process which produces the data. With a model, you can answer questions such as whether a particular cancer treatment works.
I seem to have proved that statistics is very serious. Nevertheless, in conclusion I’d like to offer another joke. Have you heard this definition of a statistician? It’s someone who has his bottom in the oven and his head in the freezer and who says that his body temperature is average.
Task 3. Answer the questions on the text
What does statistics deal with?
What is official statistics?
How is statistics used in medicine?
How does statistical procedure vary?
How is statistics connected to probability?
What is the stereotype about the job of a statistician?
What is the main task of a statistician today?
Task 4. Find equivalents of these words or expressions in the text
a. To decide.
b. To repeat exactly what someone else has said or written.
c. An official process of counting a country’s population and finding out about the people.
d. To judge how good, useful, or successful something is.
e. Happening or existing now.
f. To differ.
g. An idea that is wrong or untrue, but which people believe because they do not understand the subject properly.
h. To produce large quantities of something, especially without caring about quality.
i. Something that is done to cure someone who is ill.
Speaking
Give the reasons behind your decision to take a course in statistics.
Unit 9