- •Zahola n., Mynda o., Spenik Sz. English for Mathematicians
- •Isbn isbn 978-966-2095-20-3 © Загола н.В.
- •Contents
- •Vocabulary Notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Read the following numbers:
- •III. Make up a dialogue on the text. Lesson 2 addition
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Give the Hungarian equivalent for the following words and word combinations. Use them in sentences of your own:
- •Vocabulary Notes
- •Exercises
- •II. Give the Ukrainian for the following words and word combinations. Use them in sentences or questions of your own:
- •Lesson 4 multiplication
- •Vocabulary Notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Give the Hungarian equivalents for the following words and word combinations. Use them in sentences of your own:
- •III. Multiply the following numbers orally:
- •Lesson 5 division
- •Vocabulary Notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Give the Ukrainian words for the words and word combinations. Use them in the sentences of your own:
- •III. Divide the following numbers orally:
- •Lesson 6 algebraic expression
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Give the Hungarian for the following words and word combinations. Use them in sentences of your own:
- •Lesson 7 equations and proportions
- •Vocabulary Notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Give Hungarian translation for the following words and word combinations. Use them in the sentences of your own:
- •Lesson 8 decimal numerals
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text.
- •II. Are the following statements true or false according to the text?
- •III. Say the following in English.
- •IV. Form derivatives from the following words and translate them into Hungarian:
- •V. Find the following words and word combinations in the text. Guess their meanings. Make up your own sentences with them.
- •VI. Ask questions to which the following sentences could be answers.
- •Lesson 9 decimal and common fractions
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text:
- •III. Write your own examples of different types of fractions and read them in English. Lesson 10 mathematical sentences
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Read the following mathematical sentences and decide whether they are open or closed, true or false.
- •IV. Say the following in English.
- •V. Translate the following sentences into Hungarian paying attention to the words in bold type.
- •VI. Make up 5 open and 5 closed true/false sentences.
- •VII. Find the odd word out:
- •Lesson 11 rational numbers
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text.
- •II. Find the following words and word combinations in the text. Guess their meanings. Make up your own sentences with them.
- •III. According to the text the following statements are either true or false. If you think they are false, say why. Begin your statements with:
- •IV. Say the following in English.
- •VI. Ask questions to which the following sentences could be answers.
- •Lesson 12
- •Irrational numbers
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text.
- •II. Change the sentences to negative and to question form.
- •III. Form derivatives from the following words and translate them:
- •IV. Find in the text the following words and word combinations. Guess their meanings. Make up your own sentences with them.
- •Part II Lesson 1 geometry
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text.
- •II. According to the text are the following statements true or false? If you think they are false, say why. Begin your statements with:
- •III. Find the following words and word combinations in the text. Guess their meanings. Make up your own sentences with them.
- •IV. Write questions to which the words in bold type in the following sentences are the answers:
- •V. Find synonyms to the following words in the text, translate them into Hungarian:
- •VI. Give English equivalents to the Hungarian nouns in the left column using English verbs in the right column.
- •VII. Translate the dialogue into English and reproduce it in pairs:
- •Vocabulary Notes
- •Lesson 2 from the history of geometry
- •Vocabulary Notes
- •Exercises
- •I. According to the text, are the following statements true or false?
- •V. Find English equivalents to the given sentences in the text.
- •VI. Translate the following sentences into Hungarian, paying attention to the words in bold type. Make your own sentences with them.
- •VII. Match each word on the left with its translation on the right.
- •Lesson 3 the meaning of geometry
- •Vocabulary notes Babylonia – Babilónia
- •Exercises
- •II. According to the text are the following statements true or false? If you think they are false, say why. Begin your statements with:
- •III. Ask questions using the question words in brackets. Translate the given sentences.
- •IV. Find in the text the following words and word combinations. Guess their meanings. Make up your own sentences with them.
- •V. Form derivatives from the following words and translate them into Hungarian:
- •VI. Find in the text antonyms to the following words. Translate them into Hungarian:
- •Lesson 4 rays, angles, simple closed figures
- •Simple Closed Figures
- •Vocabulary Notes
- •Exercises
- •I. Answer the following questions on the text:
- •II. Choose the right name for the following figures. There is one extra name.
- •III. Translate into Hungarian the following geometrical definitions. Learn them by heart.
- •IV. Read the following text, say into how many logical parts it could be divided and render it either in English or Hungarian. Something about Euclidean and Non-Euclidean Geometries
- •Lesson 5 c ircles
- •Vocabulary Notes
- •Exercises
- •I. Answer the questions on the text:
- •II. Write a plan of the text “Circles”.
- •III. Translate the following sentences into Hungarian paying attention to the words in bold type.
- •IV. Say the following in English:
- •Lesson 6 the pythagorean property
- •Proof of the Pythagorean Theorem
- •Vocabulary notes
- •Exercises
- •I. Answer the questions on the text:
- •II. Ask questions using the question-words in brackets:
- •III. A) Speak on the Pythagorean Property. Draw a picture to help you while speaking.
- •IV. Read the text below and render it either in English or in Hungarian. Square Root
- •V. Translate the following into English:
- •VI. Submit your theorem in English according to the pattern.
- •Vocabulary notes
- •Exercises
- •I. Agree or disagree with the following:
- •II. Find out in the text the following word-combinations. Use them in sentences of your own:
- •III. Match each word on the left with its translation on the right.
- •IV. Read the text. Fill in the chart given below about a desktop personal computer Fantasy x22.
- •VI. Translate into Hungarian paying attention to the words in bold type.
- •VII. Try to remember.
- •VIII. Discussion.
- •IX. Choose the proper name to each part of the computer.
- •Lesson 2 from the history of computers
- •Vocabulary notes
- •Exercises
- •I. Read the text. Write the key questions about it to ask your fellow-students.
- •II. In the sentences below some statements are true and some are false. Copy out the true statements.
- •III. Check if you know the meaning of the following words. Translate them into Hungarian:
- •IV. Pay attention to the following words. Try to remember them.
- •V. Translate the following sentences into Hungarian paying attention to the words in bold type.
- •VI. Translate into English.
- •VII. Read the information about masters of invention. Be ready to speak about Charles Babbage and Howard Aiken. Charles Babbage (1792-1871).
- •Charles Babbage, Master Inventor
- •Howard Aiken (1900-1973).
- •Howard Aiken, a Step Toward Today
- •Lesson 3 what is a computer?
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions.
- •II. What is the Hungarian for:
- •IV. Match the word on the left with its translation on the right.
- •V. Pay attention to the following words. Try to remember them.
- •VI. Translate the following sentences into Hungarian.
- •VII. A) Read the text. Computers
- •Lesson 4 computers: the software and the hardware
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions.
- •III. Pay attention to the following terms. Try to remember them.
- •IV. Translate the following sentences into English.
- •V. Translate the following sentences into Hungarian paying attention to the words in bold type.
- •VI. Read the text and put key questions.
- •Lesson 5 windows
- •Vocabulary notes
- •Exercises
- •I. Read the text to find answers to the following questions.
- •II. Find in the text definitions of the terms you find to be the most important to you.
- •III. According to the text agree or disagree with the following.
- •V. Translate into English.
- •VI. Pay attention to the following terms. Try to remember them.
- •VII. Translate into Hungarian.
- •VIII. Topic “The computer we use at the university”.
- •Lesson 6 communication with computer
- •Vocabulary notes
- •Exercises
- •I. Read the text. Write the key questions about it to ask your fellow students.
- •II. In the sentences below some statements are true and some are false. Copy out the true statements.
- •III. Find out in the text the following word-combinations. Use them in sentences of your own.
- •V. Make the right choice and fill in the blanks.
- •VI. Translate the following into Hungarian.
- •VII. Look through the text. List the principal ideas.
- •VIII. Topic for discussion: Modern Programming Languages. Lesson 7 computer networks
- •Vocabulary notes
- •Exercises
- •I. Read the text and answer the following questions.
- •II. According to the text agree or disagree with the following statements.
- •III. Translate into English:
- •IV. Pay attention to the following terms. Try to remember them.
- •V. Translate into Hungarian.
- •VI. Read quickly through the text below, then make the summary.
- •Lesson 8 what is the internet?
- •Vocabulary notes
- •Exercises
- •I. Read the text .Write the key questions about it to ask your fellow students.
- •II. In the sentences below some statements are true and some are false. Copy out the true statements.
- •III. Find out the following word-combinations in the text. Translate them into Hungarian:
- •IV. Translate into Hungarian.
- •V. Translate into English.
- •VI. Read the information about the Internet. List the principle ideas.
- •VII. Retell the text. The name internet
- •Lesson 9
- •Internet innovations
- •I. Do you use the Internet? How often do you use it?
- •II. Before reading the text match the following technological words to their definitions.
- •III. Read the text.
- •What’s New?
- •Vocabulary notes
- •IV. Answer the questions.
- •V. Read the following text and answer the questions after it.
- •Questions
- •VI. Read the text about Internet cheats. Make notes about it. Discuss it with your group mates. Cheating.Com
- •VIII. Choose the correct answer to the questions.
- •Vocabulary notes
- •Exercises
- •I. Answer the following questions on the text:
- •Lesson 2 mathematics – the queen of science
- •Vocabulary notes
- •Exercises
- •I. Answer the questions on the text:
- •II. Find in the text English equivalent for:
- •IV. Find in the text words with the suffixes –al, -ous, -ment, -y, -ly. Define what part of speech they form. Translate the words into Hungarian.
- •Texts for additional reading
- •What is mathematics
- •Text 2 mathematics - the language of science
- •Text 3 myths in mathematics
- •Text 4 mathematics and art
- •Part V Outstanding mathematicians
- •Vocabulary Notes
- •Text 2. Pierre de Fermat.
- •Text 3. N.I.Lobachevsky (1792-1856 ).
- •Text 4. M.V. Keldysh.
- •Text 5. Isaac Newton.
- •Text 6. Johann Carl Friedrich Gauss
- •Text 7. Blaise Pascal
- •Mathematical symbols and expressions
- •Reading of mathematical expressions
- •Список використаної літератури:
- •Загола н.В., Минда о.І., Шпеник с.З., Ярославцева к.В.
- •Навчально-методичний посібник для студентів математичного факультету
Ungvári Nemzeti Egyetem
Idegennyelvek tanszéke
Zahola n., Mynda o., Spenik Sz. English for Mathematicians
Oktatási és módszertani tankönyv a matematikai kar diákjai számára
Uzhhorod – 2008
УДК 811.111 (075.8)
Ш 143.21-923
П-62
A tankönyvet az idegennyelvek tanszékének tanárai állították össze a matematikai kar diákjai számára. A könyv célja – felkészíténi a matematikai kar diákjait a szakmai irodalom olvasásához és megértéséhez, a szaknyelvi lexikon elsajátitásához.
A tankönyv öt részből áll: „Arithmetic and Algebra”, ,,Geometry”, „Computer”, „The development of mathematical science”, „Outstanding mathematicians”. Mindegyik rész olyan
Посібник створений групою викладачів кафедри іноземних мов для студентів математичного факультету. Мета посібника – підготувати студентів-математиків до читання та розуміння наукової літератури зi спеціальності, засвоєння термінологічної лексики.
Посібник складається з шести частин: „Arithmetic and Algebra”, ,,Geometry”, „Computer”, „The development of mathematical science”, „Outstanding mathematicians”, „Statistics”. Кожна частина складається з уроків, які містять оригінальні тексти зі спеціальності, словник, а також текстів для додаткового читання. Лексичні вправи після текстів спрямовані на закріплення активної лексики уроку.
Автори підручника висловлюють щиру подяку старшим викладачам кафедри Литвиновій В.М., Гаврилюк Н.О., Штефанюк Н.С. та Чонка О.Я за велику допомогу у підготовці даного посібника.
Рецензенти:
Бартош О.П., канд..пед.наук, доцент
Маляр М.М., канд..мат.наук, доцент
Рекомендовано до друку Редакційно-видавничою радою
Ужгородського національного університету
Протокол № 5 від 8 жовтня 2008 р.
Isbn isbn 978-966-2095-20-3 © Загола н.В.
© Минда О.І.
© Шпеник С.З.
© Ярославцева К.В.
Contents
Part I. Arithmetic and Algebra
Lesson 1. Arithmetic Lesson 2. Addition Lesson 3. Subtraction Lesson 4. Multiplication Lesson 5. Division Lesson 6. Algebraic expressions Lesson 7. Equations and proportions Lesson 8. Decimal numerals Lesson 9. Decimal and common fractions Lesson 10. Mathematical sentences Lesson 11. Rational numbers Lesson 12. Irrational numbers |
5 6 7 9 10 12 13 15 18 20 23 27 |
Part II. Geometry
Lesson 1. Geometry Lesson 2. The history of geometry Lesson 3. The meaning of geometry Lesson 4. Rays, angles, simple closed figures Lesson 5. Circles Lesson 6. Pythagorean geometry |
29 32 35 38 44 46 |
Part III. Computer
Lesson 1. The computer have changed the way we work and play Lesson 2. From the history of computers Lesson 3. What is a computer Lesson 4. Computers: software and hardware Lesson 5. Windows Lesson 6. Communication with computer Lesson 7. Computer networks Lesson 8. What is the Internet Lesson 9 Internet innovations |
50 54 58 62 65 68 71 74 77 |
Part IV. The development of mathematical science
Lesson 1. Mathematical science in Ukraine Lesson 2. Mathematics = the queen of sciences Texts for additional reading Text 1 What is mathematics Text 2 Mathematics - the language of science Text 3 Myths in mathematics Text 4 Mathematics and art |
81 83
84 86 88 89 |
Part V. Outstanding mathematicians
Text 1. Sophia Kovalevska Text 2. Pierre de Fermat Text 3. N. Lobachevsky Text 4. M. V. Keldysh Text 5. Isaac Newton Text 6. Johann Carl Friedrich Gauss Text 7. Blaise Pascal |
93 95 95 96 96 97 98 |
Additional information
Mathematical symbols and expressions Reading of mathematical expressions |
100 101 |
Part I
ARITHMETIC AND ALGEBRA
Lesson 1
ARITHMETIC
Arithmetic is the science of numbers. In the Arabic system all numbers are written with the nine digits 1,2,3,4,5,6,7,8 and 9 and the zero or nought (0). It is a decimal system. In a number written with this system, each figure has a value according to the column in which it is written: the unit’s column, the ten’s column, the hundred’s column, the thousand’s column, the ten-thousand’s column and so on. Let us illustrate it by the number 197,842, 653. To make it easy to read this number is divided by commas into groups of three columns each called periods. The first period of three columns to the right is called "units", the next period is called "thousands", and the third period is called "millions". In reading the number, the figures in a period are read as units, but the name of the period is also included. Thus, the number 197,842,653 is read as "one hundred and ninety- seven million, eight hundred and forty-two thousand, and six hundred and fifty three".
The use of the zero enables the user, in a number like 205, to write the 2 in the hundred’s column and show that there are no tens, although there are 5 units.
The four main operations in arithmetic are addition, subtraction, multiplication and division.