- •Grammar Revision
- •Indefinite Tenses (Active)1
- •Continuous Tenses (Active)1
- •Perfect tenses (Active)1
- •1. Read the text. To understand it better consult active vocabulary:
- •Active Vocabulary
- •4. Study the text and answer the following questions:
- •1. Read the names of the faculties. Give Ukrainian equivalents:
- •2. Read the names of the specialities. Give Ukrainian equivalents:
- •3. Look through the email and answer the following questions:
- •Active Vocabulary
- •2. Are these statements true or false? If they are false, say why. Use the following phrases:
- •3. Study the letter and answer the following questions:
- •1. Read the names of the schools. Give Ukrainian equivalents:
- •2. Read the names of the departments. Give Ukrainian equivalents:
- •3. Look through the email and answer the following questions:
- •History
- •Undergraduate Academics
- •Active Vocabulary
- •2. Are these statements true or false? If they are false, say why. Use the following phrases:
- •3. Study the letter and answer the following questions:
- •Grammar and Vocabulary Exercises
- •1. Find English equivalents to the following words and word combinations in the texts of the unit:
- •2. Translate the following words and word combinations from English into Ukrainian and use them in the sentences of your own:
- •3. Find in the texts synonyms for the following words and expressions and use them in the sentences of your own:
- •4. Complete the following sentences in the context of the above information:
- •6. Put the verb in brackets in the correct tense form:
- •8. Make the sentences from Ex. 6 negative. Conversational Practice
- •1. Learn the following expressions relating to the communication of opinions. Translate them into Ukrainian.
- •2. Discuss the following questions in the context of the topics of Unit 1, using as many of the above expressions as possible. Compare Ukraine and the usa.
- •3. Ask your friend the following questions, present the results to the whole group.
- •4. Translate the following words and word-combinations:
- •5. Interview Maksym in English. Find out what he knows about the faculty he studies at:
- •Writing
- •Extended reading
- •Grammar Revision Словотвір в текстах функціонального стилю науки
- •Основні префікси та їх значення
- •Основні суфікси іменників
- •Основні суфікси прикметників
- •Основні суфікси дієслів
- •Основні суфікси прислівників
- •Конверсія
- •Словоскладання
- •2. Learn to recognize the following international words and give their Ukrainian equivalents:
- •What is an Electronic Computer?
- •Grammar and Vocabulary Exercises
- •1. Study the Table of word-building means given in Grammar Revision.
- •3. Form the words after the model and translate them into Ukrainian:
- •9. For each definition write a word from the text:
- •Reading Comprehension
- •1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following questions:
- •Conversational Practice
- •1. Suppose that the information in the statement is insufficient. Repeat the statement and add your own reasoning, thus developing the idea. Use the following phrases:
- •Computers
- •2. Answer the following questions:
- •3. Reconstruct the text “Computers” into a dialogue.
- •4. Annotate the text in English. Use the phrases:
- •Writing
- •Extended reading
- •The Internet Computer.
- •Grammar Revision Passive Voice
- •Modals with the Passive Voice
- •2. Learn to recognize international words:
- •Hardware – Software – Firmware
- •Grammar and Vocabulary Exercises
- •11. Combine the words from the left-and right-hand columns to make word-combinations. Translate them into Ukrainian:
- •12. Compose sentences with the words and phrases from Ex. 11.
- •13. Write an appropriate word or phrase in the following spaces:
- •Reading Comprehension
- •1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following questions:
- •Conversational Practice
- •1. Agree with the following statements, adding your own comments. Use the introductory phrases:
- •2. Suppose that the information in the statement is insufficient. Repeat the statement and add your own reasoning, thus developing the idea. Use the following phrases:
- •3. Express your personal view on the statement given below. Use the following phrases:
- •4. Give a short summary of the text.
- •1. Read and translate the text: Computer Crime
- •2. Answer the following questions:
- •3. Reconstruct the text “Computer Crime” into a dialogue.
- •4. Annotate the text in English. Use the phrases:
- •Writing
- •Extended reading
- •Boolean Algebra
- •Grammar Revision Modal Verbs
- •2. Learn to recognize international words:
- •Artificial Intelligence. Is it Possible?
- •Grammar and Vocabulary Exercises
- •1. Look through the text and find sentences with Modal Verbs. Translate them into Ukrainian.
- •3. Choose the proper equivalents of the Modal Verbs:
- •4. Underline the affixes, state what part of speech they indicate and translate the following words into Ukrainian:
- •5. Give the Ukrainian equivalents of the following words and word-combinations:
- •6. Use the words from Ex. 5 to complete the following sentences:
- •Reading Comprehension
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Study the text and answer the following questions:
- •Conversational Practice
- •1. Agree or disagree with the statements given below. Use the introductory phrases and develop the idea further. Use the following phrases:
- •2. Choose the definition of artificial intelligence which, to your mind, is the correct one. Justify your choice:
- •3. Debate the given statement. It is advisable that the group be divided into two parties, each party advocating their viewpoint. Use the following introductory phrases:
- •4. Give a short summary of the text.
- •1. Read and translate the text:
- •2. Answer the following questions:
- •3. Reconstruct the text “Turing’s test” into a dialogue.
- •4. Annotate the text in English. Use the phrases:
- •5. Discuss the problems. The following phrases may be helpful:
- •6. Summarize the text briefly. Writing
- •Extended reading
- •To be One with the Computer
- •Grammar Revision Sequence of Tenses
- •2. Learn to recognize international words:
- •The World of Hypotheses. Was Einstein Right?
- •Active Vocabulary
- •Grammar and Vocabulary Exercises
- •1. Look through the text and find Complex Sentences. Translate them into Ukrainian.
- •2. Join the two simple sentences to make a complex sentence. Mind the sequence of tenses rule:
- •3. Turn the following statements into indirect speech:
- •4. Define meanings of the following words by their affixes:
- •5. Study the text and give Ukrainian equivalents for the following words and word-combinations:
- •Reading Comprehension
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following questions:
- •Conversational Practice
- •1. Agree or disagree with the following statements. Begin your answer with the following phrases:
- •2. Discuss the statements trying to prove your point of view. Use the following phrases:
- •3. Give a short summary of the text.
- •1. Read and translate the text: Gravitation
- •2. Answer the following questions:
- •3. Reconstruct the text “Gravitation” into a dialogue.
- •4. Annotate the text in English. Use the phrases:
- •Writing
- •Extended reading
- •Grammar Revision The Infinitive /інфінітив/
- •1) Як іменник інфінітив може бути:
- •2) Як дієслово інфінітив може
- •Форми інфінітива та їх комунікативні значення.
- •The Infinitive Constructions Інфінітивні звороти та їх функції у реченні. Складний додаток /Complex Object/
- •Складний підмет /Complex Subject/
- •Прийменниковий інфінітивний комплекс (The for-to-Infinitive –Construction)
- •Функції прийменникового інфінітивного комплексу
- •2. Learn to recognize international words:
- •The Theory of Equations
- •Grammar and Vocabulary Exercises
- •1. Look through the text and find sentences with the Infinitive and the Infinitive Constructions. Translate them into Ukrainian.
- •2. Translate the following sentences into Ukrainian:
- •7. Look through the text and give English equivalents for the following words and word-combinations:
- •8. Combine the words from the left-and right-hand columns to make word-combinations. Translate them into Ukrainian:
- •9. Compose sentences in English using the word-combinations from Ex. 8. Reading Comprehension
- •1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following questions:
- •Conversational Practice
- •1. Choose one of the words given below and illustrate the concept:
- •2. Discuss the statements given below. Summarize the discussion. Use the following phrases:
- •3. Give a short summary of the text.
- •1. Read and translate the text: The Early Algebra Babylonian Algebra – Rhetorical Style
- •Algebra in Egypt
- •Early Greek Algebra
- •Hindu and Arabic Algebra
- •Algebra in Europe
- •2. Answer the following questions:
- •3. Reconstruct the text “The early Algebra” into a dialogue.
- •4. Agree with the statements given below and develop the idea further. Use the introductory phrases:
- •5. Annotate the text in English. Use the phrases:
- •6. Discuss the statements given below. Use the following phrases:
- •Writing
- •Extended reading
- •Grammar Revision
- •Утворення дієприкметників.
- •Функції Participle I, II в реченні
- •Дієприкметникові звороти
- •Складний додаток /Complex Object/
- •Складний підмет /Complex Subject/
- •Незалежний дієприкметниковий зворот (The Absolute Participial Construction)
- •Способи перекладу “незалежного дієприкметникового зворота” на українську мову.
- •2. Learn to recognize international words:
- •Informatics
- •Active Vocabulary
- •Grammar and Vocabulary Exercises
- •1. Study the text and find sentences with the Participle. Translate them into Ukrainian.
- •2. Translate the following sentences into Ukrainian:
- •3. Observe the time of occurrence, expressed by a Participle:
- •10. Compose sentences with the words and word-combinations from Ex.9. Reading Comprehension
- •1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following questions:
- •4. Give the definitions of the terms “information” and “informatics”:
- •Conversational Practice
- •1. Agree or disagree with the statement given below. Use the introductory phrases and develop the idea further. Use the following phrases:
- •2. Discuss the following statement. Use the given phrases:
- •3. Give a short summary of the text.
- •1. Read and translate the text:
- •2. Answer the following questions:
- •3. Reconstruct the text “Cybernetics” into a dialogue.
- •4. Annotate the text in English. Use the phrases:
- •5. Discuss the statements given below:
- •Writing
- •Extended reading
- •Grammar Revision.
- •1) Як іменник герундій може:
- •2) Як дієслово герундій (перехідного дієслова)2 може:
- •Форми герундія та їх комунікативні значення. Форми герундія неперехідного дієслова
- •Форми герундія перехідного дієслова
- •Порівняйте:
- •2. Learn to recognize international words:
- •Mystery of Memory
- •Active Vocabulary
- •Grammar and Vocabulary Exercises
- •1. Study the text, and find sentences with the Gerund. Translate them into Ukrainian.
- •2. Translate the following sentences into Ukrainian:
- •8. Combine the words from the left-and right-hand columns to make word-combinations. Translate them into Ukrainian:
- •9. Compose sentences in English using the word-combinations from Ex. 8. Reading Comprehension
- •1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following questions:
- •Conversational Practice
- •5. Give a short summary of the text.
- •1. Read and translate the text: The Memory of the Modern Supercomputers
- •Active Vocabulary
- •2. Answer the following questions:
- •3. Reconstruct the text “The Memory of the Modern Supercomputers” into a dialogue.
- •4. Annotate the text in English. Use the phrases:
- •5. Discuss the problems trying to prove your point of view. Use the following phrases:
- •Writing
- •Extended reading
- •The Brain
- •2. Learn to recognize international words:
- •Math Concepts
- •Grammar and Vocabulary Exercises
- •1. Grammar revision.
- •1. Imperative Sentences.
- •2. Indefinite Tense-Aspect Forms.
- •3. Questions.
- •4. Negations.
- •8. Compose sentences with the words and word-combinations from Ex.7. Reading Comprehension
- •1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following question:
- •4. Give the definitions of the terms “the real number system” and “the maths of number”:
- •Conversational Practice
- •1. Disagree with the following negative statements and keep the conversation going where possible. Begin your answer with the opening phrases:
- •2. Agree or disagree with the statements. Use the introductory phrases:
- •4. Practise problem questions and answers. Work in pairs. Change over!
- •5. What is implied in the following assertion?
- •6. Discuss the statements given below. Use the following phrases:
- •7. Give a short summary of the text.
- •1. Read and translate the text: Programming. Multiprogramming
- •2. Answer the following questions:
- •3. Reconstruct the text into a dialogue. The main rules governing a conversation in English:
- •4. Annotate the text in English. Use the phrases:
- •5. Read the statements and develop the idea further. Use the given phrases:
- •Writing
- •Extended reading
- •The Internet Programming Languages
- •2. Learn to recognize international words:
- •Automated Factory Update
- •Active Vocabulary
- •Vocabulary Exercises
- •1. Look through the text and give Ukrainian equivalents of the following words and word-combinations:
- •2. Look through the text and give Ukrainian equivalents of the following words and word-combination:
- •3. Look through the text and find words with the same meaning:
- •4. Look through the text and find words with opposite meaning:
- •5. Combine the words from the left- and right-hand columns to make word-combinations. Translate them into Ukrainian:
- •6. Compose sentences in English using the word combinations from Ex.5. Reading Comprehension
- •1. Review the whole text again. Outline the subject matter of the text, its components structure, topic sentences and main ideas. Use the following phrases:
- •2. Say whether the following statements are true or false. Justify your choice. Use the given phrases:
- •3. Answer the following questions:
- •4. Give the terms to the following definitions:
- •Conversational Practice
- •1. Clarify what we mean by the following statements:
- •2. Discuss the advantages of cim comparing traditional manufacturing and computer-integrated manufacturing. The schemes given below will be helpful.
- •3. Debate the given problem. It is advisable that the group be divided into two parties, each party advocating their viewpoint. Use the following introductory phrases:
- •4. Give a short summary of the text.
- •1. Read and translate the text:
- •Active Vocabulary
- •2. Answer the following questions:
- •3. Reconstruct the text “Planning and Justifying Factory Automation Systems” into a dialogue. The main rules governing a conversation in English:
- •4. Annotate the text in English. Use the phrases:
- •5. Express your personal view on the statement “Integrated problems require integrated solutions”. Use the following phrases:
- •Writing
- •1. Using texts a and b of Unit 10 write a composition on “My future profession”. Take into account the following outlines or give your own version.
- •Extended reading
- •Control Engineering
- •Control Engineering Practice
- •2. "Can a computer have a mind?" Provide answers to this question, discussing it with Internet community. Consult Roger Penrose's Penguin book "The Emperor's New Mind", if necessary.
- •1. Using Internet try to find out all you can about the land of Tor'Bled-Nam.
- •2. What is the very essence of mathematical visualization? Key-words: magnification, abstract mathematics, complex numbers, miracles of mathematics.
- •1. Try to find additional information about black and white holes.
- •2. Find out the names dealt with these problems/ approaches/ theories/ hypotheses.
- •3. Present your ideas on the given subject for the students' research society.
- •1. Find the film "Time Travel".
- •2. Discuss it at the students' on line conference.
- •Appendix II
- •1. Study all the texts, collect information and write two-pages-long compositions on each of the following topics:
- •2. The following questions may direct you:
- •Number Theory and its Founders
- •Pierre de Fermat
- •Leonhard Euler
- •Georg Friedrich Bernhard Riemann
- •Active Vocabulary
- •The Greek Genius
- •Natural Numbers
- •Real Numbers
- •Toward Mathematical Structure
- •Structures
- •Appendix III greek alphabet
- •Wording Mathematical Formulae
- •Giving an Oral Presentation
- •Список рекомендованої літератури
- •Contents
Structures
The generic concept of structure may be quite simply explained, as J. Diendonne did, namely: "If the temperature is 800 F and a 20-degree rise is predicted, we expect without counting, an eventual temperature of 1000. If we have a book open at page 80 and we are told to look 20 pages further on, we turn without hesitation to page 100 without counting the intervening pages. We are using the fact that the structure of addition applies to both cases, adding the numbers gives the correct result when interpreted either for temperatures or for pages. We do not (fortunately!) have to learn a special arithmetic for thermometers and another for books...".
This is, of course, one of the simplest examples of structures, but it shows at once that the most striking feature of structures has something to do with the economy of thought and this aspect is naturally of paramount importance in maths. The structures are almost custom-made tools for mathematicians. Whenever a mathematician has been able to prove that the objects he is studying verify the axioms of a certain type of structure, he has ipso facto (by the fact itself) proved all the theorems from the theory of that type of structure for these particular objects (theorems which he would otherwise probably either miss altogether or for which he would have to devise special proofs).
Simularly, whenever two given structures are proved to be isomorphic, the number of theorems is immediately doubled, each theorem proved for one of the structures giving at once a corresponding theorem for the other (and sometimes I it is much easier to prove one than the other). No wonder, therefore, that there exist whole theories of a highly complex and difficult nature, such as the so-called "class-field theory" in the theory of numbers, whose major aim is to prove that the two structures are isomorphic.
Anyone who is familiar with the theory of groups however elementary, already knows something about the working mechanism of such structures in concrete, although he may not be explicitly aware of it. Namely, the nature of the objects or elements forming a group may vary, indeed, tremendously, but they share the same structure of group, defined by the groups themselves. If he knows, in addition, something about isomorphisms among groups, he is then even better off, since the concept of "isomorphism" is, evidently, one of those abstract notions which are closely and naturally linked to that of structure.
Generally, a structure of a certain type is defined for a set if a relation between the elements of is specifically defined such that a fixed set of axioms characteristic of the type of structure at issue can be verified. For example, the structure of the group (or ring, or field, etc.) belongs to a specific type, called algebraic structures, which in turn are characterized by the prescription for composition, namely, the unique relation for any three elements . For example, addition of numbers is a prescription in virtue of which a third number is uniquely assigned to the sum of the first two; similarly, multiplication of numbers, addition of vectors, composition of rotations, etc., exemplify algebraic structures. Some algebraic structures belong to the second type, called structures of order; for example, the set of real numbers is ordered, since one of any two distinct real numbers is greater than the other.
Then again, there is the third type, called topological structures (or topologies). A topology is given on a set if a concept of neighbourhood or limit which satisfied certain conditions (also called axioms) is adopted for the set in a suitable manner. It yields, therefore, an abstract formulation of the more or less intuitive notion of neighbourhood (or limit of continuity) to which we were originally led by our physical sense of space.
The degree of abstraction necessary for the formulation of the axioms of a topology is evidently greater than that for algebraic or order structures; but this may be considered still simple or less sophisticated in comparison with certain structures which are found strung-together, namely, mixed (or multiple) structures. For example, a structure may be both algebraic and topological, linked together by new axioms, topological algebra and algebraic topology are two specific examples of such a mixed structure (although homological algebra is still unmixed, exemplifying a pure type of structure).
The mixed structure may appear also in elementary cases; for instance, the set of real numbers reveals three kinds of structures at the same time: an algebraic structure defined by computative operations (addition and multiplication), a structure of order by which inequalities between real numbers can be treated, and, finally, a topological structure where a concept of limit is explicated. These structures are obviously associated with each other so that topology may be defined by order or relations (two inequalities added term by term, etc. may exist between order and algebra). Several other structures appear strung-together, more likely at the level of advanced examples such as topological groups, differential manifolds, analytic fibre spaces, discontinuous groups of transformations, etc.
These structures, pure or mixed, are now found everywhere at the concentric centre of the math universe. A considerable diversity can be observed among the great types of structures, some of which may be called mother structures, namely, the most general structures with the smallest number of axioms, while there are also those which are obtainable by adding more axioms such that they will yield the harvest of new consequences. Here appear, thus, a hierarchy of structures, descending from the simple and general at the top to the complex and particular at the bottom.
Farther along, at the lowest of the structural totem pole, one finally descends upon the ground of the particular and individual where certain areas have long remained or will for some time remain indeterminate, structure-wise, such that the "classical" maths begins to emerge. For example, certain fragments from the theory of numbers, of functions of a real or complex variable, of differential equations, of differential geometry, etc.
Nevertheless, after the extensive reconstructions even the hard-core areas cannot but fail to retain their former autonomy; they have become crossroads, where several more general structures meet and react upon each other. For example, the redoubtable theory of primes is now a close neighbour of the theory of algebraic curves, and the most ancient Euclidean geometry borders on a brand-new theory of integral equations. One cannot hope to have a complete and final list of such types of structures on hand; several new ones have been discovered, and we have every reason to expect new discoveries of that kind.
Still, there are many large chunks of classical material, where the structural reconstruction by the axiomatic method has rather very slowly progressed. This means only a greater challenge, or a new area to bulldoze through, revealing new types of structures which will introduce new fusions among theories. And these breakthroughs will, in turn, mean another substantial progress in the direction of pregnant abstraction, simplification and unification, the process of which will be adapted time and again as long as maths will go on growing.