Lesson one what is mathematics?

Grammar:

1. Countable and Uncountable Nouns.

2. Degrees of Comparison.

3. Indefinite Tense-Aspect Forms. Active and Passive Voice.

LAB. PRACTICE

Repeat the sentences after the instructors, Mind the logical division of the sentence.

Model. Among all the sciences / maths is distinguished / for its universality.

Математика выделяется / среди всех наук / своей универсаль­ностью.

1. It is impossible to give a concise and readily acceptable definition of maths as it is a multifield subject. 2. Maths in the broad sense of the word is a peculiar form of the general process of human knowledge of the real world. 3. Maths deals with the space forms and quantity relations abstracted from the physical world. 4. Maths abstractions are idealizations that have material or physical origin. 5. Numbers are abstracted ideas or mental notions only, for numbers do not exist in nature. 6. In maths the abstracted notions and laws become divorced from the real world. 7. In a formal maths sys­tem the content is put aside as irrelevant. 8. Maths enjoys an un-parallel world-wide reputation of objectivity. 9. Contemporary maths is a mixture of much that is very old and still important (e. g., counting, the Pythagorean theorem) with new concepts such as sets, axiomatics, structure. 10. The totality of all abstract maths scien­ces is called Pure Maths. 11. Pure maths is borrowed from the physical world; it represents only one part of its forms of intercon­nection. 12. The totality of all concrete interpretations is called Applied Maths. Together they constitute Maths as a science. 13. Maths is the science dealing primarily with what can be obtained by reasoning alone. 14. Human thought moves from the concrete to the ab­stract, from specific individual cases to general principles. 15. Maths thought involves special kind of thinking and reasoning. 16. Despite the usefulness of analogy and induction, maths does not rely upon these methods to establish its conclusions. All maths proofs must be deductive. 17. The need for careful and rigorous reasoning in proofs is not at once intuitively apparent to a non- mathematician. 18. Mastery of maths does not demand a "maths mind", peculiar talents or genius. The subject is within anybody's grasp. 19. The common phrase "There is no royal road to maths" can be paraphrased by saying that "There is no royal road to learning". 20. "Language is as old as the mind" (Karl Marx). 21. Human knowledge and notions about the uni­verse are expressed, represented and stored in Language. 22. There are two main forms of Language. They are distinguished in the concepts of Language as a specific written Code and Speech. 23. Speech is the reali­zation and representation of this written code. 24. Language is a fore­most means of both human communication and human knowledge. 25. Na­tural spoken language has numerous and limitless applications. 26. The mass media — the press, radio and TV — make for the correctness of the formal language spoken in the country. 27. Colloquial language is vague, ambiguous and unreliable for science. 28. Spoken words may have different meanings determined by the context. 29. Scientists set up formalized languages to avoid confusion. 30. The essential and peculiar feature of modern maths is its symbolic language. 31. Maths language is designed and-ingeniously devised by the prominent mathematicians. 32. Much of the maths language has the form of signs, symbols, equations and formulas. 33. The development of a mea­ningful, adequate and consistent system of notations in various branches of maths is part of the history of maths. 34. Modern termino­logy and symbolism are a relatively new development. 35. Maths notation involves signs and symbols that represent objects, concepts, statements, operations, relations, functions, etc. 36. Symbols permit clear, concise, unambiguous representation of ideas which are sometimes very complex. 37. Maths writing is remarkable because it encompasses much information in few words.8. Most maths texts involve the basic symbols used in algebra, analytic geometry, calculus, set theory and maths logic with the meanings usually ascribed to them. 39. The precise signification of the symbol is fixed by usage, i. е., by the context. 40. A formal maths system bears some analogy to a natural lan­guage, for it has its own vocabulary and rules. 41. Symbols of a formali­zed language are combined in strict accordance with the rules of seman­tics and syntax. 42. The creations of calculus, non-Euclidean geometries, set theory and cybernetics may be considered as revolutions in maths. 43. Modern methods of carrying out arithmetic operations (addi­tion, subtraction, multiplication and division) and their applications be­come sophisticated through modern computers. 44. Nowadays mathematicians frequently liken maths to art or game rather than to scien­ce. 451 Most mathematicians claim there is great beauty in maths. 46. Maths and scientific problems demand solution. Mathematicians seek to solve problems in the most beautiful, elegant and simple manner. 47. The solution of difficult maths problems evokes aes­thetic emotions. 48. There is an agreement on the fact that a "beautiful" maths result must be nontrivial. 49. An essential element in the "beauty" of a theorem lies in its simplicity and generality. 50. The search for simplicity is a leitmotive of scientific thought in general. 51. To deve­lop a rigorous and elegant proof the mathematician builds a structure of logic and form which to his eye is as beautiful as the finest poem.

I. Translate the following sentences and a) locate and analyze the Predicate Tense-Aspect forms; b) qualify the parts of speech.

1. Among the many adjectives given to the present century (e. g., electronic, atomic and space) the term "mathematization of science age" is often come across. 2. Some people define the unprecedented develop­ment of modern maths as the "revolution in maths". Others call it "maths power". 3. However correct or incorrect these terms may seem, one thing is obvious: maths is a key science nowadays. 4. Maths has a peculiar and remarkable language. 5. Certainly, it is unlike any human language as, in a sense, it is an unspoken language. 6. Maths language may be called the language of science. 7. Scientific language must be precise, concise and universal, i. е. (=that is,) it must be the same throughout the world. 8. Unlike the natural languages, the language of science is man-made or artificial. 9. Some laymen unaccustomed to its forms find it confusing. 10. Maths reasoning is of the highest level known to man.

II. Translate the following sentences.

1. Obviously, the meaning of the word becomes clear from the con­text. 2. No mathematician prefers a wordy and lengthy statement of a theorem or law. 3. A maths sentence of signs and symbols is formed by means of rules of syntax of a corresponding formalized theory. 4. Scientists determine the meaning of symbols by definitions and use them by common agreement.5. The attention paid to rigour and precision in maths points to the requirements underlying maths research. 6. Certainly, maths is more than a language or technique; it is, in fact, a body of knowledge that serves all other sciences. 7. The study of maths is sometimes discouraging to weak-willed minds, indeed.

The sentence: 1) simple; 2) compound; 3) complex.