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УДК 802.0 Федеральное агентство по образованию ББК 81.2Англ.ж721 Омский государственный университет им. Ф.М. Достоевского П69 Рекомендован к изданию редакционно-издательским советом ОмГУ Рецензент – ст. преподаватель кафедры иностранных языков Э.К. Сопелева П69 Практикум для подготовки к экзамену по английскому языку (для студентов математического факультета I и II курсов) / Сост. Л.В. Жилина. – Омск: Изд-во ОмГУ, 2005. – 44 с.

ISBN 5-7779-0600-1 Состоит из 5 разделов: I – тексты для письменного перевода со Практикум словарем; II – тексты и ключевые выражения для реферирования;

для подготовки к экзамену по английскому языку III – разговорные темы; IV – чтение математических формул; V – лексический минимум, кроссворды для закрепления лексики и кон(для студентов математического факультета I и II курсов) трольные тесты.

Для студентов математического факультета I и II курсов.

УДК 802.0 ББК 81.2Англ.ж721 ISBN 5-7779-0600-1 © Омский госуниверситет, 2005 Изд-во Омск ОмГУ 2005 2 ПРЕДИСЛОВИЕ PART I Практикум для подготовки к экзамену по английскому язы- Text 1 ку предназначен для студентов I и II курсов математического фаTranslate the Text with dictionary in written form (time 45 культета и включает в себя 5 разделов.

minutes) Первый раздел содержит 3 текста, по сложности соответствующие экзаменационным текстам для письменного перевода с About a Line and a Triangle использованием словаря.

Given ABC, extend the side AB beyond the vertices. Now, roВторой раздел посвящен реферированию текста без словаtate the line AB around the vertex A until it falls on the side AC. Next ря. Для облегчения выполнения этого задания помимо текста даrotate it (from its new position) around C until it falls on the side BC.

ется план реферирования и фразы, помогающие грамотно излоLastly, rotate it around B till it takes up its erstwhile position.

жить содержание статьи.

It is virtually obvious that although the line now occupies exТретий раздел – изложение разговорной темы. Он состоит actly the same position as before, something has changed. After three из 6 текстов (ко второй и третьей теме даны дополнительные текrotations, the line turned around 180°. So, for example, the point A will сты), являющихся примерными разговорными темами, включенnow lie on a different side from B than before. We say that turning the ными в экзамен.

line around the triangle changed its orientation.

Четвертый раздел поможет студентам научиться читать It appears that the line occupies the same position but not quite:

математические формулы, встречающиеся в текстах.

points on the line did not preserve their locations. However, since there Пятый раздел – приложение, в которое входят слова и слоare just two possible orientations of the line, we come up with an interвосочетания, часто встречающиеся в специализированных текстах, esting question: what happens to the line after it turns around the trianпосвященных разным разделам математики, два кроссворда на gle twice Will it occupy its original position exactly (point-for-point) знание математической лексики, три грамматических теста-задаThe answer is easily obtained from the following observation.

ния и пример экзаменационного билета.

After the first rotation the line occupies the same position but with a Практикум предназначен для более эффективной подготовdifferent orientation. Let's turn the line into coordinate axis. In other ки студентов к экзамену по английскому языку.

words, let's choose the origin – point O, the unit of measurements, and the positive direction. If, after the rotation, the point originally at the distance x from O will be now located at the position b-x. Therefore, there exists one point on the line that does not move even after a single rotation. This is the fixed point of the transformation. The fixed point solves the equation x = b-x. The rotation of the line around the triangle is simply equivalent to the rotation of the line around that point through 180°.

3 Text 2 Text Translate the Text with dictionary in written form (time 45 Translate the Text with dictionary in written form (time minutes) minutes) Computer Algebra Computer Software in Science and Mathematics Symbols as well as numbers can be manipulated by a computer. Computation offers a new means of describing and investigating scientific New, general-purpose algorithms can undertake a wide variety of routine and mathematical systems. Simulation by computer may be the only way mathematical work and solve intractable problems by Richard Pavelle, to predict how certain complicated systems evolve by Stephen Wolfram Michael Rothstein and John Fitch Scientific laws give algorithms, or procedures for determining Of all the tasks to which the computer can be applied none is how systems behave. The computer program is a medium in which the more daunting than the manipulation of complex mathematical expresalgorithms can be expressed and applied. Physical objects and mathesions. For numerical calculations the digital computer is now thormatical structures can be represented as numbers and symbols in a oughly established as a device that can greatly ease the human burden computer, and a program can be written to manipulate them according of work. It is less generally appreciated that there are computer proto the algorithms. When the computer program is executed, it causes grams equally well adapted to the manipulation of algebraic expresthe numbers and symbols to be modified in the way specified by the sions. In other words, the computer can work not only with numbers scientific laws. It thereby allows the consequences of the laws to be themselves but also with more



Abstract

symbols that represent numerideduced.

cal quantities.

Executing a computer program is much like performing an exIn order to understand the need for automatic systems of algeperiment. Unlike the physical objects in a conventional experiment, braic manipulation it must be appreciated that many concepts in scihowever, the objects in a computer experiment are not bound by the ence are embodied in mathematical statements where there is little laws of nature. Instead they follow the laws embodied in the computer point to numerical evaluation. Consider the simple expression 32/.

program, which can be of any consistent form. Computation thus exAs any student of algebra knows, the fraction can be reduced by cantends the realm of experimental science: it allows experiments to be celling from both the numerator and the denominator to obtain the performed in a hypothetical universe. Computation also extends theosimplified form 3. The numerical value of 3 may be of interest, but it retical science. Scientific laws have conventionally been constructed in may also be sufficient, and perhaps of greater utility, to leave the exterms of a particular set of mathematical functions and constructs, and pression in the symbolic, nonnumerical form. With a computer prothey have often been developed as much for their mathematical simgrammed to do only arithmetic, the expression 3 2/ must be evaluplicity as for their capacity to model the salient features of a phenomeated; when the calculation is done with a precision of 10 significant non. A scientific law specified by an algorithm, however, can have any figures, the value obtained is 9,424777958. The number, besides being consistent form. The study of many complex systems, which have rea rather uninformative string of digits, is not the same as the number sisted analysis by traditional mathematical methods, is consequently obtained from the numerical evaluation (to 10 significant figured) of 3.

being made possible through computer experiments and computer The latter number is 9,424777962; the discrepancy in the last two models. Computation is emerging as a major new approach to the scidecimal places results from round-off errors introduced by the comence, supplementing the long-standing methodologies of theory and puter. The equivalence of 3 2/ and 3 would probably not be recogexperiment.

nized by a computer programmed in this way.

5 PART II This paper contains two main results. The first one coincides with the title, the second consists in a description of free inverse semiText groups (if a free inverse semigroup is presented as a quotient algebra of a free involuted semigroup, then each element of F is a class of Rendering of the text (15 min) equivalent words, we give a canonical form of the words). Certain corActa Mathematica Academiae Scientiarum ollaries with properties of free inverse semigroups follow.

Hungaricae Tomus 26 (1–2), (1975), 41–52.

All results of the paper were reported by the author at a meeting of the semin-nar "Semigroups" in Saratov State University on October FREE INVERSE SEMIGROUPS 21, 1971.

ARE NOT FINITELY PRESENTABLE By В.М. SCHEIN (Saratov) In the memory of Professor A. Kertesz Free inverse semigroups became a subject of intense studies in the last few years. Their existence was proved long ago: as algebras with two operations (binary multiplication and unary involution) inverse semigroups may be characterized by a finite system of identities, i.e. they form a variety of algebras. Therefore, free inverse semigroups do exist.

A construction of a free algebra in a variety of algebras (as a quotient algebra of an absolutely free word algebra) is well known.

Free inverse semigroups in such a form were considered by V.V. VAGNER who found certain properties of such semigroups. A monogenic free inverse semigroup (i.e. a free inverse semigroup with one generator) was described by L.M. GLUSKIN. Later this semigroup was described by H.E. SCHEIBLICH in a slightly different form. The most essential progress in this direction was made in a paper by H.E. SCHEIBLICH who described arbitrary free inverse semigroups. A relevant paper by C. EBERHART and J. SELDEN should be mentioned. There are papers on some special properties of free inverse semigroups. N.R. REILLY described free inverse subsemigroups of free inverse semigroups, results in this direction were obtained also by W.D. MUNN and L. O'CARROLL.

Let Fx denote the free inverse semigroup with the set X of free generators. A monogenic free inverse semigroup will be denoted F1.

Time and then we will write F instead of Fx. We do not consider F a one-element inverse semigroup.

7 THE PLAN FOR RENDERING THE ARTICLE Finally...

The author comes to the conclusion that...

1. The headline of the article, the author of the article, where and when the article was published 4. Your opinion on the article, your attitude towards it The article is headlined... I find the article interesting, important, useful, informative, upThe headline of the article I have read... to-date, disputable, dull, of no value, too hard to understand... On readThe article is entitled... ing the article I realize the fact that… The headline of the article is...

The author of the article is...





The article is written by... Additional task It was published in...(newspaper) on...(date) (on May 23d, 2003) It was printed in... Reproduce the text in your own words The article under the title... was published in... on...

Differential equations give adequate models for the overall properties of physical processes such as chemical reactions. They describe, 2. The main idea of the article for example, the changes in the total concentration of molecules: they The main idea of the article is... do not, however, account for the motions of individual molecules.

Basically, the article is about... These motions can be modelled as random walks: the path of each The article is devoted to the problem of... molecule is like the path that might be taken by a person in a milling The article touches upon... crowd. In the simplest version of the model the molecule is assumed to The article dwells upon... travel in a straight line until it collides with another molecule; it then The article tells the readers about... recoils in a random direction. All the straight-line steps are assumed to The author discusses an important problem of... be of equal length. It turns out that if a large number of molecules are The purpose of the article is to give the reader some information following random walks, the average change in the concentration of on... molecules with time can in fact be described by a differential equation The aim of the article is to provide the reader with some material called the diffusion equation.

(data) on... There are many physical processes, however, for which no such average description seems possible. In such cases differential equations 3. The contents of the article (some facts, figures) are not available and one must resort to direct simulation. The motions of many individual molecules or components must be followed explicThe author starts by telling the reader that...

itly; the overall behavior of the system is estimated by finding the averThe author writes (states, stresses, thinks, points out) that...

age properties of the results. The only feasible way to carry out such The author highlights the fact that...

simulations is by a computer experiment: essentially no analysis of the The author focuses on the fact that...

systems for which analysis is necessary could be made without the According to the text...

computer.

Further the author reports (says) that...

The article goes on to say that...

In conclusion...

9 PART III postulates. Each geometry became, from this point of view, a particular branch of mathematics.

Speak on the topic In the twentieth century the study of abstract spaces was inaugurated and some very general studies came into being. A space became 1. Read and translate the text merely a set of objects together with a set of relations in which the obTopic jects are involved, and a geometry became the theory of such a space.

The boundary lines between geometry and other areas of mathematics A modern view of geometry became very blurred, if not entirely obliterated.

For a long time geometry was intimately tied to physical space, There are many areas of mathematics where the introduction of actually beginning as a gradual accumulation of subconscious notions geometrical terminology and procedure greatly simplifies both the unabout physical space and about forms, content, and spatial relations of derstanding, and the presentation of some concept or development. The specific objects in that space. We call this very early geometry "subbest way to describe geometry today is not as some separate and preconscious geometry". Later, human intelligence evolved to the point scribed body of knowledge but as a point of view – a particular way of where it became possible to consolidate some of the early geometrical looking at a subject. Not only is the language of geometry often much notions into a collection of somewhat general laws or rules. We call simpler and more elegant than the language of algebra and analysis, but this laboratory phase in the development of geometry "scientific geit is at times possible to carry through rigorous trains of reasoning in ometry". About 600 B.C. the Greeks began to inject deduction into gegeometrical terms without translating them into algebra or analysis. A ometry giving rise to what we call "demonstrative geometry".

great deal of modern analysis becomes singularly compact and unified In time demonstrative geometry becomes a material-axiomatic through the employment of geometrical language and imagery.

study of idealized physical space and of the shapes, sizes, and relations of idealized physical objects in that space. The Greeks had only one 2. Retell the text space and one geometry; these were absolute concepts. The space was not thought of as a collection of points but rather as a realm or locus, in which objects could be freely moved about and compared with one another. From this point of view, the basic relation in geometry was that of congruence With the elaboration of analytic geometry in the first half of the seventeenth century, space came to be regarded as a collection of points; and with the invention, about two hundred years later of the classical non-Euclidean geometries. But space was still regarded as a locus in which figures could be compared with one another. Geometry came to be rather far removed from its former intimate connection with physical space, and it became a relatively simple matter to invent new and even bizarre geometries.

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