вход по аккаунту


235.Практикум для подготовки к экземену по английскому языку

код для вставкиСкачать
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Федеральное агентство по образованию
Омский государственный университет им. Ф.М. Достоевского
УДК 802.0
ББК 81.2Англ.ж721
Рекомендован к изданию редакционно-издательским советом ОмГУ
Рецензент – ст. преподаватель
кафедры иностранных языков Э.К. Сопелева
для подготовки к экзамену по английскому языку
(для студентов математического факультета I и II курсов)
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
словарем; II – тексты и ключевые выражения для реферирования;
III – разговорные темы; IV – чтение математических формул; V –
лексический минимум, кроссворды для закрепления лексики и контрольные тесты.
Для студентов математического факультета I и II курсов.
УДК 802.0
ББК 81.2Англ.ж721
ISBN 5-7779-0600-1
© Омский госуниверситет, 2005
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Практикум для подготовки к экзамену по английскому языку предназначен для студентов I и II курсов математического факультета и включает в себя 5 разделов.
Первый раздел содержит 3 текста, по сложности соответствующие экзаменационным текстам для письменного перевода с
использованием словаря.
Второй раздел посвящен реферированию текста без словаря. Для облегчения выполнения этого задания помимо текста дается план реферирования и фразы, помогающие грамотно изложить содержание статьи.
Третий раздел – изложение разговорной темы. Он состоит
из 6 текстов (ко второй и третьей теме даны дополнительные тексты), являющихся примерными разговорными темами, включенными в экзамен.
Четвертый раздел поможет студентам научиться читать
математические формулы, встречающиеся в текстах.
Пятый раздел – приложение, в которое входят слова и словосочетания, часто встречающиеся в специализированных текстах,
посвященных разным разделам математики, два кроссворда на
знание математической лексики, три грамматических теста-задания и пример экзаменационного билета.
Практикум предназначен для более эффективной подготовки студентов к экзамену по английскому языку.
Text 1
Translate the Text with dictionary in written form (time 45
About a Line and a Triangle
Given ∆ ABC, extend the side AB beyond the vertices. Now, rotate the line AB around the vertex A until it falls on the side AC. Next
rotate it (from its new position) around C until it falls on the side BC.
Lastly, rotate it around B till it takes up its erstwhile position.
It is virtually obvious that although the line now occupies exactly the same position as before, something has changed. After three
rotations, the line turned around 180°. So, for example, the point A will
now lie on a different side from B than before. We say that turning the
line around the triangle changed its orientation.
It appears that the line occupies the same position but not quite:
points on the line did not preserve their locations. However, since there
are just two possible orientations of the line, we come up with an interesting question: what happens to the line after it turns around the triangle twice? Will it occupy its original position exactly (point-for-point)?
The answer is easily obtained from the following observation.
After the first rotation the line occupies the same position but with a
different orientation. Let's turn the line into coordinate axis. In other
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
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Text 2
Text 3
Translate the Text with dictionary in written form (time 45
Translate the Text with dictionary in written form (time 45
Computer Algebra
Computer Software in Science and Mathematics
Symbols as well as numbers can be manipulated by a computer.
New, general-purpose algorithms can undertake a wide variety of routine
mathematical work and solve intractable problems by Richard Pavelle,
Michael Rothstein and John Fitch
Computation offers a new means of describing and investigating scientific
and mathematical systems. Simulation by computer may be the only way
to predict how certain complicated systems evolve by Stephen Wolfram
Of all the tasks to which the computer can be applied none is
more daunting than the manipulation of complex mathematical expressions. For numerical calculations the digital computer is now thoroughly established as a device that can greatly ease the human burden
of work. It is less generally appreciated that there are computer programs equally well adapted to the manipulation of algebraic expressions. In other words, the computer can work not only with numbers
themselves but also with more abstract symbols that represent numerical quantities.
In order to understand the need for automatic systems of algebraic manipulation it must be appreciated that many concepts in science are embodied in mathematical statements where there is little
point to numerical evaluation. Consider the simple expression 3π2/π.
As any student of algebra knows, the fraction can be reduced by cancelling π from both the numerator and the denominator to obtain the
simplified form 3π. The numerical value of 3π may be of interest, but it
may also be sufficient, and perhaps of greater utility, to leave the expression in the symbolic, nonnumerical form. With a computer programmed to do only arithmetic, the expression 3 π2/π must be evaluated; when the calculation is done with a precision of 10 significant
figures, the value obtained is 9,424777958. The number, besides being
a rather uninformative string of digits, is not the same as the number
obtained from the numerical evaluation (to 10 significant figured) of 3π.
The latter number is 9,424777962; the discrepancy in the last two
decimal places results from round-off errors introduced by the computer. The equivalence of 3 π2/π and 3π would probably not be recognized by a computer programmed in this way.
Scientific laws give algorithms, or procedures for determining
how systems behave. The computer program is a medium in which the
algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a
computer, and a program can be written to manipulate them according
to the algorithms. When the computer program is executed, it causes
the numbers and symbols to be modified in the way specified by the
scientific laws. It thereby allows the consequences of the laws to be
Executing a computer program is much like performing an experiment. Unlike the physical objects in a conventional experiment,
however, the objects in a computer experiment are not bound by the
laws of nature. Instead they follow the laws embodied in the computer
program, which can be of any consistent form. Computation thus extends the realm of experimental science: it allows experiments to be
performed in a hypothetical universe. Computation also extends theoretical science. Scientific laws have conventionally been constructed in
terms of a particular set of mathematical functions and constructs, and
they have often been developed as much for their mathematical simplicity as for their capacity to model the salient features of a phenomenon. A scientific law specified by an algorithm, however, can have any
consistent form. The study of many complex systems, which have resisted analysis by traditional mathematical methods, is consequently
being made possible through computer experiments and computer
models. Computation is emerging as a major new approach to the science, supplementing the long-standing methodologies of theory and
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Rendering of the text (15 min)
Acta Mathematica Academiae Scientiarum
Hungaricae Tomus 26 (1–2), (1975), 41–52.
This paper contains two main results. The first one coincides
with the title, the second consists in a description of free inverse semigroups (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
equivalent words, we give a canonical form of the words). Certain corollaries with properties of free inverse semigroups follow.
All results of the paper were reported by the author at a meeting
of the semin-nar "Semigroups" in Saratov State University on October
21, 1971.
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
Let F£x denote the free inverse semigroup with the set X of free
generators. A monogenic free inverse semigroup will be denoted F£1.
Time and then we will write F£ instead of F£x. We do not consider F£∅
a one-element inverse semigroup.
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
1. The headline of the article, the author of the article, where
and when the article was published
The article is headlined...
The headline of the article I have read...
The article is entitled...
The headline of the article is...
The author of the article is...
The article is written by...
It was published in ...(newspaper) on...(date) (on May 23d, 2003)
It was printed in...
The article under the title... was published in ... on ...
2. The main idea of the article
The main idea of the article is...
Basically, the article is about...
The article is devoted to the problem of...
The article touches upon...
The article dwells upon...
The article tells the readers about...
The author discusses an important problem of...
The purpose of the article is to give the reader some information
The aim of the article is to provide the reader with some material
(data) on...
3. The contents of the article (some facts, figures)
The author starts by telling the reader that...
The author writes (states, stresses, thinks, points out) that...
The author highlights the fact that...
The author focuses on the fact that...
According to the text...
Further the author reports (says) that...
The article goes on to say that...
In conclusion...
The author comes to the conclusion that...
4. Your opinion on the article, your attitude towards it
I find the article interesting, important, useful, informative, upto-date, disputable, dull, of no value, too hard to understand... On reading the article I realize the fact that…
Additional task
Reproduce the text in your own words
Differential equations give adequate models for the overall properties of physical processes such as chemical reactions. They describe,
for example, the changes in the total concentration of molecules: they
do not, however, account for the motions of individual molecules.
These motions can be modelled as random walks: the path of each
molecule is like the path that might be taken by a person in a milling
crowd. In the simplest version of the model the molecule is assumed to
travel in a straight line until it collides with another molecule; it then
recoils in a random direction. All the straight-line steps are assumed to
be of equal length. It turns out that if a large number of molecules are
following random walks, the average change in the concentration of
molecules with time can in fact be described by a differential equation
called the diffusion equation.
There are many physical processes, however, for which no such
average description seems possible. In such cases differential equations
are not available and one must resort to direct simulation. The motions
of many individual molecules or components must be followed explicitly; the overall behavior of the system is estimated by finding the average properties of the results. The only feasible way to carry out such
simulations is by a computer experiment: essentially no analysis of the
systems for which analysis is necessary could be made without the
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Speak on the topic
1. Read and translate the text
Topic 1
A modern view of geometry
For a long time geometry was intimately tied to physical space,
actually beginning as a gradual accumulation of subconscious notions
about physical space and about forms, content, and spatial relations of
specific objects in that space. We call this very early geometry "subconscious geometry". Later, human intelligence evolved to the point
where it became possible to consolidate some of the early geometrical
notions into a collection of somewhat general laws or rules. We call
this laboratory phase in the development of geometry "scientific geometry". About 600 B.C. the Greeks began to inject deduction into geometry giving rise to what we call "demonstrative geometry".
In time demonstrative geometry becomes a material-axiomatic
study of idealized physical space and of the shapes, sizes, and relations
of idealized physical objects in that space. The Greeks had only one
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.
At the end of the last century, Hilbert and others formulated the
concept of formal axiomatics. There developed the idea of branch of
mathematics as an abstract body of theorems deduced from a set of
postulates. Each geometry became, from this point of view, a particular
branch of mathematics.
In the twentieth century the study of abstract spaces was inaugurated and some very general studies came into being. A space became
merely a set of objects together with a set of relations in which the objects are involved, and a geometry became the theory of such a space.
The boundary lines between geometry and other areas of mathematics
became very blurred, if not entirely obliterated.
There are many areas of mathematics where the introduction of
geometrical terminology and procedure greatly simplifies both the understanding, and the presentation of some concept or development. The
best way to describe geometry today is not as some separate and prescribed body of knowledge but as a point of view – a particular way of
looking at a subject. Not only is the language of geometry often much
simpler and more elegant than the language of algebra and analysis, but
it is at times possible to carry through rigorous trains of reasoning in
geometrical terms without translating them into algebra or analysis. A
great deal of modern analysis becomes singularly compact and unified
through the employment of geometrical language and imagery.
2. Retell the text
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
1. Read and translate this text
Topic 2
N.L. Lobachevsky
Non-Euclidean geometry has developed into an extremely useful
instrument for application in the physical world.
After 1840 Lobachevsky published a number of papers on convergence of infinite series and the solution of defined integrals. In
modern books on defined integrals about 200 integrals was solved by
N.I. Lobachevsky was born in 1792 in Nizhny Novgorod. After
his father death in 1797 the family moved to Kazan where Lobachevsky graduated from the University. He stayed in Kazan all his
life occupying the position of dean of the faculty of Physics and
Mathematics and rector of the University. He lectured on mathematics,
physics and astronomy.
Lobachevsky is the creator of non-Euclidean geometry. His first
book appeared in 1829. Few people took notice of it. Non-Euclidean
geometry remained for several decades an obscure field of science.
Most mathematicians ignored it. The first leading scientist who realized
its full importance was Riemann.
There is one axiom of Euclidean geometry. This is the famous
postulate of the unique parallel, which states that through any point not
on a given line one and only one line can be drawn parallel to the given
line. It goes without saying that there are many lines through a point,
which do not intersect a given line within any distance, however large.
So, this axiom can never be verified by experiment. All the other axioms of Euclidean geometry have a finite character since they deal with
finite portions of lines and with plane figures of finite extent. The fact
that the parallel axiom is not experimentally verifiable raises the question of whether or not it is independent of the other axioms. If it were a
necessary logical consequence of the other, then "it would be possible
not to regard it as an axiom and to give a proof of it in terms of the
other Euclidean axioms. For centuries mathematicians have tried to
find such a proof and in the long run were appeared that the parallel
postulate is really independent of the others.
What does the independence of the parallel postulate mean?
Simply that it is possible to construct a consistent system of geometrical statements dealing with points and lines, by deduction from a set of
axioms in which the parallel postulate is replaced by a contrary postulate. Such a system is called non-Euclidean geometry.
Lobachevsky settled the question by constructing in all detail a
geometry in which the parallel postulate does not hold.
An extraordinary woman, Sofia Kovalevskaya was not only a
great mathematician, but also a writer and advocate of women's rights
in the 19th century. It was her struggle to obtain the best education
available which began to open doors at universities to women. In addition, her ground-breaking work in mathematics made her male counterparts reconsider their archaic notions of women's inferiority to men
in such scientific arenas.
Sofia Kovalevskaya was born in 1850. As the child of a Russian
family of minor nobility, Sofia was raised in plush surroundings. She
was not a typically happy child, though. She felt very neglected as the
middle child in the family of a well admired, first-born daughter, Anya,
and of the younger male heir, Fedya. For much of her childhood she
was also under the care of a very strict governess who made it her personal duty to turn Sofia into a young lady. As a result, Sofia became
fairly nervous and withdrawn – traits which were evident throughout
her lifetime.
Sofia's exposure to mathematics began at a very young age. She
claims to have studied her father's old calculus notes that were papered
on her nursery wall in replacement for a shortage of wallpaper. Sofia
2. Retell the text
Additional text (Topic 2)
Read and translate this text
Sofia Kovalevskaya
January 15, 1850 – February 10, 1891
Kovalevskaya Stamps issued in 1951 and 1996.
Written by Becky Wilson, Class of 1997 (Agnes Scott College)
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
credits her uncle Peter for first sparking her curiosity in mathematics.
He took an interest in Sofia and found time to discuss numerous abstractions and mathematical concepts with her. When she was fourteen
years old she taught herself trigonometry in order to understand the
optics section of physics book that she was reading. The author of the
book and also her neighbor, Professor Tyrtov, was extremely impressed with her capabilities and convinced her father to allow her to
go off to school in St. Petersburg to continue her studies.
After concluding her secondary schooling, Sofia was determined
to continue her education at the university level. However, the closest
universities open to women were in Switzerland, and young, unmarried
women were not permitted to travel alone. To resolve the problem
Sofia entered into a marriage of convenience to Vladimir Kovalevsky
in September 1868. The couple remained in Petersburg for the first few
months of their marriage and then travelled to Heidelburg where Sofia
gained a small fame. People were enthralled by the quiet Russian girl
with an outstanding academic reputation.
In 1870, Sofia decided that she wanted to pursue studies under
Karl Weierstrass at the University of Berlin. Weierstrass was considered one of the most renowned mathematicians of his time, and at first
he did not take Sofia seriously. Only after evaluating a problem set he
had given her did he realize the genius at his hand. He immediately set
to work privately tutoring her because the university still would not
permit women to attend. Sofia studied under Weierstrass for four years.
She is quoted as having said, "These studies had the deepest possible
influence on my entire career in mathematics. They determined finally
and irrevocably the direction I was to follow in my later scientific
work: all my work has been done precisely in the spirit of Weierstrass".
At the end of her four years she had produced three papers in the hopes
of being awarded a degree. The first of these, "On the Theory of Partial
Differential Equations," was even published in Crelle's journal, a tremendous honor for an unknown mathematician.
In July of 1874, Sofia Kovalevskaya was granted a Ph.D. from
the university of Gottingen. Yet even with such a prestigious degree
and the help of Weierstrass, who had grown quite fond of his pupil, she
was not able to find employment. She and Vladimir decided to return
to her family in Palobino. Shortly after her return home, her father died
unexpectedly. It was during this period of sorrow that Sofia and
Vladimir fell in love. Their marriage produced one daughter. While at
home, Sofia neglected her work in mathematics but instead developed
her literary skills. She tried her hand at fiction, theater reviews, and
science articles for a newspaper.
In 1880, Sofia returned to work in mathematics with a new fervor. She presented a paper on Abelian integrals at a scientific conference and was very well received. Once again she was faced with the
dilemma of finding employment doing what she loved most – mathematics. She decided to return to Berlin, also home to Weierstrass. She
was not there long before she learned of Vladimir's death. He had
committed suicide when all of his business ventures had collapsed.
Sofia's grief threw her into her work more passionately than ever.
Then, in 1883, Sofia's luck took a turn for the better. She received an invitation from an acquaintance and former student of Weierstrass, Gosta Mittag-Leffler, to lecture at the University of Stockholm.
In the beginning it was only a temporary position, but at the and of a
five year period, Sofia had more than proved her value to the university.
Then came a series of great accomplishments. She gained a tenured
position at the university, was appointed an editor for a mathematics
journal, published her first paper on crystals, and in 1885, was also appointed Chair of Mechanics. At the same time, she co-wrote a play,
"The Struggle for Happiness," with her friend, Anna Leffler.
In 1887, Sofia again received devastating news. The death of her
sister, Anya, was particularly hard on Sofia because the two had always
been very close. Fortunately, it was not long afterward that Sofia
achieved "her greatest personal triumph". In 1888, she entered her paper, "On the Rotation of a Solid Body about a Fixed point," in a competition for the Prix Bordin by the French Academy of Science and
won. "Prior to Sofia Kovalevsky's [Sofia Kovalevskaya] work the only
solutions to the motion of a rigid body about fixed point had been developed for the two cases where the body is symmetric". In her paper,
Sofia developed the theory for an unsymmetrical body where the center
of its mass is not on an axis in the body. The paper was highly regarded
that the prize money was increased from 3000 to 5000 francs.
Also at this time, a new man entered her life. Maxim Kovalesky
came to Stockholm for a series of lectures. There he met Sofia, and the
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
two had a scandalous, rocky affair. The basic problem was that they
were both too passionate about their work to give it up for the other.
Maxim's work took him away from Stockholm and he wanted Sofia to
give up her hard-earned positions to simply be his wife. Sofia flatly
rejected such an idea but still could not bear the loss of him. She remained in France with him for the summer and fell into another one of
her frequent depressions. Again, she turned to her writing. While she
was in France, she finished Recollections of Childhood.
In the fall of 1889, she returned to Stockholm. She was still miserable at the loss of Maxim even though she frequently travelled to
France to visit him. She eventually became ill with depression and
pneumonia. On February 10, 1891, Sofia Kovaleskaya died and the
scientific world mourned her loss. During her career she published ten
papers in mathematics and mathematical physics and also several literary works. Many these scientific papers were ground-breaking theories
or the impetus for future discoveries. There is no question that Sofia
Krukovsky Kovalevskaya was an incredible person. The President of
the Academy of Sciences, which awarded Sofia the Prix Bordin, once
said: "Our co-members have found that her works bear witness not
only to profound and broad knowledge, but to mind of great inventiveness".
1. Read and translate the text
Topic 3
The Nature of Mathematics
Mathematics reveals hidden patterns that help us understand the
world around us. Now much more than arithmetic and geometry,
mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction,
and proof; and with mathematical models of natural phenomena, of
human behavior, and of social systems.
As a practical matter, mathematics is a science of pattern and order. Its domain is not molecules or cells, but numbers, chance, form,
algorithms, and change. As a science of abstract objects, mathematics
relies on logic rather than on observation as its standard of truth, yet
employs observation, simulation, and even experimentation as means
of discovering truth.
The special role of mathematics in education is a consequence of
its universal applicability. The results of mathematics – theorems and
theories – are both significant and useful; the best results are also elegant and deep. Through its theorems, mathematics offers science both a
foundation of truth and a standard of certainty.
In addition to theorems and theories, mathematics offers distinctive modes of thought which are both versatile and powerful, including
modeling, abstraction, optimization, logical analysis, inference from
data, and use of symbols. Experience with mathematical modes of
thought builds mathematical power – a capacity of mind of increasing
value in this technological age that enables one to read critically, to
identify fallacies, to detect bias, to assess risk, and to suggest alternatives. Mathematics empowers us to understand better the informationladen world in which we live.
During the first half of the twentieth century, mathematical
growth was stimulated primarily by the power of abstraction and deduction, climaxing more than two centuries of effort to extract full
benefit from the mathematical principles of physical science formulated by Isaac Newton. Now, as the century closes, the historic alliances of mathematics with science are expanding rapidly; the highly
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
developed legacy of classical mathematical theory is being put to broad
and often stunning use in a vast mathematical landscape.
Several particular events triggered periods of explosive growth.
The Second World War forced development of many new and powerful methods of applied mathematics. Postwar government investment
in mathematics, fueled by Sputnik, accelerated growth in both education and research. Then the development of electronic computing
moved mathematics toward an algorithmic perspective even as it provided mathematicians with a powerful tool for exploring patterns and
testing conjectures.
At the end of the nineteenth century, the axiomatization of
mathematics on a foundation of logic and sets made possible grand
theories of algebra, analysis, and topology whose synthesis dominated
mathematics research and teaching for the first two thirds of the twentieth century. These traditional areas have now been supplemented by
major developments in other mathematical sciences – in number theory,
logic, statistics, operations research, probability, computation, geometry, and combinatorics.
In each of these subdisciplines, applications parallel theory.
Even the most esoteric and abstract parts of mathematics – number
theory and logic, for example – are now used routinely in applications
(for example, in computer science and cryptography). Fifty years ago,
the leading British mathematician G.H. Hardy could boast that number
theory was the most pure and least useful part of mathematics. Today,
Hardy's mathematics is studied as an essential prerequisite to many
applications, including control of automated systems, data transmission
from remote satellites, protection of financial records, and efficient algorithms for computation.
In 1960, at a time when theoretical physics was the central jewel
in the crown of applied mathematics, Eugene Wigner wrote about the
"unreasonable effectiveness" of mathematics in the natural sciences:
"The miracle of the appropriateness of the language of mathematics for
the formulation of the laws of physics is a wonderful gift which we
neither understand nor deserve." Theoretical physics has continued to
adopt (and occasionally invent) increasingly abstract mathematical
models as the foundation for current theories. For example, Lie groups
and gauge theories – exotic expressions of symmetry – are fundamental
tools in the physicist's search for a unified theory of force.
During this same period, however, striking applications of
mathematics have emerged across the entire landscape of natural, behavioral, and social sciences. All advances in design, control, and efficiency of modern airliners depend on sophisticated mathematical models that simulate performance before prototypes are built. From medical
technology (CAT scanners) to economic planning (input/output models
of economic behavior), from genetics (decoding of DNA) to geology
(locating oil reserves), mathematics has made an indelible imprint on
every part of modern science, even as science itself has stimulated the
growth of many branches of mathematics.
Applications of one part of mathematics to another – of geometry to analysis, of probability to number theory – provide renewed evidence of the fundamental unity of mathematics. Despite frequent connections among problems in science and mathematics, the constant discovery of new alliances retains a surprising degree of unpredictability
and serendipity. Whether planned or unplanned, the cross-fertilization
between science and mathematics in problems, theories, and concepts
has rarely been greater than it is now, in this last quarter of the twentieth century.
2. Retell the text
Additional text (Topic 3)
Read and translate the text
Mathematics is queen
of natural knowledge
Mathematics grew up with civilization as man’s quantitative
needs increased. It arose out of practical and man’s needs. As soon as
man began to count even on his fingers mathematics began. It was the
first of sciences to develop formally. It is growing faster today than in
its early beginnings . New questions are always arising partly from
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
practical problems and partly from pure theoretical problems. In each
generation men have developed new methods and ideas to solve these
Why has mathematics become so impotent in recent years? Can
the new electronic brains solve mathematical problems faster and more
accurately than a person and eliminate the needs for mathematicians?
To answer these questions we need to know what mathematics is
and how it is used. Mathematics is much more than the arithmetic,
which is the science of number and computation. It is algebra, which is
the language of symbols, operations and relations. It is much more than
the geometry, which is the study of shape, size and space. It is much
more than the statistics, which is the science of interpreting data and
graphs. It is much more than the calculus, which is the study of change,
limits, and infinity. Mathematics is all these and more.
Mathematics is a way of thinking and a way of reasoning, where
new ideas are being discovered every day. It is way of thinking that is
used to solve all kinds of problems in the government and industry.
Mathematics method is reasoning of the highest level known to man
and every field of investigation – be it law, politics, psychology, medicine or anthropology – has felt its influence.
There are various ways in which mathematics serves scientific
1. Mathematics supplies a language for the treatment of the
quantitative problems of the physical and social sciences.
2. Mathematics supplies science with numerous methods and
3. Mathematics enables the science to make predictions.
4. Mathematics supplies science with ideas to describe phenomena.
The language of mathematics is precise and concise, it is a language of symbols, that is understood in all civilized nations of the
world. Mathematics style aims at brevity and formal perfections.
The student must always remember that the understanding of any
subject in mathematics a clear and define knowledge of what precedes.
This is the reason why the study of mathematics is discouraging to
weak minds.
1. Read and translate the text
Topic 4
Students studies at the faculty of Mathematics
Last year I passed my entrance exams successfully, and entered
Omsk State University, which was founded in 1974. Now I am a second year student at the faculty of mathematics. The faculty of mathematics is one of the largest in our university, It trains research workers,
school teachers and instructors for higher school, and technical schools.
So the graduates of the faculty work in different branches of industry,
research laboratories, computer centers and educational establishments.
There are 7 chairs in the faculty: the chair of mathematical
analysis, the chair of mathematical modeling, the chair of methods of
teaching, the chair of algebra, the chair of logic and logical programming, the chair of applied mathematics and the new chair of informational systems.
The teaching staff of our faculty is highly qualified. 8 doctors of
sciences and many candidates of sciences work there.
The academic year is divided into 2 terms. At the end of each
term students have their credit tests and take their terminal exams. State
scholarship is paid to the advanced students. At the end of the course of
studies students are to submit a graduation paper and pass their final
state examinations.
The full university course lasts 5 years. During this period of
time the maths students take 3 years of general courses followed by 2
year of specialized training in some special fields of mathematics. The
main aim of the first stage of the mathematics program is to provide a
broad and solid foundation for professional knowledge. The curriculum
is rather wide and versatile.
The math students study general education subjects, such as philosophy, political economy, foreign languages and so on. All the students study modern computers and the way of using them in different
kinds of calculations. They spend a lot of time in the well-equipped
labs of the faculty operating with computers and compiling programs.
The syllabus also offers a wide range of specialized courses. Acquiring
skills in research is the major goal of the final stage of the mathematics
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
The student does research mainly for his graduation paper,
which reflects the knowledge and practical skills; he has gained in his
special field. It is, as a rule, a small research project carried out by the
student under the guidance of a supervisor. Then the student submits
his graduation paper and defends it before an examination board. If he
does this with honors he may be recommended to take postgraduate
2. Retell the text
1. Read and translate the text
Topic 5
20th century mathematics
Twentieth-century mathematics is highly specialized and abstract. The advance of set theory and discoveries involving infinite sets,
transfinite numbers, and purely logical paradoxes caused much concern as to the foundations of mathematics. In addition to purely theoretical developments, devices such as high-speed computers influenced
both the content and the teaching of mathematics. Among the areas of
mathematical research that have been developed in the 20th century are
abstract algebra, non-Euclidean geometry, abstract analysis, mathematical logic, and the foundations of mathematics.
Modern abstract algebra includes the study of groups, rings, algebras, lattices, and a host of other subjects developed from a formal,
abstract point of view. This approach formed the cornerstone of the
work of a group of mathematicians called Bourbaki. Bourbaki uses abstract algebra in an axiomatic framework to develop virtually all
branches of higher mathematics, including set theory, algebra, and general topology.
The significance of non-Euclidean geometry was realized early
in the 20th century when the geometry was applied in mathematical
physics. It has come to play an essential role in the theory of relativity.
Another area of mathematics, abstract analysis, has produced
theories of the derivatives and integrals in abstract and infinitedimensional spaces. There are many areas of special interest in the field
of abstract analysis, including functional analysis, harmonic analysis,
families of functions and so on.
The most notable development in the area of logic began in the
20th century with the work of two English logicians and philosophers,
Bertrand Russell and Alfred North Whitehead. The object of their
three-volume publication, "Prinseipia Mathematical” was to show that
mathematics can be deduced from a very small number of logical principles.
The foundations of mathematics have many "schools". At the
turn of the century, David Hilbert was determined to preserve the powerful methods of transfinite set theory and the use of the infinite in
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
mathematics, despite apparent paradoxes and numerous objections (see
Hilbert). His program was virtually abandoned in the 1930s when Kurt
Godel demonstrated that for any general axiomatic system there are
always theorems that cannot be proved or disproved (see Godel).
Hilbert's followers, known as formalists, view mathematics in
terms of abstract structures. The oldest philosophy of mathematics is
usually ascribed to Plato. Platonism asserts the existence of eternal
truths, independent of the human mind. In this philosophy the truths of
mathematics arise from an abstract, ideal reality.
2. Retell the text
1. Read and translate the text
Topic 6
Algebra from arabic means the reunion of broken parts. The
branch of mathematics, which deals in the most general way with properties and relations of numbers. The first known use of the word is in
the title of a book by Muhammad ibn-Musa al-Khwarizmi, one of the
most important Arab mathematicians of the 9-th century. The story of
algebra begins from 1800 B.C. when any problem that we should now
solve by algebra was solved by guessing or by some cumbersome
arithmetic process. Then Alexandrian school had appeared and geometric method was in use. In the 3rd century mathematicians began to use
symbols to write an equation. And in 17th century algebra already allows us the equation ax2+bx+c=0.
Algebra is a generalization of arithmetic. Each state of arithmetic
deals with particular numbers.
The square of the sum of any two numbers a and b can be computed by the rule (a+b)2 = a +2ab+b. This is a general rule which remains true no matter what particular numbers may replace the symbols
a and b. A rule of this kind is often called a formula. Algebra is the system of rules concerning the operations with numbers. The operations of
addition, subtraction, multiplication, division, raising to a power are
called algebraic expressions. Algebraic expressions consisting of more
than one term are called multinomials.
Algebra is the base of modern science, so formulas and expressions are widely used not only in mathematics but also in physics,
chemistry, biology and others. Many branches of science need to handle formulas and expressions automatically. That's why computer algebra is the rapidly developed branch of algebra
For numerical calculations the digital computer is now thoroughly established as a device that can greatly ease the human burden
of work. It is less generally appreciated that there are computer programs equally well adapted to the manipulation of algebraic expressions. Algebraic programs have three advantages over purely numerical
ones. First it is frequently more economical of computer time to simplify an expression algebraically before evaluating it numerically. Sec26
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
ond, unlike the numerical approximations generated by a computer,
algebraic answers are exact. The third and perhaps the most important
advantage is that the goals of scientific investigation are often better
served by a result in algebraic form.
The algebra developing history shows that algebra is gradually
transforming in many other branches of science that have their own
2. Retell the text
Wording of mathematics formulae
u = x2
F = m*a
U= 1/(1+x2)
½ bh
y = 1 + cosx
– a half , one half
– [ou], zero [‘zirou]
– plus
– minus
– multiplication sign
– round brackets
– a prime
– a second prime; a double prime; a
twice dashed
– F sub one; F first
– F sub two; F second
– a multiplied by b prime
– x square; x squared; x to the second
power; x raised to the second power; the
square of x; the second power of x;
– y cube; y cubed; y to the third
(power); y raised to the third power; the
cube of y; the third power of y;
– z to minus tenth (power)
– constant
– x is greater than 0
– x is less than 0
– a is equal to x
– u is equal to(equals) x square
– force is equal to mass multiplied by
acceleration; F is equal to m multiplied
by a
– u is equal to the ratio of one to one
plus x square
– half of the reoduct bh
– y is equal to one plus cosine x
– sub n tends to A
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
q = m`/n`
q = nm`/N
y = f(x)
u = f(x) – a0 + a1 x +
+ a2 x2+…an xn
d2 = (y1 – y2)2
x2 + 2n –3 = f(x)
log x
– q is equal to m prime divided by n
– q is equal to n multiplied by m prime
divided by N
– y is a function of x
– u is a function of x is equal to a sub 0
ou plus a sub one more one multiplied
by x plus a sub two multiplied by x to
the 2nd power plus a sub multiplied by x
to the n-th power
– d square is equal to, round brackets
opened, y sub one minus y sub two,
round brackets closed, square
– x square plus two multiplied by n minus three is a function of x
– first derivative of s with to x
– corresponds to the Russian ln x
ADDITION: Words and words combinations used in texts
approx (approximately)
bring down
common denominator
deal with
decimal fraction
decimal place
decimal point
dependent variable
depth of an element
общий знаменатель
имеющий кубовидную форму
иметь дело с
десятичная дробь
десятичный разряд
запятая в десятичном числе
зависимая переменная
высота элемента
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
improper fraction
in column
irrational expression
it turns out
like sings
literal coefficient
LCD (lowest common
by means of
mixed number
множитель, фактор
дробь, дробная часть
график, диаграмма
неправильная дробь
целое число
менять порядок, переставлять
иррациональное выражение
подобные знаки
буквенный коэффициент
определять, назначать место
общий наименьший знаменатель
при помощи
смешанное число
a needed level
number names
number of places
number system
place over
by point
positional notation
positive and negative
rational expression
repeated decimal
reverse order
необходимый уровень
название чисел
число разрядов
система чисел
помещать над
часть, доля
позиционное обозначение
положительные и отрицательные
производить, совершать
продукт, произведение
величина, количество
рациональное выражение
сокращать, преобразовывать
соотношение, отношение
повторное десятичное число
обратный порядок
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
right-angled corner
root sign
a set of rules
simultaneous equations
stand for
two times two
two-(three-, four-) place
unlike signs
vertical column
whole number
прямой угол
корень, знак корня
набор правил
знак, символ
система уравнений
трехмерное тело
круг, шар
символизировать, означать
состояние, положение
в три раза
дважды два
двух- (трех-, четырех-) значное
знаки "плюс" и "минус"
вертикальный столбик
целое число
1. The expression consists from one term, like x² or 3x.
2. It can be two dimensional or three dimensional.
3. The ratio of two to three.
4. Axiom, which is proved.
5. It means from Arabic the reunion of broken parts.
6. A rule, like a² – b² = (a + b)(a – b) is often called… how?
7. How is called “x” in equation: (x² + 3x + 2).
8. Action, when A minus B.
9. In Z5 it is “0”and in it is “1”.
10. Square, which has length and width.
11. It also means addition.
Main word: Science which is queen of natural knowledge.
(C.F. Gause)
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Crossword 1
1. Monomial
2. Space
3. Fraction
4. Theorem
5. Algebra
6. Formula
7. Variable
8. Subtraction
9. Unit
10. Rectangle
11. Sum
Crossword 2
1. Monomial
2. Subtraction
3. Rectangle
4. Theorem
5. Algebra
6. Geometry
7. Addition
8. Integer
9. Expression
10. Fraction
11. Sphere
1. Polynomial from one variable.
2. The difference of two or more numbers.
3. Geometric shape that has 4 right-angled corners and where
each 2 parts are equal.
4. Mathematical consolidation that you must prove.
5. The branch of mathematics which studies fields, rings, groups.
6. The branch of mathematics which studies space, shapes, solids.
7. The sum of two or more numbers.
8. Another name of whole number.
9. The operations of addition, subtraction, multiplication, division.
10. The ratio of two numbers: where first number is called numerator, second number is called denominator.
11. Geometric solid.
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Task I
Translate the sentences and state the function of the verb “to
be”, “to have”, “to do”
than sunspots farther to the north or south did. 19. When surfaces meet
along curves or when curves and surfaces meet at points, they do so at
equal angles. 20. It was a long time, probably more than 20 years, before Galileo realized what the medieval writers had always assumed,
namely that there does exist a uniform motion equivalent to any uniformly accelerated motion from rest. A trace of this realization first
appeared as theorem I, that does not employ any mean speed to represent accelerated motion in free fall. 21. At that time many people did
everything but help Galileo. 22. We do not consider the definition entirely satisfactory, however, until we indicate a procedure for determining it effectively after a finite number of operations. 23. The time required to do the work determines the rate of working but has nothing to
do with the amount of work.
1. Numerical solutions of the Navier-Stokes equations have proliferated in the past ten years. The range of these solutions has expanded rapidly and several methods of solution have been developed to
high degrees of sophistication. 2. In what follows we will have to make
use of multi-dimensional spaces and we will have need for the basic
concepts of analytic geometry. 3. Extremal problems have to do with
finding maxima and minima. 4. Before proving a mathematical fact,
one has to discover it, guess it, conjecture it. 5. The sensitivity of the
apparatus required for the test has to be so great that the results so far
are at best inconclusive. 6. The word “set”, “function”, “relation” and
“operation” have mathematical meanings, that are entirely divorced
from their every day meaning. 7. We have no means of finding out
what is the actual magnitude of the force between two bodies during
the impact. 8. The theory in question has received considerable attention recently. 9. Suppose we are to find the mean of several approximate numbers. When one approximate number is to be subtracted from
another, they must both be rounded off at the same place before subtracting. 10. The principal advantage of the integro-differential approach is its ability to confine the numerical computation to the region
of viscous flow. 11. The primary purpose of this work is to demonstrate
the applicability of the integro-differential approach for various types
of viscous flow problems. 12. The purpose of this paper is to describe a
numerical method of solution of the Navier-Stokes equations for timedependent incompressible flow problems. 13. The purpose of the present study is to show how the internal molecular energy may be accounted for in the simulation of a reacting gas. 14. The simplest type of
elastic wave is the longitudinal wave, in which the material is alternately compressed and expanded. 15. The fact remains that liquids do
have tensile strength, and it can be measured. 16. Experiments that he
did describe as having been actually carried out have been repeated and
they work well. 17. Galileo did not, however, describe many such experiments and he did not give his results in numerical form. 18. Sunspots near the equator traveled more rapidly across the face of the sun
1. They promised that they (to bring) us all the necessary books.
2. He did it better than I (to expect) he would. 3. He said that the tractors (to be) there soon. 4. I think it all happened soon after the meeting
(to end). 5. He said that he (can) not do it without my help. 6. The astronomer told us that the Moon (to be) 240,000 miles from the Earth.
7. We asked the delegates whether they ever (to see) such a demonstration. 8. It was decided that we (to start) our work at four o’clock. 9. I
told you that I (to leave) town on the following day. 10. I did not know
that you already (to receive) the letter. 11. The boy did not know that
water (to boil) at 100º. 12. He wanted to know what (to become) of the
books. 13. I was told that the secretary just (to go out) and (to come
back) in half an hour. 14. We were afraid that she not (to be able) to
finish her work in time and therefore (to offer) to help her. 15. He said
we (may) keep the book as long as we (to like). 16. When I called at his
house, they (to tell) me that he (to leave) an hour before. 17. It (to be)
soon clear to the teacher that the new pupil (to cause) much trouble. 18.
I was thinking what a pleasure it (to be) to see my old friend again; I
not (to see) him since my schooldays. 19. I have not yet told them that I
(to get) them those books in the nearest future.
Task II
1. Use the verbs in brackets in appropriate tenses observing the
rules of the sequence of tenses:
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
2. Translate into English observing the rules of the sequence of
1. Я её спросила, почему она так расстроена (upset). 2. Они
сказали нам, что немного выше по реке есть место, где легко перебраться на другой берег. 3. Он обещал, что принесет нам английские книги для домашнего чтения. 4. Я ему сказала, когда пришла
и сколько сделала за это время. 5. Он сказал, что скоро вернется
обратно, и тогда мы напишем вместе программу. 6. Вы знали, что
я больна, почему же вы меня не навестили? 7. Я вам сказала по
телефону, что я её ещё не видела, но надеюсь увидеть её в четверг.
8. Он заявил, что никогда не брал этой книги из библиотеки и что
у него самого есть такая книга. 9. Я не знала, что вы так долго были больны. Мне только вчера сказали, что вы пропустили десять
занятий. 10. Было решено, что мы пойдем в лес за грибами и не
вернемся домой до вечера. 11. Она сказала мне, что у неё не было
времени прочесть эту статью, но она собирается сделать это в ближайшем будущем. 12. Я не знала, что у вас есть маленькая дочка.
13. Он выразил сожаление, что заставил меня ждать так долго, но
добавил, что это была не его вина, так как его задержали на работе.
Task III
1. Translate into English
А.1. Петр закончил первую главу диссертации и сейчас пишет вторую. Он работает над диссертацией уже год. Я думаю, что
к концу будущего года он ее закончит. Обычно аспирант должен
напечатать 2–3 статьи перед защитой. В этом году Петр уже напечатал две статьи. 2. Наконец, почтальон принес письмо. Я жду это
письмо уже несколько недель. Обычно мои родители пишут мне
2–3 письма в месяц. В этом месяце я получил только одно письмо.
3. Вот и ты, наконец, пришел. Я жду тебя уже 20 минут. Каждый
раз ты опаздываешь. 4. Вы написали свой доклад? Сколько дней
вы работаете над ним? – (Я пишу его) с прошлого вторника. Надеюсь, что к следующей субботе я его закончу. 5. Когда она забо39
лела? – Она заболела до того, как мать вернулась из города. 6. Ты
вчера работал над докладом? – Да. Я вчера в шесть часов вечера
занимался в читальном зале. К их приходу я прочитал уже две
главы. 7. Не входите в класс. Студенты сдают сейчас экзамены.
Петров отвечает уже 20 минут. – Он уже ответил на первый вопрос? – Да. Сейчас он отвечает на второй вопрос. 8. Я видел этот
фильм. Он очень интересный. – Когда ты его видел? – (Я видел
его), когда был в командировке два месяца назад. В этом году я
видел много интересных фильмов. Как только я куплю билеты на
новый фильм, я тебе позвоню. 9. Когда вы приехали в Москву? Из
какого города вы приехали? 10. Она уже давно разговаривает по
телефону. Ей уже пора закончить разговор. 11. Вы изучали английский язык до того, как поступили в институт? 12. Вы написали
доклад? – Нет еще. К концу недели я напишу его. Я пишу его
только с прошлого четверга. Завтра в это время профессор Иванов
будет просматривать его. 13. Экзаменаторы только что пришли.
Трое студентов уже готовятся отвечать. 14. Он вернулся домой,
пообедал и стал читать газету. Он читал газету уже 20 минут к тому времени, когда позвонил его друг. 15. Он будет изучать французский язык, как только станет студентом II курса. 16. Ваша сестра много читает по-английски? – О, да. Она прочитала очень
много английских книг. – Скажите, какие книги она прочитала? –
Мне трудно ответить на этот вопрос, так как я не знаю языка и не
читала этих книг. 17. Сегодня пятница. Вы видели Петра на этой
неделе? Да, я видел его в среду. Завтра в пять вечера он будет
ждать вас на работе. 18. Вы вчера были у врача? – Да. – Он вас
принял сразу? – Нет. Я ждал около часа, прежде чем он меня принял.
В.1. Каждый год весной и зимой студенты сдают экзамены.
2. На прошлой неделе мы сдали экзамены по литературе. 3. Весной мы будем сдавать экзамены по четырем предметам. 4. Не входите в ту комнату, там студенты сдают экзамен. 5. Завтра в 10 часов утра я буду сдавать экзамен по истории. 6. Студенты нашей
группы сдали экзамены очень хорошо. 7. Перед тем как мы сдали
экзамен, мы много занимались. 8. К концу месяца мы сдадим экзамены. 9. Если она не выучит эти правила, она не сдаст экзамен.
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
2. Translate into Russian
А.1. Has Sergei come? – Yes, he has. – When did he come? –
He came yesterday. 2. Ring me up later. My father is having a rest after
dinner. 3. My friend has been waiting for you since two o'clock. Why
haven't you come in time? 4. How long have you been translating this
article and how much of it have you translated? 5. I'll have returned
from the library by three o'clock. 6. Don't come to me at five o'clock,
I'll be having an English lesson. 7. When I began to teach at the institute the students in my group had been already studying English for
two years. 8. My friend studies in the library every day. On Sunday we
go to the library together. We read books on medicine, learn English
and translate texts. 9. Have you ever been to the Urals? – Yes, I have.
I`ve been there this year. Rogov was there last year. 10. I'll write this
book in a year if I have more free time. 11. I'll have typed the article
before you come. 12. Have you ever learnt English? 13. Had you learnt
English before you entered the College? 14. By the 1st of September he
will have been working here for 20 years.
В.1. The students take a test in English at the end of the term
every year. 2. I am doing an exercise. (Don't bother me.) 3. I have been
writing this exercise for twenty minutes (since ten o'clock in the morning). 4. I have written this exercise. Please, see if it is right. 5. What
were you doing at this time yesterday? – 1 was writing a letter to my
sister. 6. I have written several letters to my friends this week.7. J. I
had been writing this exercise for an hour when you came to my
place.8. I'll take a test in this subject tomorrow. 9. Tomorrow, at ten
o'clock in the morning we'll be taking a test in this subject. 10. Tomorrow by two o'clock in the afternoon we'll have taken a test in this subject. 11. I had already written a letter to my sister when you came to
my place yesterday. 12. How long will you have been writing the test
before you give it to the teacher? 13. Yesterday I came home, wrote a
letter to my parents, looked through the newspapers and went to bed.
14. I'll send you a letter as soon as I write it.
иностранных языков
английский язык
Экзаменационный билет № 13
1. Translate the Text with dictionary in written form (time 45 minutes).
Computer Software in Science and Mathematics (by Stephen Wolfram)
2. Rendering of the text (15 min)
Free inverse semigroups are not finitely presentable (by B.M. Schein) Acta
Mathematica Academiae Scientiarum Hungaricae Tomus 26 (1–2), (1975),
3. Speak on the topic
Зав. кафедрой
Примечание. Название разговорной темы дается непосредственно
на экзамене. Список тем может дополняться в течение учебного процесса.
Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис»
Introduction ................................................................................................... 3
Part I............................................................................................................... 4
Text 1......................................................................................................... 4
Text 2......................................................................................................... 5
Text 3......................................................................................................... 6
Part II ............................................................................................................. 7
Text............................................................................................................ 7
The plan for rendering the article............................................................... 9
Additional task......................................................................................... 10
Part III.......................................................................................................... 11
Topic 1..................................................................................................... 11
Topic 2..................................................................................................... 13
Additional text (Topic 2) ......................................................................... 14
Topic 3..................................................................................................... 18
Additional text (Topic 3) ......................................................................... 20
Topic 4..................................................................................................... 22
Topic 5..................................................................................................... 24
Topic 6..................................................................................................... 26
Part IV. Wording of mathematics formulae ............................................. 28
Part V. ADDITION: Words and words combinations used in texts............ 30
Crossword 1 ............................................................................................. 34
Crossword 2 ............................................................................................. 35
Answers ................................................................................................... 36
Task I ....................................................................................................... 37
Task II..................................................................................................... 38
Task III .................................................................................................... 39
Ticket’s blanc........................................................................................... 42
для подготовки к экзамену по английскому языку
(для студентов математического факультета I и II курсов)
Технический редактор Н.В. Москвичёва
Редактор О.А. Сафонова
Подписано в печать 31.05.05. Формат бумаги 60х84 1/16.
Печ. л. 2,75. Уч.-изд. л. 2,8. Тираж 150 экз. Заказ 236.
Издательство Омского государственного университета
644077, г. Омск-77, пр. Мира, 55а, госуниверситет
Размер файла
329 Кб
практикум, язык, экземену, английского, 235, подготовки
Пожаловаться на содержимое документа