Практикум для подготовки к экзамену по английскому языку (для студентов математического факультета I и II курсов). Жилина Л.В. - 10 стр.

developed legacy of classical mathematical theory is being put to broad      and gauge theories – exotic expressions of symmetry – are fundamental
and often stunning use in a vast mathematical landscape.                     tools in the physicist's search for a unified theory of force.
       Several particular events triggered periods of explosive growth.             During this same period, however, striking applications of
The Second World War forced development of many new and power-               mathematics have emerged across the entire landscape of natural, be-
ful methods of applied mathematics. Postwar government investment            havioral, and social sciences. All advances in design, control, and effi-
in mathematics, fueled by Sputnik, accelerated growth in both educa-         ciency of modern airliners depend on sophisticated mathematical mod-
tion and research. Then the development of electronic computing              els that simulate performance before prototypes are built. From medical
moved mathematics toward an algorithmic perspective even as it pro-          technology (CAT scanners) to economic planning (input/output models
vided mathematicians with a powerful tool for exploring patterns and         of economic behavior), from genetics (decoding of DNA) to geology
testing conjectures.                                                         (locating oil reserves), mathematics has made an indelible imprint on
       At the end of the nineteenth century, the axiomatization of           every part of modern science, even as science itself has stimulated the
mathematics on a foundation of logic and sets made possible grand            growth of many branches of mathematics.
theories of algebra, analysis, and topology whose synthesis dominated               Applications of one part of mathematics to another – of geome-
mathematics research and teaching for the first two thirds of the twen-      try to analysis, of probability to number theory – provide renewed evi-
tieth century. These traditional areas have now been supplemented by         dence of the fundamental unity of mathematics. Despite frequent con-
major developments in other mathematical sciences – in number theory,        nections among problems in science and mathematics, the constant dis-
logic, statistics, operations research, probability, computation, geome-     covery of new alliances retains a surprising degree of unpredictability
try, and combinatorics.                                                      and serendipity. Whether planned or unplanned, the cross-fertilization
       In each of these subdisciplines, applications parallel theory.        between science and mathematics in problems, theories, and concepts
Even the most esoteric and abstract parts of mathematics – number            has rarely been greater than it is now, in this last quarter of the twenti-
theory and logic, for example – are now used routinely in applications       eth century.
(for example, in computer science and cryptography). Fifty years ago,
the leading British mathematician G.H. Hardy could boast that number               2. Retell the text
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            Additional text (Topic 3)
from remote satellites, protection of financial records, and efficient al-         Read and translate the text
gorithms for computation.
       In 1960, at a time when theoretical physics was the central jewel                                MATHEMATICS
in the crown of applied mathematics, Eugene Wigner wrote about the
                                                                                                                                     Mathematics is queen
"unreasonable effectiveness" of mathematics in the natural sciences:                                                                 of natural knowledge
"The miracle of the appropriateness of the language of mathematics for
the formulation of the laws of physics is a wonderful gift which we                 Mathematics grew up with civilization as man’s quantitative
neither understand nor deserve." Theoretical physics has continued to        needs increased. It arose out of practical and man’s needs. As soon as
adopt (and occasionally invent) increasingly abstract mathematical           man began to count even on his fingers mathematics began. It was the
models as the foundation for current theories. For example, Lie groups       first of sciences to develop formally. It is growing faster today than in
                                                                             its early beginnings . New questions are always arising partly from

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