ВУЗ:
Составители:
Рубрика:
23
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
course.
2. Retell the text
24
1. Read and translate the text
Topic 5
20th century mathematics
Twentieth-century mathematics is highly specialized and ab-
stract. The advance of set theory and discoveries involving infinite sets,
transfinite numbers, and purely logical paradoxes caused much con-
cern as to the foundations of mathematics. In addition to purely theo-
retical 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, mathe-
matical logic, and the foundations of mathematics.
Modern abstract algebra includes the study of groups, rings, al-
gebras, 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 ab-
stract algebra in an axiomatic framework to develop virtually all
branches of higher mathematics, including set theory, algebra, and gen-
eral 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 infinite-
dimensional 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 prin-
ciples.
The foundations of mathematics have many "schools". At the
turn of the century, David Hilbert was determined to preserve the pow-
erful methods of transfinite set theory and the use of the infinite in
The student does research mainly for his graduation paper, 1. Read and translate the text
which reflects the knowledge and practical skills; he has gained in his Topic 5
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 20th century mathematics
his graduation paper and defends it before an examination board. If he Twentieth-century mathematics is highly specialized and ab-
does this with honors he may be recommended to take postgraduate stract. The advance of set theory and discoveries involving infinite sets,
course. transfinite numbers, and purely logical paradoxes caused much con-
cern as to the foundations of mathematics. In addition to purely theo-
2. Retell the text retical 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, mathe-
matical logic, and the foundations of mathematics.
Modern abstract algebra includes the study of groups, rings, al-
gebras, 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 ab-
stract algebra in an axiomatic framework to develop virtually all
branches of higher mathematics, including set theory, algebra, and gen-
eral 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 infinite-
dimensional 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 prin-
ciples.
The foundations of mathematics have many "schools". At the
turn of the century, David Hilbert was determined to preserve the pow-
erful methods of transfinite set theory and the use of the infinite in
23 24
Страницы
- « первая
- ‹ предыдущая
- …
- 10
- 11
- 12
- 13
- 14
- …
- следующая ›
- последняя »
