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Saidova Muhtarama Bozor qizi
, Bukhara State University, Student of the
faculty of Physics
PERIODS OF DEVELOPMENT OF MATHEMATICS
Saidova M
Abstract: This article provides information about the stages of
development of mathematical science ancient times and the work being
done today to develop the field of mathematics.
Keywords: A.N.Kolmogorov , elementary mathematics , Khwarizmi ,
M.Merson, analytic geometryю
Most mathematicians of history prefer the periodicity of the
development of mathematics recommended by A.N.Kolmogorov. The main
reason for this is tha Kolmogorov’s periodization is based on important
methods , ideas, and results of mathematics. The division of the development
of mathematics into such special periods does not completely solve the
essence of the history of mathematics but will be an additional tool for a
better understanding of the objective laws of mathematical development.
1. The emergence of Mathematics. This period began in the 6
th
century
BC. That is during this period mathematics became an independent science
with its own subject and methods. The beginning of the period dates back to
the earliest period – the primitive community system – collection of
mathematical facts.
2. The period of elementary mathematics (the period of mathematics of
variables). It lasted from the 6
th
to the 5
th
centuries BC to the 17
th
century
BC. During this period great achievements were made in the study of
variables. Mathematics courses taught in secondary schools can give some
idea.
The creation of the science of algebra by the Uzbek scientist Muhammad
ibn Muso al- Khwarizmi (780-850) , the creation of analytical geometry by
Dascartes , the beginning of the development of infinitely small quantities.
In general , the concept of elementary mathematics is difficult to define.
There is no clear definition of it but it is correct to distinguish such a period
in the history of mathematics and it makes easier to study its history.
3. Mathematics of variable quantities. The definitive creation of analytic
geometry begins with the emergence of differential and integral calculus by
I.Newton (1642-1727) and Leibniz (1646-1716). The end of this period goes
back to the end of the 19
th
century. At the same time all the scientific
foundations of mathematics, called classical mathematics were formed.
4.Modern mathematics. It dates back to the mid-19
th
century. This
period is ,characterized by the growing role of mathematical abstraction ,
the widespread use of mathematical modeling in mathematics. It was during
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this period that what I called classical mathematics became much narrower
to apply to itself , to other areas of mathematics. The reason is that
mathematics has split into many branches.
The axiomatic method was widely developed in it . As a result, a new
mathematical concept – a mathematical structure – emerged. The concept of
mathematical structure helps to teach a unit of mathematical facts and
methods that seem too far apart at first glance creates different
mathematical structures. In recent years various branches of mathematics
and even some mathematical subjects have begun to be interpreted as the
material of those structures. Therefore, modern mathematics can be
described as a science of mathematical structures and their models.
Mathematics like all other sciences, is constantly evolving. There are two
reasons for this : first , its development requires daily life and practice.
Second , development is required by the internal needs of mathematics. The
rapid development of mathematics with pictures has a great influence on the
development of technology , economics , production management , as well
as the development of other neighboring disciplines. Mathematics (Greek
thematics, mathema-knowledge science ) is a science of knowledge based
on clear logical observations. In today`s mathematics , calculations, even
operations on formulas, take up very little space. Mathematics in the oldest
branch of science and has a long history of development and at the same
time the answer to the question “What is mathematics?” . Has changed and
deepened. In Greece mathematics is understood as geometry. In the 9
th
and
13
th
centuries the concept of mathematics was expanded by algebra and
trigonometry. From the 17
th
and 18
th
centuries analytical geometry ,
differential and integral calculus became central to mathematics and until
the early 20 th century it was defined as “ the science of quantitative
relations and spatial forms”. In the late 19
th
and 20
th
centuries, various
geometries ( such as Lobachevsky geometry, projective geometry ,
Riemannian geometry ), algebras (Bull algebra, quaternion algebra, Kelly
algebra ), infinitely dimensional spaces, etc. were very diverse in content,
often artificial in nature. As objects began to be studied , the above definition
of mathematics became too narrow. During this period as a result of the
formation of a specific style and language of observation based on
mathematical logic and set theory , the idea emerged in mathematics that
feature is strictly logical observation ( J.Peano, G.Frege, B.Russell, D.Hilbert).
In the mid- 20
th
century a group of French mathematicians and revised
the definition of mathematics under the pseudonym Burbaki developed this
idea and introduced the definition of “Mathematics – the science of
mathematical structures”. Although this approach was broader and more
precise than previous definitions, it was still limited – the relationship
between structures (mathematics, series theory, algebraic topology ),
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177
practical and applied theories, especially mathematical models in physics,
engineering and social sciences. In the last century diversity has a very deep
relationship between different mathematical objects and the results based
on this show that it plays a key role in further development of mathematics.
Along with electronic computing , the expansion of mathematical
applications (biometrics, sociometry, econometrics, psychometry,etc.) and
the rapid penetration of mathematical methods into various spheres of life
have expanded the subject of mathematics beyond comprehension. So
mathematics is axiomatic is a science that studies theories and mathematical
models , the relationships between them and whose conclusions are based
on rigid logical observations. The scholars of the Muslim East also developed
geometry (Thabit ibn Qurra, Abulvafo, Umar Khayyam), the founders of
trigonometry as a science (Ibn al-Haytham, Beruni, Tusi), in particular
Ahmad al-Farghani’s proof of Ptolomy’s theory of steographic projection .
He showed a deep study of geometry at the academy. The wats in which
mathematicians who wrote in Arabic solved third and fourth- order
equations geometrically later led to the creation of analytical geometry.
The Khorezm Mamun Academy (Ibn Iraq , Beruni) also played an
important role in the development of mathematics . The culmination of the
development of Eastern mathematics dates back to the Samarkand Scientific
School. Ulugbek and his scientists (Qozizoda Rumi , Giyosiddin Kashi, Ali
Kushchi, Miram CHalabi, Hussein Birjani,etc.) built a huge observatory , stars
coordinates and precision, as well as methods for calculating the spherical
coordinates of lamps based on the results of observations , interpolation
formulas, a method later called the Gorner scheme and a method of
sequential approximations. There are also tables of trigonometric functions
with high accuracy from the age of Ulugbek “Ziji jadidi Koragoniy”.
From the 17
th
century began a new era in the history of mathematics ,
associated with the name of J.Wallis, I.Kepler, R.Dakart, B.Cavalieri, P.Fermat
, F.Villette and others Pascal. Mathematical definitions are widely
introduced. Has a positive effect on the development of mathematics.
Analytical geometry forms the basis of probability theory , projective
geometry and number theory. During this period mathematics became the
main subject in the newly opened universities had to work with new
problems. Due to the lack of elementary methods in solving such problems,
they began to resort to infinitely repetitive actions. B.Cavalieri used the
“indivisible method” in calculating the volume of rotating bodies. F.Viet
found equality , J.Vallis equated 12,32,52,72 , Mercator found the formula .
At the end of the 17
th
century research in this area led to the creation of
differential and integral calculus was identified as one the complaints. Over
the past period , a number of systematic works have been carried out to
bring mathematics science and education to a new level of quality.
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178
Secondly, a system of incentives for the work of our young people and
their teachers , winners of the International Science Olympiads was
introduced. Thirdly, in order to ensure the integration of higer education
and scientific prohibitions. A new and modern building was built. Founding
for fundamental research in the field of mathematics has been increased by
one and a half times , supercomputers , modern machinery and equipment
have been purchased at the expense of the budget. Fourth, the connection
between scientific research in the field of mathematics and practice and
production remains weak. Further improvement of the system of teaching
mathematics at all stages , support of effective work of teachers, expansion
of the scope and practical significance of scientific research , strengthening
ties with the international community , as well as five priorities for the
development of the Republic of Uzbekistan in 2017-2021 in order to ensure
the implementation of the tasks set out in the state program for the
implementation of the Action Strategy in the “ Year of Science,
Enlightenment and Digital Economy”.
Improving the quality of education in mathematics , developing
scientific research Priorities for the implementation of work and scientific
developments in practice have been identified : Formation of an integrated
system that provides close cooperation between preschool, general
secondary , secondary special , professional , higher education institutions
and research institutions ; Introduction of modern pedagogical technologies
for the formation of the first mathematical concepts in preschool children
on the basis of advanced foreign experience; Teaching mathematics in
general secondary and secondary special education institutions , improving
the quality , teaching mathematics in the regions , development of the
system of training and retraining of personnel in mathematics, especially in
rural ereas , the development of textbooks and manuals on mathematics
Determining talented young people and their math Ensuring successful
participation in local and international science Olympiads and winning
prizes, Creation and implementation of an online education platform ,
improving the effectiveness of distance learning , ensuring the transparency
of the assessment system introduction of mechanisms , increase of lessons
on mathematics and improvement of quality of education in the
corresponding directions and specialties of higher education ;
President of the Republic of Uzbekistan from July 9, 2019 “ Mathematics
education and amendments to the Resolution of Uzbekistan” PP-4387 . “On
measures to radically improve the activities of the Institute of Mathematics
named after Viromanovsky of the Academy of Sciences of the Republic of
Uzbekistan, as well as state support for further development of science”.
National Agency “Uzbekkino”, the National Television and Radio Company
of Uzbekistan , the Ministry of Finance and the Academy of Sciences in
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179
accordance with the decision of President from September 1, 2021, a
monthly bonus of 50 % of the base rate for teachers of specialized schools
will be made, It is planned to submit a draft government resolution on the
procedure for payment to the Cabinet of Ministers of the Republic of
Uzbekistan.
References
1.
N.U.Bikbaeva and the others. “ Methodology of teaching mathematics
in primary school”.Toshkent. “O’qituvchi” 1996
2.
B.Toshmurodov. “ Improving the method of teaching mathematics in
primary school”. Toshkent . “O’qituvchi” 2000
3.
M.E.Jumaev “ Methods of teaching mathematics”. Toshkent 2004
4.
M.Akhmedov and the others “Textbook for math teacher”. Toshkent
“O’qituvchi” 2003
5.
https//uz.m.wikipedia
6.
https//enc.for.uz
7.
https//lex.uz
Seytimbetova Gulbadan Azatovna, Berdak Karakalpak state university
Assistant of the department of Semiconductor physics, faculty of physics
METHODS OF TEACHING PHYSICS FOR NON-PHYSICAL BACHELORS BY THE
METHOD OF "WORKING IN SMALL GROUPS"
G. Seytimbetova
At present, modern teaching methods are widely used in the educational
process. The use of modern teaching methods leads to high efficiency in the
teaching process. When choosing teaching methods, it is advisable to choose
based on the didactic function of each lesson.
While maintaining the traditional form of the lesson, enriching it with
methods that activate the activities of various learners leads to an increase
in the level of mastery of learners. To do this, high efficiency can be achieved
through the rational organization of training, the interest of learners by the
educator, the choice of methods and tools in accordance with the content of
the studied material. The level of mastery, practical skills and competencies
of learners can be developed through interactive or interactive teaching
methods.
Interactive methods are methods that activate students and encourage
independent thinking, which serve to achieve high efficiency in the
educational process in the cooperation of student-student. When these