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Muhtarama Saidova, Bukhara State University Student of the faculty of
Physics, Math
PERIODS OF DEVELOPMENT OF MATHEMATICS
M. Saidova
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 geometry
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 makeseasier 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
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between structures (mathematics, series theory, algebraic topology ),
practical and applied theories, especially mathematical models in physics,
engineering and social sciences. In the last centurydiversity 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
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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.
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 childrenon 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
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20
meAndijan State University named after Z.M.Boburres 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 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
Rajabov Azizbek Norbekvich, Rajabov Hikmatbek Otabek o'g'li Yo'ldosheva
Norjongul Davronbek qizi
IMPROVING LEGAL CULTURE IN SOCIETY
A. Rajabov, H. Rajabov, N. Yo'ldosheva
Abstract: Legal education for the implementation of legal culture in
society the creation of a model, in which the division into stages of legal
education, education continuity and consistency, in its non-repetition
Keywords: society, legal, reform, law, legal consciousness, legal culture,
continuity education, national program, legal education stages.
The future of independent Uzbekistan is humane, democratic and legal
state building. It is economic, social, political, spiritual, cultural in the pursuit
of a great goaland huge historical reforms are underway in the legal field.
All the legal bases for the implementation of reforms have been created,
and these changesthe initiator and chief reformer is also the state. The rule
of law and the rule of law are ours is one of the basic development principles
