European International Journal of Multidisciplinary Research
and Management Studies
110
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TYPE
Original Research
PAGE NO.
110-113
DOI
OPEN ACCESS
SUBMITED
20 February 2025
ACCEPTED
19 March 2025
PUBLISHED
21 April 2025
VOLUME
Vol.05 Issue04 2025
COPYRIGHT
© 2025 Original content from this work may be used under the terms
of the creative commons attributes 4.0 License.
The Importance of
Mathematical Formulas in
Working with Information
Pulatov Mumin is the son of Muratali
Andijan Institute of Mechanical Engineering, Teacher of the Department
of "Information Technologies", Uzbekistan
Abstract:
This article discusses the importance of
mathematical formulas in working with information
and their application to programming issues. In
particular, it provides detailed information about the
formulas necessary for determining the efficiency of
information
compression,
principal
component
analysis, information classification, and probabilistic
forecasting.
Keywords:
Information, program, formula, Bayes
theorem, coding, encryption, quadratic equation,
algorithm, equation, decoding, entropy.
Introduction:
It is an important task today to focus on
ensuring that future specialists studying in higher
education institutions have thorough professional
training based on modern requirements and become
skilled masters of their profession.
This idea is confirmed by the Resolution of the
President of the Republic of Uzbekistan No. PQ-3775
dated June 5, 2018 "On additional measures to improve
the quality of education in higher educational
institutions and ensure their active participation in the
comprehensive reforms being implemented in the
country."
The more educated and skilled the specialist personnel
are, the more they can contribute to the development
of the country. To do this, they must first have
theoretical knowledge of mathematics, computers, and
various technical knowledge and the skills to apply
them
in
practice.
Mathematical formulas are one of the main tools for
encoding,
analyzing,
and
efficiently
storing
information. Many scientists have contributed to this
field.
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and Management Studies
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European International Journal of Multidisciplinary Research and Management Studies
The following famous scientists have contributed to
this field
1. Claude Shannon
He is known among young people as the founder of
information theory.
He developed information theory, which used
mathematical formulas and algorithms to show how
effective methods can be used to encode and transmit
information.
Shannon's most important work was aimed at ensuring
maximum efficiency in information transmission
through mathematical formulas, which are now used in
computer networks, cryptography, and many other
technological fields.
2. Alan Turing
The concept of the Turing machine and its
mathematical foundations form the theoretical basis of
information processing.
Turing's work is related to solving problems of
automatic information processing and computation, in
particular, the principles and algorithms of computer
operation.
Turing's ideas were greatly influenced by the
development of computer science by expressing them
in the form of mathematical formulas and algorithms.
3. John von Neumann
Von Neumann made significant contributions to the
application of mathematical formulas to information
storage and processing.
He was involved in creating the foundations of
computer architecture and developed mathematical
formulas that allowed these systems to store and
process information efficiently.
4. Andrey Kolmogorov
Kolmogorov is known as the founder of probability
theory and made significant contributions to the
application of probability calculations in the encoding
and transmission of information.
Kolmogorov's
work
is
particularly
useful
in
mathematical modeling of information and noise
problems. These concepts use mathematical formulas
to show which measurements and rules should be used
to transmit information.
5. Donald Knuth
Donald Knuth is a renowned scholar of algorithms and
the
mathematical
foundations
of
computer
programming.
His work, The Art of Computer Programming, covers
mathematical approaches to algorithms and data
structures and is considered the most important guide
to using mathematical formulas to effectively process
information.
6. Niklaus Wirth
Applied mathematical approaches to the creation of
algorithms and programming languages.
He created the Pascal programming language and is
known for his work on optimizing algorithms and
programming languages using mathematical formulas.
7. David Huffman
He created the Huffman coding algorithm, which is
used to encode information in an efficient and
compressed way.
Huffman's formulas are used to increase the efficiency
of information transmission in computer networks.
The work of these scientists has had a significant impact
on the development of mathematics, computer
science, and information technology, and has now
created the ability to efficiently store, encode, and
process information using mathematical formulas and
algorithms.
Today, the rapid development of information and
telecommunications and the resulting spread of
information in various forms to all sectors of society
create the need to perform many operations on them.
The main part of these operations is working with
mathematical formulas.
Formulas present mathematical concepts and
relationships in a concise and clear form, which allows
for quick and efficient processing of information.
Mathematical formulas are needed to perform a
number of operations on information, and one of these
is to summarize data. Formulas can be used to express
large amounts of information in a concise and
understandable way. The goal is to save time and
reduce errors.
Expressing information through mathematical formulas
or equations often helps to describe various systems
and processes in a clear and simplified form.
In particular, the Entropy-based formula for data
compression is of the form
𝐶 = 𝐻(𝑋) ∙ 𝑅
and this formula is used to determine and enhance the
efficiency of information compression. In this formula,
𝐶
represents the compression efficiency,
𝐻(𝑋)
represents the information entropy, and
𝑅
represents
the compression ratio (the ratio of compressed
information to the original information).
The next use case is to analyze this data. Mathematical
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European International Journal of Multidisciplinary Research and Management Studies
formulas are used to simplify data, reduce its size, and
find the main differences between them, as well as to
determine the performance of systems and the
relationships between variables. An example of this is
the formula
𝑍 = 𝑋𝑊
used for principal component analysis.
Here,
𝑍
represents the new indicators (principal
components),
𝑋
represents the original data matrix,
and
𝑊
represents the vectors for the principal
components.
Formulas are used in various fields in optimization and
forecasting processes. For example, in many branches
of economics, physics, and engineering, formulas are
used to predict future outcomes. An example of this is
Bayes' theorem.
Bayes theorem
𝑃(𝐴\𝐵) =
𝑃(𝐵\𝐴) ∙ 𝑃(𝐴)
𝑃(𝐵)
Here:
𝑃(𝐴\𝐵) −
the probability of event
𝐴
given event
𝐵,
𝑃(𝐵\𝐴) −
the probability of event
𝐵
given
event
𝐴,
𝑃
(
𝐴)
and
𝑃(𝐵) −
the separate probabilities of
events
𝐴
and
𝐵.
This theorem is used in statistical analysis and decision-
making, particularly in machine learning. It can be used
to classify information and make probabilistic
predictions.
In information processing, mathematical formulas are
used in algorithms and programming languages. They
make it possible to automate many processes in data
analysis and processing in programming processes.
For example, if we consider the algorithm for finding
solutions to a quadratic function, this function is given
in the form
𝑎𝑥
2
+ 𝑏𝑥 + 𝑐 = 0
The quadratic equation formula can be used to find
solutions to this equation. The general algorithm for
finding solutions to a quadratic equation is as follows.
1.
To determine whether a quadratic equation
has solutions, we calculate the discriminant. The
discriminant is denoted by the letter
𝛥
and is calculated
as follows:
𝛥 = 𝑏
2
− 4𝑎𝑐
2.
Finding solutions based on the value of the
discriminant is performed under the following
conditions:
If
𝛥 > 0,
the equation has two real and distinct
roots.
If
𝛥 = 0,
the equation has one real root.
If
𝛥 < 0,
the equation has no real roots (there
are complex roots).
Of course, these conditions are only valid for
the set of real numbers.
If
𝛥 > 0,
the equation accepts two real values
𝑥
1
and
𝑥
2
as solutions, and they are found by the
following formulas:
𝑥
1
=
−𝑏 + √Δ
2𝑎
,
𝑥
2
=
−𝑏 − √Δ
2𝑎
If
𝛥 = 0,
the equation has a unique solution.
That is:
𝑥 = −
𝑏
2𝑎
If
𝛥 < 0,
there are no real roots. This is because the
expression under the root must always be positive in
the set of real numbers.
When working with information, it is necessary to
encode all data to keep it confidential, or to separate
information of certain types from each other and
encrypt it to perform certain functions on it. This work
can be theoretically calculated using certain
mathematical formulas.
Information encryption is theoretically calculated using
the following formula:
𝐶 = 𝑀
𝑒
𝑚𝑜𝑑
𝑛
Here:
𝐶 −
encrypted message,
𝑀 −
message,
𝑒 −
encryption exponent,
𝑛 −
RSA modulus.
𝑅𝑆𝐴
is an asymmetric encryption algorithm
used to encrypt and decrypt data.
When it is necessary to perform some functions on
encoded information, it is necessary to decode it, and
this can be theoretically calculated using the following
formula:
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and Management Studies
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European International Journal of Multidisciplinary Research and Management Studies
𝑀 = 𝐶
𝑑
𝑚𝑜𝑑
𝑛
Here: d- decoding exponent.
When measuring the maximum transmission rate of a
channel or the maximum transmission rate for a noisy
channel, the following formula is used and it is called
the Shannon-Hartley theorem.
𝐶 = 𝐵 log
2
(1 +
𝑆
𝑁
)
Here,
𝐶 −
maximum channel transmission rate
(number of bits),
𝐵 −
channel width (Hertz),
𝑆 −
signal strength,
𝑁 −
noise strength.
For example: If the channel width
𝐵 = 1000 𝐻𝑧,
signal
power
𝑆 = 10 𝑊,
and noise power
𝑁 = 1 𝑊,
the
maximum transmission rate is calculated as follows:
𝐶 = 1000 log
2
(1 +
10
1
) = 1000 log
2
(11) ≈
1000 × 3.459 = 3459
bit/s
So, from the above examples, we can briefly conclude
that mathematical formulas are used in various fields
such as error detection and correction, system
modeling, and many others. In general, these formulas
are the main tools for correct and efficient processing,
analysis, and forecasting of information. They are
necessary for the formation of knowledge, decision-
making, and the implementation of a systematic
approach.
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