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The Role of Fundamental Programs in Higher Education Cover Image

Фундаменталната подготовка във висшето образование.
The Role of Fundamental Programs in Higher Education

Author(s): Rosen Nikolaev, Tanka Milkova, Radan Miryanov, Emil Hristov, Sava Grozdev, Veselin Nenkov, Tatiana Madjarova, Maria Shabanova, Larisa Udovenko, Alexander Yastrebov, Alexander Lukankin, Margarita Lambova, Michal Stoyanov, Deyan Mihaylov, Jordan Petkov, Silvia Gospodinova, Vanya Stoyanova, Lyubomir Lyubenov, Svetlana Todorova, Vesela Dimitrova, Slaveya Zhelyazkova, Velina Yordanova, Dimitria Karadimova, Manya Maneva, Julieta MIhaylova, Imrel Nizam
Subject(s): Social Sciences, Economy, Education, National Economy, Business Economy / Management, Energy and Environmental Studies, School education, Adult Education, Higher Education , Human Resources in Economy, ICT Information and Communications Technologies, Sociology of Education, Transport / Logistics, Distance learning / e-learning
ISSN: 2815-3863
Published by: Икономически университет - Варна
Keywords: Fundamental Program; Education; Mathematics; Statistics; Economics
Summary/Abstract: The book is published as a result of the international scientific conference, which took place at 8 November 2024. The scientific forum was organized by “Statistics and Applied Mathematics” Department of University of Economics – Varna.

  • Page Count: 184
  • Publication Year: 2024
  • Language: Bulgarian, Russian
Приложение на математически методи за конструиране на двуфакторен икономически модел

Приложение на математически методи за конструиране на двуфакторен икономически модел
(Application of Mathematical Methods for Constructing a Two-Factor Economic Model)

  • Author(s):Rosen Nikolaev, Tanka Milkova, Radan Miryanov
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education
  • Page Range:11-17
  • No. of Pages:7
  • Keywords:Mathematical Methods; Two-factor economic model
  • Summary/Abstract:In the field of economic science and its manifestations, there is almost no creation of scientific knowledge without the participation of fundamental knowledge in mathematics. A number of branches of mathematics such as linear algebra, analytical geometry, financial mathematics, differential and integral calculus, probability theory, statistics, game theory, mass service theory, stock theory, risk theory and many others are widely used. The aim of this paper is to investigate a two-factor model by applying knowledge of differential calculus of two variables and the method of least squares.
Математически методи за еднозначни (неусловни) решения на адитивни факторни анализи на промените на обемни резултативни величини (продукции) с два фактора в икономиката

Математически методи за еднозначни (неусловни) решения на адитивни факторни анализи на промените на обемни резултативни величини (продукции) с два фактора в икономиката
(Mathematical Methods for Unique (Unconditional) Solutions of Additive Factor Analysis of Changes of Volume Output Values (Product) with Two Factors in Economy)

  • Author(s):Emil Hristov
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education
  • Page Range:18-37
  • No. of Pages:20
  • Keywords:Mathematical methods; Factor analysis
  • Summary/Abstract:The one-valued (unconditional) solutions of additive factor quantities with two factors in the economy are presented. The elementary factor dependence of the production of an individual commodity with the product of two factors was used, where is the price of the commodity (intensive factor), is its natural quantity (extensive factor). For the solution of the additive factor analysis, a simple geometric method is proposed with two rectangles, the areas of which represent the volumes and production of the commodity. The bases of the two rectangles represent the values of the extensive factor and , and the heights of the rectangles represent the values of the intensive factor from the base and reporting periods. True and accurate effects are obtained by multiplying each factor change (the difference between the factor's reporting and base value) by the lesser of the other factor's value from the base or reporting period. The smaller values are determined simply and easily with the suggested elementary but strict mathematical criteria, which are the inequalities between the reported and the base value of each factor. The single-valued solution and elementary mathematical criteria are summarized by the discrete odd function of the mathematical signum. With it, all additive factor analyzes from all areas of life are solved unequivocally.
Обратна функция и обратни тригонометрични функции

Обратна функция и обратни тригонометрични функции
(Inverse Function and Inverse Trigonometric Functions)

  • Author(s):Sava Grozdev, Veselin Nenkov, Tatiana Madjarova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education
  • Page Range:38-50
  • No. of Pages:13
  • Keywords:Inverse function; Inverse trigonometric functions
  • Summary/Abstract:The concept of inverse function is one of the most difficult for students to understand. On the other hand, the introduction of inverse trigonometric functions further complicates the understanding of inverse functions. Therefore, here we have tried to show one way of introducing the concept of an inverse function. At the same time, special attention was paid to obtaining the inverse trigonometric functions.
Методологический аспект проблемы преемственности школьного и вузовского математического образования

Методологический аспект проблемы преемственности школьного и вузовского математического образования
(Methodological Aspect of the Problem of Continuity of School and University Mathematical Education)

  • Author(s):Maria Shabanova, Larisa Udovenko
  • Language:Russian
  • Subject(s):Social Sciences, Education, School education, Higher Education
  • Page Range:51-60
  • No. of Pages:10
  • Keywords:Mathematical education at the university; Тhe problem of continuity; Мethodological aspect;
  • Summary/Abstract:The unresolved problem of continuity of school and university mathematical education is one of the reasons for the expulsion of students from the first courses of those areas of training that provide for the continuation of mathematical education. The complexity of solving this problem is related to its complex nature: the difference in the requirements for the level of mathematics of graduates of secondary schools and university students, the rupture of meaningful links between school and university mathematics courses, the change in the form of the organization of the educational process. The article highlights and reveals another aspect of this problem – the methodological one. The authors present the theoretical foundations and an example of creating methodological conditions that facilitate the student's transition from one form of educational cognition to another.
Об экспериментальном изучении неевклидовых геометрий в процессе подготовки учителей

Об экспериментальном изучении неевклидовых геометрий в процессе подготовки учителей
(On Experimental Study of Non-Euclidean Geometries within Training Teachers)

  • Author(s):Alexander Yastrebov
  • Language:Russian
  • Subject(s):Social Sciences, Education, School education, Adult Education, Higher Education
  • Page Range:61-69
  • No. of Pages:9
  • Keywords:Dynamic geometry system; Experimental study; Instrument; Lobachevskian geometry; Model by Cayley–Klein
  • Summary/Abstract:A set of computer instruments, created by the author within dynamic geometry system GeoGebra, is described. Some special methods of using these instruments are proposed. The instruments help students to create dynamic drawings within the model by Cayley–Klein for discovering some theorems of Lobachevskian geometry.
Образование в XXI веке – пути развития и риски

Образование в XXI веке – пути развития и риски
(Education in the 21st Century – Development Paths and Risks)

  • Author(s):Alexander Lukankin
  • Language:Russian
  • Subject(s):Social Sciences, Education
  • Page Range:70-72
  • No. of Pages:3
  • Keywords:: Education system; System thinking
  • Summary/Abstract:The article presents the authors' point of view on the role and place of fundamental natural mathematical knowledge in modern society. The main idea is the need to review the tasks facing the education system. It is concluded that the creation of moral guidelines, the formation of systemic thinking and knowledge should become priorities.
Компетентностният образователен модел – революционен скок или срутване в бездната на безпаметното невежество?

Компетентностният образователен модел – революционен скок или срутване в бездната на безпаметното невежество?
(The Competence Educational Model - a Revolutionary Leap Or a Crash into the Abyss of Memoryless Ignorance?)

  • Author(s):Margarita Lambova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education
  • Page Range:73-81
  • No. of Pages:9
  • Keywords:Collapse of education; Competency-based education (CBE); PISA; Democratic values; OECD
  • Summary/Abstract:Reasoning and evidence are presented in support of the thesis that the competency education approach, based on a controversial definition of the term "competence", by shifting the focus from personal development to meeting the needs of the global economy by adaptive, unified and culturally disconnected human resources, is not only one of the main reasons for the collapse of education, but it is partly incompatible with democratic values, as it does not create prerequisites for the formation of critically thinking individuals who are free and capable of selfdetermined management of their lives based on their own world, knowledge, attitudes and preferences.
Изследване на осигуреността с търговска мрежа от обекти за продажба на дребно на горива в България

Изследване на осигуреността с търговска мрежа от обекти за продажба на дребно на горива в България
(Study on the Availability of a Commercial Network of Retail Fuel Outlets in Bulgaria)

  • Author(s):Michal Stoyanov
  • Language:Bulgarian
  • Subject(s):Economy, Transport / Logistics
  • Page Range:82-89
  • No. of Pages:8
  • Keywords:Retail trade network; Commercial outlets; Sale of fuels; Fossil fuels
  • Summary/Abstract:The research objective of this work is to keep track of the availability of fuel retail outlets to the Bulgarian population between 2013 and 2022. In parallel, the evolution of the number of registered passenger cars in the country, which should be provided with an appropriate level of fuel retail outlets, is traced. A disproportionate change in the growth of the car fleet is noted, compared to the distribution of fuel retail outlets. The prospects for development in the direction determined by the gradual massification of electric vehicles and the deployment of the infrastructure of alternative charging stations in the country are examined.
Използване на афинни трансформации в средата на MS Excel за повишаване на мотивацията за изучаване на елементи от линейната алгебра

Използване на афинни трансформации в средата на MS Excel за повишаване на мотивацията за изучаване на елементи от линейната алгебра
(Using Affine Transformations in MS Excel to Improve Motivation to Learn Elements of Linear Algebra)

  • Author(s):Deyan Mihaylov
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education
  • Page Range:90-96
  • No. of Pages:7
  • Keywords:Affine Transformation; MS Excel
  • Summary/Abstract:Basic tools of linear algebra are vectors and matrices and operations with them. They are abstract in nature and in many students are not motivated to learn them. To improve motivation in this matter, an application of matrices to affine transformations in the plane is proposed in this paper. An example implemented in the MS Excel environment is presented. It is recommended to use appropriate funny images as transformation objects.
Една практическа задача по аналитична геометрия

Една практическа задача по аналитична геометрия
(A Practical Problem in Analytic Geometry)

  • Author(s):Jordan Petkov, Radan Miryanov
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education
  • Page Range:97-105
  • No. of Pages:9
  • Keywords:Interior point; Triangle; Analytical geometry; Computer graphics
  • Summary/Abstract:The report presents a possible application of the knowledge provided by the fundamental mathematical discipline “Linear Algebra and Analytic Geometry” in solving an informatics problem, more precisely, a Computer Graphics problem. In addition, the given task provides a good opportunity to exercise the theoretical statements related to vectors and an equation of a line in the plane.
Предимства и недостатъци на бета и сигма конвергентния анализ при изследване на структурната конвергенция на икономиките

Предимства и недостатъци на бета и сигма конвергентния анализ при изследване на структурната конвергенция на икономиките
(Advantages and Disadvantages of Beta and Sigma Convergence Analysis in the Study of Structural Convergence of Economies)

  • Author(s):Silvia Gospodinova
  • Language:Bulgarian
  • Subject(s):Economy, National Economy
  • Page Range:106-113
  • No. of Pages:8
  • Keywords:Structural convergence; β&σ convergent analysis
  • Summary/Abstract:Through β and σ convergence analysis, the real convergence in the economies of the European Union can be traced. For this purpose, the main criteria for convergence policies are sought and shown, as well as their results, as this is important for the efficiency and competitiveness of these economies. The task of this type of analysis is to trace the extent to which convergent policies create trends and change policies in individual countries, because sometimes countries take decisions that differ from the single policy of the European Community. When carrying out this type of analysis, it is necessary to know the advantages and disadvantages of each of the methods and indicators for analysis and to assess in the specific situation which is more reliable.
„Загубеното поколение“ в България –изменение и прогноза

„Загубеното поколение“ в България –изменение и прогноза
(“Lost Generation” in Bulgaria – Development and Forecast)

  • Author(s):Vanya Stoyanova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Economy, Education, Human Resources in Economy, Sociology of Education
  • Page Range:114-118
  • No. of Pages:5
  • Keywords:Lost generation; NEET; Adaptive exponential smoothing
  • Summary/Abstract:The report looks at the “lost generation” – those who are not employed and not in education – as a potential opportunity to increase the labor force. The development of this social group for the period 2018 – 2024 is under consideration. A forecast is made using an adaptive exponential smoothing model.
Цената на петрола и външната търговия на България в контекста на фундаменталните икономически изследвания

Цената на петрола и външната търговия на България в контекста на фундаменталните икономически изследвания
(The Oil Price and the External Bulgaria's Trade in the Context of Fundamental Economic Research)

  • Author(s):Lyubomir Lyubenov
  • Language:Bulgarian
  • Subject(s):Social Sciences, Economy, Education, National Economy, Higher Education
  • Page Range:119-125
  • No. of Pages:7
  • Keywords:Elasticity; Energy resourses; Foreign trade; Oil; Regression
  • Summary/Abstract:The objective of this report is to assess the impact of oil price dynamics on Bulgaria's foreign trade using elasticity theory and one-factor linear regression. This involves the use of specific methods that require fundamental knowledge and research experience. Bulgaria's foreign trade was found to be inelastic in general with respect to oil prices. This was explained by the particularities of the period studied, the type of data and the method used. The study provides a good basis for a more in-depth study using the Almon model. Bulgaria's imports of energy resources and crude oil are mainly determined by the oil price. This makes it a significant factor for our economy and suggests that it is determined by factors external to the EU.
Big data в обучението по статистика

Big data в обучението по статистика
(Big Data in Statistics Teaching)

  • Author(s):Svetlana Todorova, Vesela Dimitrova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Economy, Education, Higher Education , ICT Information and Communications Technologies
  • Page Range:126-132
  • No. of Pages:7
  • Keywords:Big Data; Statistical Significance; Effect Size
  • Summary/Abstract:Today businesses and organizations generate and gather data at an increasing pace. The term big data is a catch-phrase, meaning a massive amount of structured, semi-structured and unstructured data. Despite the fact that big data is used in advanced analytics to solve all sorts of problems and make informed decisions, they are extremely difficult to manage, process, and analyze using traditional data-processing tools. This research aims to present the opportunities and challenges of big data. For instance, the huge sample sizes may detect differences that are quite small and trivial. This problem is associated with the relationships among sample size, pvalue, and effect size. To report an effect size is a critical step for scientific studies and may show significant differences according to research types. Despite the challenges, big data presents a great opportunity to gain knowledge of all fields of our life.
Приложение на динамичното времево изкривяване за анализ на сходството във формата на времеви редове

Приложение на динамичното времево изкривяване за анализ на сходството във формата на времеви редове
(Applying Dynamic Time Warping to Analyze Shape Similarities in Time Series Data)

  • Author(s):Slaveya Zhelyazkova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Economy, Education, Business Economy / Management, Higher Education
  • Page Range:133-145
  • No. of Pages:13
  • Keywords:Dynamic time warping; Cluster analysis; dtwclust; Real house price indices
  • Summary/Abstract:The paper explores the potential of dynamic time warping (DTW) to detect shape-based similarities in time series data and assesses its effectiveness for cluster analysis using the "dtwclust" package in R. Theoretical considerations are demonstrated with an empirical analysis of real house price indices for 46 countries, utilizing OECD data spanning 2010–2023. Results indicate that employing DTW significantly influences clustering outcomes, as it enables the detection of shape similarities in time series, even in cases of temporal shifts and asynchronous patterns. This may lead to the identification of fewer clusters compared to standard clustering approaches. Furthermore, the choice of distance measure—Euclidean versus Manhattan—affects the clustering structure, with validity indices suggesting that DTW using Manhattan distance achieves better-defined, more distinct clusters. Comparative analysis with conventional hierarchical clustering highlights consistencies when similar distance metrics are applied.
Съвременни перспективи, възможности и предизвикателства на дистанционното обучение във висшето образование

Съвременни перспективи, възможности и предизвикателства на дистанционното обучение във висшето образование
(Contemporary Perspectives, Opportunities and Challenges of Distance Learning in Higher Education)

  • Author(s):Velina Yordanova, Dimitria Karadimova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education , Distance learning / e-learning
  • Page Range:146-150
  • No. of Pages:5
  • Keywords:Higher education; Opportunities; Distance learning; Perspectives
  • Summary/Abstract:This scientific material examines the modern perspectives and possibilities provided by distance learning in higher education. In view of rapidly developing technologies and changing educational requirements, distance learning is becoming an increasingly important part of the educational process. In this context, the author attempts to systematize and indicate some of the most essential features of distance learning, as well as the opportunities it provides in higher education.
От теоретични знания до практическо приложение: финансовата грамотност в българското училище

От теоретични знания до практическо приложение: финансовата грамотност в българското училище
(From Theoretical Knowledge to Practical Application: Financial Literacy in The Bulgarian School)

  • Author(s):Manya Maneva
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, School education, Higher Education
  • Page Range:151-160
  • No. of Pages:10
  • Keywords:Literacy; Numeracy; Financial literacy; PISA
  • Summary/Abstract:Financial literacy is essential for preparing students to manage their personal finances responsibly and to develop skills that are useful throughout life. The purpose of this article is to demonstrate how financial education can be integrated into the teaching of mathematics, which is a basic science. Early financial education prepares students for the realities of working life, including paying taxes and making investments. This integration of financial education into mathematics not only increases students' financial literacy, but also strengthens their analytical skills, which are essential for successful personal finance management.
Възможности за прилагане на модела на математическото оптимиране в различните сектори на икономиката

Възможности за прилагане на модела на математическото оптимиране в различните сектори на икономиката
(Application of the Mathematical Optimization Model in the Various Sectors of the Economy)

  • Author(s):Julieta MIhaylova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education
  • Page Range:161-166
  • No. of Pages:6
  • Keywords:Mathematical Optimization; Economics; Economic Sectors
  • Summary/Abstract:One of the popular definitions of economics as a science is that it studies human behaviour as a relationship between objectives and scarce resources which have alternative uses. This paper proposes that the suitable formal method for such a research is mathematical optimization. Examples from different sectors of the economy are considered. It may be concluded that mathematical optimization is fundamental to economic theory.
Създаване на линейни модели на икономически процеси: Моделиране на разхода на гориво

Създаване на линейни модели на икономически процеси: Моделиране на разхода на гориво
(Creating Linear Models of Economic Processes: Modelling Fuel Consumption)

  • Author(s):Julieta MIhaylova
  • Language:Bulgarian
  • Subject(s):Social Sciences, Education, Higher Education
  • Page Range:167-171
  • No. of Pages:5
  • Keywords:System of Linear Equations; Аpproximation Мethod; Fuel Consumption
  • Summary/Abstract:Mathematics is a fundamental discipline in higher education. It is essential that students are motivated and that their interest in the material is stimulated so that they can acquire the basic knowledge they need as fully as possible. In this paper, it is argued that presenting the material through practical examples that have applicable solutions would lead to increased student interest.
Методи за оценка на риска на инвестиционен проект за изгражданe на фотоволтаична система

Методи за оценка на риска на инвестиционен проект за изгражданe на фотоволтаична система
(Methods for Assessing the Risk of an Investment Project Built on a Photovoltaic System)

  • Author(s):Imrel Nizam
  • Language:Bulgarian
  • Subject(s):Social Sciences, Economy, Education, Energy and Environmental Studies, Higher Education
  • Page Range:172-183
  • No. of Pages:12
  • Keywords:Risk; Investment projects; Returnability
  • Summary/Abstract:The report examines risk and the management of risk factors in investment projects, with a focus on constructing a photovoltaic system for electricity generation in Bulgaria. The assessment of investment risk is crucial due to the high uncertainty and the scale of capital investments. The project includes identifying risk factors, quantitative measurement, planning management measures, and monitoring the execution of risk-related activities. Various approaches to risk measurement are introduced, including statistical methods such as variance analysis, which allow for assessing deviations in returns and forecasting future income. The report also explains specific risks associated with photovoltaic projects, such as technological risk (equipment and system selection), risks from weather conditions and the nature of solar radiation, financial risks from fluctuations in component prices, and business risk from market fluctuations. To minimize adverse effects, strategies such as monitoring, pre-negotiation with suppliers, and planning emergency actions are suggested.
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