Робоча програма навчальної дисципліни "Університетські студії" 111 «Математика

Мета та завдання 1) забезпечити адаптацію студентів у освітньому середовищі Університету і студенській групі зокрема; 2) ознайомити студентів із основними ідеями лідерства, зокрема лідерства-служіння, з місією Університету в контексті лідерства-служіння; 3) сприяти розвиненню мотивації та успішній професійній адаптації майбутніх математиків/учителів математики шляхом ознайомлення їх із місцем математики у різних сферах життєдіяльності людини і суспільства, специфікою професійної діяльності, професійними спільнотами. - У результаті вивчення навчальної дисципліни студент повинен ознайомитись з правилами «студентського життя» в Університеті; усвідомити свою роль і місце в освітньому середовищі Університету; знати: - предмет науки «Математика» та основні методи математичних досліджень; - найвизначніші математичні відкриття, імена видатних вчених математиків, у їх числі й українських; - взаємозв’язок математики з іншими галузями науки, життєдіяльностю суспільства; - суть методу математичного моделювання; - роль математичної освіти, специфіку професії математика/вчителя математики; - початкові відомості про професійні спільноти та фахові видання; - найвідоміші математичні задачі минулого і сучасності вміти: - користуватись бібліотекою, підібрати і реферувати наукову, науково-популярну літературу на задану тему; - презентувати свою реферативну роботу; - пояснити роль математики у сучасному світі; - обґрунтувати свій вибір професії

Monitoring the quality of education as a management tool for changes in higher educational institution

The purpose of this article is to elaborate means of intellectualizing management of changes in higher educational institutions, analysis of monitoring components as one of the tools for managing system of higher education, identifying problems of its organization and implementation. In the course of the research, we used the following methods: the method of expert assessments; document analysis; analysis of structural divisions work experience; sociological methods: observation, questioning. Every higher educational institution depending to their self-organization creates the internal monitoring model, that is, in any case, an integral system, which, in our opinion, should comprise the following components: purpose; task; requirements; object and subjects, monitoring criteria.Priority in this research is given to "consumer monitorin

Теорія ймовірностей та математична статистика у прикладах і задачах

Навчальний посібник призначений для навчання студентів нематематичних спеціальностей, а також для всіх, хто опановує цей матеріал самостійно, у тому числі і з метою проходження тестування, наприклад, GMA

Students' mathematical training for professional self-realization in a modern, inventive society

In the framework of their professional self-realization on the contemporary job market, the paper explores the issues with professionals' training for mathematics at universities. The structure of students' mathematical proficiency is taken into consideration, and its key elements are substantively presented (the ability to ask and answer questions in and with mathematics, the ability to deal with mathematical language and tools). The initial (ascertaining) step of the pedagogical experiment allowed for the establishment of the level of students' mathematical proficiency and formation in accordance with the predetermined structure. It has been demonstrated that students, both of mathematical and non-mathematical majors, lack the mathematical knowledge and abilities necessary to solve complicated issues, particularly those involving modeling in the context of future professional engagement. The following fundamental strategies for developing students' mathematical competence are supported: research-focused instruction, an interdisciplinary approach with a practical focus, and the use of digital learning environments and related resources. The implementation strategies for these techniques are described in the authors' optional course "Methods of formation of students' mathematical competence for the future successful career" for math specialist students. The research will continue with the introduction of the aforementioned discipline to the educational system, which will include the subsequent assessment of future teachers' readiness to employ the suggested methods in their professional work.In the framework of their professional self-realization on the contemporary job market, the paper explores the issues with professionals' training for mathematics at universities. The structure of students' mathematical proficiency is taken into consideration, and its key elements are substantively presented (the ability to ask and answer questions in and with mathematics, the ability to deal with mathematical language and tools). The initial (ascertaining) step of the pedagogical experiment allowed for the establishment of the level of students' mathematical proficiency and formation in accordance with the predetermined structure. It has been demonstrated that students, both of mathematical and non-mathematical majors, lack the mathematical knowledge and abilities necessary to solve complicated issues, particularly those involving modeling in the context of future professional engagement. The following fundamental strategies for developing students' mathematical competence are supported: research-focused instruction, an interdisciplinary approach with a practical focus, and the use of digital learning environments and related resources. The implementation strategies for these techniques are described in the authors' optional course "Methods of formation of students' mathematical competence for the future successful career" for math specialist students. The research will continue with the introduction of the aforementioned discipline to the educational system, which will include the subsequent assessment of future teachers' readiness to employ the suggested methods in their professional work

Hybrid Study of the Geophysical Situation in the Depressed Zone of Hydroelectric Power Plants Reservoir

The purpose of the study is to research the prospects of joint use of signals caused by standing waves of water bodies when studying the geophysical situation near hydroelectric power plants. The study is preceded by the development of recommendations for the protection of telecommunications. The main variables taken into account in the analysis of standing wave oscillations are considered in detail: amplitude of oscillations and their attenuation, period. The seismic-acoustic method of studying the geophysical situation in the depressive zone of a hydroelectric power station reservoir is modified by supplementing the hybrid seismic-acoustic signal with electromagnetic waves excited by microseismic oscillations. A generalized hybrid study of natural phenomena and anthropogenic events is reduced to the measurement and subsequent analysis of a hybrid signal that has more than one manifestation. Manifestations are determined by the number of signal transmission media, taking into account their physical nature

Multifunctional CRS Encryption Scheme on Isogenies of Non-Supersingular Edwards Curves

A multifunctional cryptosystem RCNIE on isogenies of non-supersingular Edwards curves is proposed, which solves the problems of Diffie-Hellman secret sharing, digital signature, and public key encryption. The problems of choosing the parameters of non-supersingular Edwards curves forming pairs of quadratic twist with orders p + 1 ± t ≡ 0mod8 over a prime field Fp are considered. Encryption algorithms with mutual authentication of Alice and Bob based on the sharing of their secrets are given, while the length of the key and the size of the digital signature are minimally short and do not exceed the size of the field Fp element. An illustration is given of the operation of the cryptosystem model on 4 degrees of isogenies {3,5,7,37} over the field F863 for a pair of quadratic twist curves with orders 840 and 888. It is shown that for non-supersingular curves there are main and dual cryptosystems, each of which has also an isomorphic cryptosystem. This allows you to perform parallel computing and speed up algorithms. A comparative evaluation of the arithmetic and properties of CSIDH and RCNIE is given. It is noted that we have not found strong arguments for the slow implementation of the CRS scheme in comparison with CSIDH. Taking into account the peculiarities of each of them, both schemes are certainly promising

Collaboration in research activities: ICT tools assessment

The article is devoted to the design of high-quality electronic environment of the University in the context of European quality standards in the educational space of universities

Computing of Odd Degree Isogenies on Supersingular Twisted Edwards Curves

An overview of the properties of three classes of curves in generalized Edwards form Ea,d with two parameters is given. The known formulas for the odd degree isogenies on curves Ed with one parameter are generalized to all classes of curves in Edwards form, and Theorem 1 on the isogenic mapping of the points of these curves is proved. The analysis of the known effective method for computing isogenies in Farashahi-Hosseini w-coordinates, justified for the curve Ed, is given. Theorem 2 proves the applicability of this method to the class of twisted Edwards curves. Examples of 3- and 5-isogenies of twisted Edwards curves are given. Methods for bypassing the exceptional points of such curves in PQC cryptosystems like CSIDH are proposed

Modeling CSIKE Algorithm on Non-Cyclic Edwards Curves

An original key encapsulation scheme is proposed as a modification of the CSIDH algorithm built on the isogenies of non-cyclic Edwards curves. The corresponding CSIKE algorithm uses only one public key of the recipient. A brief review of the properties of non-cyclic quadratic and twisted supersingular Edwards curves is given. We use a new scheme for modeling the CSIKE algorithm on isogenies of 4 degrees 3, 5, 7, 11 for p = 9239. In contrast to the CSIDH models of previous works, this scheme does not use precomputations and tabulation of the parameters of isogenic chains, but uses one known supersingular starting curve Ed with the parameter d = 2. Examples of calculations of isogenic chains by Alice and Bob at three stages of CSIKE operation using a randomized algorithm are given. It also proposes to abandon the calculation of the isogenic function ϕ(R) of a random point R, which significantly speeds up the algorithm

Method for Increasing the Various Sources Data Consistency for IoT Sensors

The paper represents importance of performing data consistency operations with data sets, where it is possible and essential. Producing vast amounts of data by the Internet of Things (IoT) devices and sensors, all electronic data must be organized and processed. The approach presented in this paper may help researchers look for new areas of processing data, making it more consistent and reviewing already presented, maybe not so efficient methods. Learning from real-life examples, the efficiency of using smart devices, and the coverage of cellular or global positioning systems show many exciting and inspirational ways to work on science and practical success. This paper aims to create a method for combining data from different sources to obtain the best quality of the resulting data. The paper shows that we continue to increase number of sources to process and operate data, making it essential to process correctly and qualitatively. Researching approaches to make data more consistent and precise will be present almost all tim