Bulletin 1 (50) 2024

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I. Development of a web service for automating the process of professional development for employees of government organizations based on the generation of individual educational routes


Yuriy V. Golchevskiy – Pitirim Sorokin Syktyvkar State University, yurygol@mail.ru

Artem S. Garmatko – LLC “Philosophy IT”, garmatko.art@mail.ru


Abstract. Thе paper presents a study of the problem of creating a web service for automating control over the professional development of employees process using the example of a state agencies working in the field of art and culture. An approach has been used that implies
individual training routes generation containing sets of courses, as a result of which the employee will receive all the necessary competencies. At the same time, the process becomes completely
controlled by the employer, who also has the opportunity to form and/or confirm an individual employee training route and track the progress.

Keywords: professional development, individual educational route, automation, web resource.


  1. Golchevskiy Yu., Novokshonova E., Yermolenko A. Digital economy competencies as a vital necessity of a modern successful specialist. Advances in Economics, Business and Management Research.Vol. 156. Pp. 291–296. DOI: 10.2991/aebmr.k.201205.048.
  2. Galkin O. A. Professional development in the system of lifelong professional education in the sphere of culture: the role and issues of content. Problemy i perspektivy razvitiya vysshego obrazovaniya v sfere kul’tury i iskusstv [Problems and prospects for the development
    of higher education in the field of culture and the arts]. Proc. of the scientific and methodological conference of the educational institution teaching staff. Minsk: The Belarusian State University of Culture and Arts, 2023. Pp. 103–111. EDN: PCPNDH. (In Russ.)
  3. Babikova N. N. Education in the digital age: remember or google. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics]. 2022. No 3 (44). Pp. 33–46. DOI:
    10.34130/1992-2752_2022_3_33. (In Russ.)
  4. Normansky N. S. Gamification as a Mechanism of Digital Transformation of Personnel Training in the Field of Culture and Art. Kul’turnaya zhizn’ Yuga Rossii [Cultural Studies of Russian South].No 1 (84). Pp. 101–110. DOI: 10.24412/2070-075X-2022-1-101-(In Russ.)
  5. Karavaev N. L., Soboleva E. V. Analysis of software services and platforms that have the potential for educational process gamification.Nauchno-metodicheskiy elektronnyy zhurnal «Kontsept» [Scientific and methodological electronic journal “Concept”]. 2017. No 8. Pp. 14–25.
    EDN: ZEGUJZ.(In Russ.)
  6. Golchevskiy Yu. V., Babenko V. V. Problems of gaming technologies introducing into business processes and interfaces of business-oriented software systems. Informatsionnyye tekhnologii v
    modelirovanii i upravlenii: podkhody, metody, resheniya: sbornik nauchnykh statey I Vserossiyskoy nauchnoy konferentsii. 12–14 dekabrya 2017 g.: v 2 ch. [Information technologies in modeling and management: approaches, methods, solutions: collection of scientific articles of the I All-Russian Scientific Conference. December 12–14,
    2017: at 2 a.m.]. Tolyatti: TSU, 2017. Part 2. Pp. 318–324. EDN: YWGOJL. (In Russ.)
  7. Zeybek N., Saygı E. Gamification in Education: Why, Where, When, and How? – A Systematic Review. Games and Culture. 2024. Vol. 19. Issue 2. Pp. 237–264. DOI: 10.1177/15554120231158625.
  8. Oliveira W., Hamari J., Shi L. et al. Tailored gamification in education: A literature review and future agenda. Education and Information Technologies. 2023. Vol. 28. Pp. 373–406. DOI:
  9. Tatarova S. P., Zateeva N. A. Experience of organizing professional upgrading courses of cultural workers as the implementation of informal education principles. Vestnik Vostochno-Sibirskogo gosudarstvennogo instituta kul’tury [Bulletin of the East Siberian State Institute of
    Culture]. 2019. No 3 (11). Pp. 127–133. DOI: 10.31443/2541-8874-2019- 3-11-127-133. (In Russ.)
  10. Dorofeeva E. V. Professional retraining for the cultural sphere of the region: problems and prospects. Obrazovaniye i obshchestvo [Education and Society]. 2019. No 3 (116). Pp. 72–80. EDN: VDEPEQ. (In Russ.)
  11. Novikova T. B. Modeling RUP: Collaboration, class, activity, sequence, use case diagrams. Mezhdunarodnyy zhurnal eksperimental’nogo obrazovaniya [International Journal of
    Experimental Education]. 2017. No 1. Pp. 74–78. EDN: XVGSSD. (InRuss.)
  12. Kochnev A. A. Web Development with PHP and Laravel framework. Vostochno-Yevropeyskiy nauchnyy zhurnal [East European Scientific Journal]. 2023. No 1 (86). Pp. 4–11. EDN: XNGITS. (In Russ.)
  13. Chavan P. R., Pawar S. Comparison Study Between Performance of Laravel and Other PHP Frameworks. International Journal of Research in Engineering, Science and Management. 2021. Vol. 4. Issue 10. Pp. 27–29.
  14. Taipalus T. Database management system performance comparisons: A systematic literature review. Journal of Systems and Software. 2024. Vol. 208. 111872. DOI: 10.1016/j.jss.2023.111872.

II. What is a semiring


Evgeny M. Vechtomov – Vyatka State University, vecht@mail.ru


Abstract. The article discusses the beginnings of the theory of semirings. The author analyzes the definition (axiomatics) of a semiring and introduces the initial concepts of the theory of
semirings. The work provides basic examples, indicates the most important classes of semirings, and also formulates the first structure theorems about semirings. The presented material is educational and mathematical in nature, includes comments, explanations and 25 exercises.

Keywords: algebraic structure, semiring, study of the theory of semirings


  1. Vechtomov E. M. Vvedeniye v polukol’tsa [Introduction to Semirings]. Kirov: Izd-vo vyatsk. gos. ped. un-ta, 2000. 44 p. (In Russ.)
  2. Vechtomov E. M. Student educational and research seminar on algebra. Matematicheskiy vestnik Vyatskogo gosudarstvennogo universiteta [Mathematical Bulletin of Vyatka State University]. 2021. No 3. Pp. 36–45. (In Russ.)
  3. Vechtomov E. M. Studying the basics of the theory of semirings. Prime Ideals. Matematicheskiy vestnik Vyatskogo gosudarstvennogo universiteta [Mathematical Bulletin of Vyatka State University]. 2021. No 4. Pp. 4–14. (In Russ.)
  4. Vechtomov E. M. Matematika: osnovnyye matematicheskiye struktury: uchebnoye posobiye. 2-e izd. [Mathematics: basic mathematical structures: study guide. 2nd ed.]. Moscow: Urait.296 p. (In Russ.)
  5. Vechtomov E. M., Sidorov V. V. Abstraktnaya algebra. Bazovyy kurs : uchebnoye posobiye [Abstract algebra. Basic course : study guide]. Kirov: OOO «Izdatelstvo “Raduga-PRESS”», 2014. 260 p. (In Russ.)
  6. Sidorov V. V. Algebra: algebraicheskiye struktury. kompleksnyye chisla. mnogochleny : uchebnoye posobiye [Algebra: algebraic structures, complex numbers, polynomials : study guide]. Kirov: OOO «Izdatelstvo “Raduga-PRESS”», 2013. 232 p. (In Russ.)
  7. Vechtomov E. M., Lubyagina E. N., Sidorov V. V., Chuprakov D. V. Elementy funktsionalnoy algebry: monografiya: v 2 t. [Elements of functional algebra: monograph: in 2 vol.]. Kirov: OOO
    «Izdatelstvo “Raduga-PRESS”», 2016. Vol. 1. 384 p. (In Russ.)
  8. Vechtomov E. M., Lubyagina E. N., Chermnykh V. V. Elementy teorii polukolets: monografiya [Elements of the theory of semirings: monograph]. Kirov: OOO «Izdatelstvo “Raduga-PRESS”», 2012. 228 p.(In Russ.)
  9. Vechtomov E. M., Petrov A. A. Funktsionalnaya algebra i polukoltsa. Polukoltsa s idempotentnym umnozheniyem : uchebnoye posobiye [Functional algebra and semirings. Semirings with idempotent multiplication : study guide]. Sankt-Peterburg: Lan’, 2022. 180 p.
    (In Russ.)
  10. Vechtomov E. M., Cheraneva A. V. Semifields and their properties. Fundamentalnaya i prikladnaya matematika [Fundamental and applied mathematics]. 2008. Vol. 14. No 5. Pp. 3–54. (In Russ.)
  11. Vechtomov E. M., Chermnykh V. V. Main directions of development of the theory of semirings. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin
    of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2021. No 4. Pp. 4–40. (In Russ.)
  12. Chermnykh V. V. Functional representations of semirings. Fundamentalnaya i prikladnaya matematika [Fundamental and applied mathematics]. 2012. Vol. 17. No 3. Pp. 111–227. (In Russ.)
  13. Golan J. S. Semirings and their applications. Dordrecht: Kluwer Academic Publishers, 1999. 382 p.
  14. Vechtomov E. M. We are introduced to abstract algebra: semigroups. Nauchno-metodicheskiy elektronniy zhurnal «Kontsept» [Scientific and methodological electronic journal «Concept»]. 2014. No 12. Pp. 61–65.Available: https://e-koncept.ru/2014/14335.htm (accessed: 20.01.2024).
    (In Russ.)
  15. Vandiver H. S. Note on a simple type of algebra in which thecancellation law of addition does not hold. Bulletin of the American Mathematical Society. 1934. Vol. 40. No 12. Pp. 914–920.
  16. Vechtomov E. M., Shirokov D. V. Uporyadochennyye mnozhestva i reshetki : uchebnoye posobiye [Ordered sets and lattices : study guide]. Sankt-Peterburg: Lan’, 2024. 248 p. (In Russ.)
  17. Gr¨atzer G. Obshchaya teoriya reshetok [General Lattice Theory]. Moscow: Mir, 1982. 456 p. (In Russ.)
  18. Mal’tsev A. I. Algebraicheskiye sistemy [Algebraic systems]. Moscow: Nauka, 1970. 392 p. (In Russ.)

For citation: Vechtomov E. M. What is a semiring. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics.
Mechanics. Informatics], 2024, no 1 (50), pp. 21−42. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_21

III. About one of the axiomatics for determining trigonometric functions when training future mathematics teachers


Elena N. Shustova – Pitirim Sorokin Syktyvkar State University, shustovaen@yandex.ru


Abstract. The article outlines the main theoretical principles of the methodology for teaching future mathematics teachers at a university the definition of trigonometric functions using one of the
axiomatics. The sequence of studying the properties of functions and axioms of the proposed system is given, as well as a brief description of the results of applying the described approach in the process of training students in pedagogical areas of university training.

Keywords: axiomatic method, trigonometric functions, university training for future mathematics teachers


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    oblastnogo universiteta. Seriya: Pedagogika [Bulletin of Moscow State Regional University. Series: Pedagogy]. 2020. No 3. Pp. 86–94. (In Russ.)
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    matematika” [Mathematical analysis : in 3 volumes. T. 1: Initial course: textbook for university students studying in the specialty “Mathematics”, “Applied Mathematics”]. Pod red. A. N. Tihonova. 2-e izd., pererab. Moscow: Izd-vo MGU, 1985. 660 p.
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    collection of abstracts of the Fifth Republican Scientific and Practical Conference]. Syktyvkar: Moscow Region and Higher School of the Komi Republic, SGU, 2002. Pp. 34–41 (In Russ.)
  9. Alexyuk V. N., Shustova E. N. Elementarnye funkcii. 2 [Elementary functions. 2]. Ped. in-t. Syktyvkar, 2010. 12 p. Dep v VINITI 25.10.2010, no 610-B2010 (In Russ.)
  10. Alexyuk V. N. Elementarnye funkcii. 1 [Elementary functions. 1]. Ped. in-t. Syktyvkar, 2010. 13 p. Dep v VINITI 11.10.2010, no 577- B2010 (In Russ.)
  11. Shustova E. N. Methodology for presenting the course “Theory of elementary functions”. Vestnik KGPI [Bulletin of KSPI]. Syktyvkar: Komi Pedagogical Institute, 2010. Pp. 268–270. (In Russ.)
  12. Shustova E. N. Features of using the axiomatic method of introducing elementary functions in teaching future teachers of mathematics at the university. Obrazovatel’nyj vestnik “Soznanie” [Educational Bulletin “Consciousness”]. 2022. Vol. 24. No 4. Pp. 23–30. (In Russ.)
  13. Shustova E. N. Formation of components of methodological competence of mathematics teachers when studying the axiomatic method of introducing elementary functions at a university. Mir nauki, kul’tury, obrazovaniya [World of science, culture, education]. 2022.
    No 3 (94). Pp. 78–81. (In Russ.)
  14. Popov N. I., Shustova E. N. Elementarnye funkcii v shkol’nom kurse matemayiki : uchebnoe posobie. 2-e izd., ispr. i dop. [Elementary functions in a school mathematics course : a textbook. 2nd ed., rev. and additional]. Syktyvkar: Izd-vo SGU im. Pitirima Sorokina, 2023. 165 p.
    (In Russ.)

For citation: Shustova E. N. About one of the axiomatics for determining trigonometric functions when training future mathematics teachers. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 1 (50), pp. 43−54. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_43

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IV. Computer games and combinatorial problems

Nadezhda N. Babikova – Pitirim Sorokin Syktyvkar State University, valmasha@mail.ru

Nadezhda O. Kotelina – Pitirim Sorokin Syktyvkar State University, valmasha@mail.ru

Marija A. Valueva – St. Petersburg State University of Culture

Nikolaj A. Startsev – St. Petersburg State Electrotechnical University “LETI” named after V. I. Ulyanov (Lenin)


Abstract. The author’s problems in combinatorics, based on computer games, are offered for discussion in the article. Examples of problems for practical classes and laboratory work are presented on the following topics: sum and product rules, permutations with and without repetitions, placements with and without repetitions, combinations with and without repetitions, partitioning a number into terms and partitioning a number into terms, each of which does
not exceed given value, inclusion and exclusion formula. The problems were tested in the process of teaching the discipline “Discrete Mathematics” to students in the field of study “Applied Informatics”.

Keywords: combinatorics, combinatorial problems, computer games, training, author’s problems


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    [Education and pedagogical science in the XXI century: current issues, achievements and innovations : collection of articles of the international scientific and practical conference : in 2 parts]. Penza, 2017. Part. 1. Pp. 93–100. (In Russ.)
  7. Babikova N. N. Education in the digital age: remember or google Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University. Series 1: Mathematics. Mechanics. Computer science]. 2022. No 3 (44). Pp. 33–46. DOI
    10.34130/1992-2752_2022_3_33.(In Russ.)
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For citation: Babikova N. N., Kotelina N. O., Valueva M. A., Startsev N. A. Computer games and combinatorial problems. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika.
Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 1 (50), pp. 55−72. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_55

V. Educational and innovative potential of network interaction between organizations using the example of the development of research and project activities of students


Irina V. Kleshcheva – Herzen State Pedagogical University of Russia, iv-kl@list.ru

Abstract. The article examines the substantive, organizational, and functional problems of implementing network interaction in the field of education. The timeliness and effectiveness of network interaction as a tool for integrated and effective solution of various problems in education is argued. The pedagogical feasibility of using network interaction to improve the quality of mathematics education has been scientifically substantiated and experimentally confirmed.
The methodological basis of network educational interaction is motivated by a systematic approach that determines the design and functioning of the educational network at the conceptual, structural
and elemental levels. The system-forming factor in this case is most often common goals, for the sake of which pedagogical efforts are consolidated.

Keywords: networking, systems approach, research activities, project activities, quality of mathematical education


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For citation: Kleshcheva I. V. Educational and innovative potential of network interaction between organizations using the example of the development of research and project activities of
students. Vestnik Syktyvkarskogo universiteta. Seriya 1: Matematika. Mekhanika. Informatika [Bulletin of Syktyvkar University, Series 1: Mathematics. Mechanics. Informatics], 2024, no 1 (50), pp. 73−93. (In Russ.) https://doi.org/10.34130/1992-2752_2024_1_73

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