** EDUCATIONAL MATTERS**

### Some Problems in Engineering Education with Computer Science Profile During COVID-19

**Abstract.** The COVID-19 pandemic introduced many limitations and changes in our lives and in particular in education. This article presents problems in distance learning in the field of computer networks and information security between March and June 2020 in the training of engineers with computer science profile.

*Keywords:* distance learning; computer science; COVID-19; digital competence

**Dr. Georgi Tsochev, Assist. Prof.**

*Technical University of Sofia (Bulgaria)*

### Мathematics As Music For The Soul

**Abstract.** The article deals with issues related to the manifestation of mathematical talent from an early age and the attitude of professionals to such a phenomenon as Terry Tao. Epizodes from his biography and several tasks he faces at different ages are considered. The main emphasis is on Terry Tao‘s contribution to the proof of Sendov‘s conjecture and his lecture on this topic, organized by the International Center for Mathematical Sciences - Sofia at the Institute of Mathematics and Informatics at BAS together with the the Union of Bulgarian Mathematicians.

*Keywords:* mathematical talent; Terry Tao; Erdős discrepancy problem; Sendov‘s conjecture

**Dr. Evgenia Sendova, Assoc. Prof.**

*Institute of Mathematics and Informatics – BAS*

**EDUCATIONAL TECHNOLOGIES**

### Challenging the Students‘ Sense of Mathematics Via Decoding Problems in Chernorizec Hrabar Tournament

**Abstract.** Under consideration is a thematic branch from the Chernorizec Hrabar (ChH) math tournament, which aims to check and develop the student’s sense of mathematics. The ChH competition papers include several types of test items related to codes. These test items require just basic math knowledge but a high level of nonstandard reasoning and a kind of synthetic mathematical abilities. The authors’ standing point is to present by examples how the idea of (de)coding evolves in competition papers for students in different ages.

*Keywords:* mathematic competitions; sense of mathematics; (de)coding problems; synthetic competence; gifted education

**Prof. Dr. Borislav Lazarov, Dr. Ivailo Kortezov, Assoc. Prof.**

*Bulgarian Academy of Sciences – Sofia (Bulgaria)*

### The Problem of Images’ Classification: Neural Networks

**Abstract.** The article discusses the employment of an artificial neural network for the problem of image classification. Based on the compiled dataset, a convolutional neural network model was implemented and trained. An application for images classification was created. The practical value of the developed application allows an efficient use of a smartphone camera’s storage facilities. The article presents a detailed methodology of the application’s development.

*Keywords:* image classification; convolutional neural network; Python programming language libraries; graphical user interface (GUI)

**Assoc. Prof. Larisa Zelenina, Assoc. Prof. Liudmila Khaimina, **

**Evgenii Khaimin, D. Khripunov, Assoc. Prof. Inga Zashikhina**

*Northern (Arctic) Federal University named after M.V. Lomonosova (Russia)*

**EDUCATIONAL ISSUES**

### Midlines of Quadrilateral

**Abstract.** In this section we deal with an interesting fact which will imply ABCD some well known theorems. Namely we prove that in a convex quadrilateral whose diagonals meet at O, the midline of the triangle ∆BOC parallel to BC, the midline of the triangle ∆AOD parallel to AD, and the midline of the quadrilateral ABCD connecting the sides AB and CD meet at one point, or are parallel.

*Keywords:* Ceva; Menelaus; Stewartes; cevian; concurrency; collinearity; Fermat; Torricelli

**Prof. Dr. Sead Rešić, Prof. Dr. Maid Omerović, **

**Anes Z. Hadžiomerović, Ahmed Palić**

*Bosnia and Herzegovina*

### Virtual math class

**Abstract.** The challenge of conducting an electronic environment for remote mathematics education is a condition for finding effective methods, forms, approaches, and platforms for a successful learning process. One of the solutions for the implementation of a „virtual lesson“ in mathematics is the cloud environment of GeoGebra. The article discusses various aspects of the application of the online platform GeoGebra in mathematics education: creating interactive worksheets, virtual classrooms, online boards, tools for classroom management, monitoring, and evaluation of student achievement. The attitudes of mathematics teachers about the use of GeoGebra online applications in math lessons are researched and analyzed.

*Keywords:* e-learning in mathematics; virtual class; GeoGebra

**Dr. Sevdalina Georgieva**

*Department for Information Qualification and Lifelong Learning – Varna
Konstantin Preslavsky University of Shumen*

### Where is the error in my solution? ─ a talk with Oleg Mushkarov in front of the white board

**Abstract.** The article is dedicated to the 70th anniversary of Prof. Oleg Mushkarov – a full professor at the Institute of Mathematics and Informatics, Bulgarian Academy of Sciences (IMI-BAS) and a corresponding member of BAS. Currently, he is the Head of the Analysis, Geometry and Topology Department and Deputy Director of IMI-BAS. His main research interests are in the areas of Complex Analysis, Complex Differential Geometry, and Twistor theory. Another important aspect of Oleg’s professional involvements is his work with mathematically gifted high school students. He himself benefited from the Bulgarian system of identifying mathematical talents at an early age leading to his participation in IMO’1969, Romania. Since then, he has been involved in numerous activities dealing with nurturing and developing young mathematical talents.

We present a conversation with him illustrating what his favorite problems are and why. Unlike the traditional situations in which the professor expects the students to come to a solution (possibly with his help), he presents a solution containing mistakes to a well-defined problem and “throw the gauntlet down” for them: Find the mistakes in the solution! We provide a specific example in support of his conviction that such problems are crucial in math education (since everyone, even a professional mathematician, makes errors on an everyday basis). The phases the talk in front of the white board went through were:
To feel that something is wrong in his original solution.
To discover where the mistake is.
Finally, to find a correct solution to the problem.
The very process of starting with a wrong idea, becoming aware of the error in reasoning, and finally, succeeding to correct it, which Oleg Mushkarov has kept reproducing when teaching a course on extracurricular math activities to his undergraduate students, reveals his dedication and talents to teaching in addition to his research achievements.

Keywords: errors in the proof; Olympic problems; extracurricular math activities

**Dr. Evgenia Sendova, Assoc. Prof.**

*Institute of Mathematics and Informatics – BAS*

**CONTEST PROBLEMS**

### Решения на задачите от брой 2, 2021

**IN MEMORIAM**

### In Мemory of Prof. Doru Stefanesku, DSc.

С чувство за голяма загуба съобщаваме на нашите читатели, че на 09.05.2021 година на 69-годишна възраст напусна този свят членът на редакционния съвет на списание „Математика и информатика“ проф. д.м.н. Дору Стефанеску. Отиде си един уважаван румънски учен математик, старши заместник-председател на Румънското математическо общество и изпълнителен редактор на Бюлетина на това общество, трикратен президент на Математическото общество на Югоизточна Европа.

Математическите способности на Дору Стефанеску проличават още в училище. Участва в редица състезания и олимпиади. Завършва математика в Университета в Букурещ, Румъния. Има специализации в Италия, бил е гостуващ професор в чуждестранни университети. Смъртта го застига като професор по математика във Факултета по физика на Университета в Букурещ. Научните му трудове покриват значителен спектър от чисто научни и приложни направления, като въпросите на образованието по математика винаги са заемали подобаващо място в неговите дейности.

Ще запомним професор Дору Стефанеску със сериозното и високо професионално отношение към всичко, с което се занимаваше. Почтеността и добронамереността му ще ни служат за пример. Почивай в мир, Дору!

### In Мemory of Prof. Doru Stefanesku, DSc.

**Editorial Board**

Mathematics and Informatics Journal

Sofia, Bulgaria

E-mail: mathinfo@azbuki.bg