“Mathematics Days in Sofia”

Section “Mathematics Education and History of Mathematics”


Invited Section Speakers

  • Eugenia Kovatcheva, University of Library Studies and Information Technologies, Bulgaria

  • Toni Chehlarova, Institute of Mathematics and Informatics, Bulgaria


  • Daniela Nikolova, Florida Atlantic University, USA

  • Delyan Boychev,

  • Dragomir Marchev, Shumen University, Bulgaria

  • Emil Kolev, Institute of Mathematics and Informatics, Bulgaria

  • Liubomir Nenov,

  • Miroslav Marinov, Institute of Mathematics and Informatics, Bulgaria

  • Maria Brauchle, Institute of Mathematics and Informatics, Bulgaria

  • Stanislav Harizanov, Institute of Mathematics and Informatics, Bulgaria

Program and Abstracts

The talk presents the work of the International Summit on ICT in Education EDUsummIT22-23 which took place in Kyoto, Japan May 29-June 1. EDUsummIT is a global community of researchers, practitioners, and policymakers. Its main role is to observe the current situation and suggest and support the main player in education on how to integrate information technology more effectively.

EDUsummIT A Call to Action represents the summit conclusions in several directions: Personalized and Flexible Learning, Teacher Professional Learning and Development, Equity and Inclusion, Artificial Intelligence (AI), and Social Emotional Learning. The last topic is new for the EDUsummIT but it is very important nowadays especially after the two years in lockdown because of Covid-19.

These topics were discussed in 9 thematic working groups: TWG 1: Artificial Intelligence ( AI) and big data for teaching and learning: implications for school leaders, teachers, policymakers, and learners. TWG 2: Special Needs: addressing challenges and opportunities using IT. TWG 3: Inclusion of excluded populations: access and learning optimization via IT in the post-pandemic era. TWG 4: Fostering self-regulatory skills in learners: challenges and opportunities for assessment. TWG 5: Learning beyond formal schooling: human-computer-human interactions in a digital inter-connected era. TWG 6: Aligning Educational Policies with the New Realities of Schooling. TWG 7: Post-pandemic online learning: Sharing the lessons learned on digital teaching for future education. TWG 8: Pedagogical reasoning and reflective practice: Teacher’s Professional Development (TPD) in online education. TWG 9: Social Emotional aspects in new modes of learning.

The vision of the future of learning is the learning with extended boundaries of formal education to include teaching and learning in informal and non-formal contexts using diverse technologies, in order to foster self-directed learning of students and teachers. Privacy prioritization and ethical considerations through a multiperspective and interdisciplinary approach as the core of AI in education. Integrate social-emotional learning in digital educational contexts in pre- and in-service teacher training programs and conduct research across different countries and cultures to understand the role of technology in its impact on learning and flourishing of students.

Today there exist many software packages/systems which effectively present and dynamically manipulate mathematical objects and problems. They help the students familiarize themselves with these objects and problems, and, more importantly, allow them to explore and discover their essential properties by experimenting and using their own intuition. In a certain sense, such systems bring the teaching and learning of mathematics closer to the teaching and learning of the other disciplines which rely on experimenting, not only on deduction.

The major goal of the competition “Mathematics with Computer” is to promote the use of such systems in the teaching and learning of mathematics. It demonstrates that the circle of problems considered at the school level can be enlarged considerably so that meaningful problems with practical flavor can also be included.

The participants of Mathematics Days in Sofia’2023 will have the opportunity to try a special issue of the competition. In the presentation, some competition problems, results, and organizational issues will be discussed.

Symmetric structures are beautiful and powerful mathematical concepts that are prevalent in many fields, including art, science, and music.

Part 1: “The Mathematics and Art Connection”. We witnessed the usefulness of Group theory as it relates to symmetry through our investigation of the 2D 17-Wallpaper Groups, where a classification algorithm for the presence of these groups within tessellation artwork and natural patterns was implemented.

Part 2: Virology.  Some viral capsid shells – the protein shell that encapsulates a virus – follow a quasi-equivalent icosahedral arrangement, which sheds light on structure and virus classification. Through this project, we again use Group theory to explore symmetric structures prevalent within viruses and methods of modeling viral capsid symmetries. We have also found connections between symmetric structures and vaccinology.

Part 3: Music. “Each symmetry of music is defined by a set of transformations, which, when applied in some way to music, leaves some perceived aspect of that music at least approximately unchanged.” We analyze classical pieces (Mozart, Bach), as well as some modern musical compositions in jazz, video games. We focus on the similarities and differences in folk music of different cultures.

The aim of this talk is to present the pan-European LOFAR project. Paying attention to the goals, the methods for solving them and the first results. Special attention is paid to the Bulgarian LOFAR-BG station and its benefits. This project is multidisciplinary, bringing together specialists from engineering, mathematical and physical sciences. The place of mathematical sciences is also indicated, namely in the processing of “big data” datasets. Last but not least, the participation of the University of Shumen in the LOFAR-BG consortium was commented on.

The development of technologies needs well-trained STEM professionals. The transition to quality STEM education requires a clear STEM school strategy with key elements such as instruction, professionalization of staff, connections, assessment, school leadership and culture, school infrastructure, and curriculum implementation. The STEM School Label is a platform that supports European schools in developing STEM school strategies. Several Bulgarian schools have already joined the platform. The report presents the steps and criteria required to obtain one of the three types of STEM school labels and some statistics related to the Bulgarian participant in the platform.

Dummit, Granville and Kisilevsky have recently shown that the proportion of semiprimes (products of two primes) not exceeding a given x, whose factors are congruent to 3 modulo 4, is more than a quarter when x is sufficiently large. They have also conjectured that this holds from the very beginning, that is, for all x bigger than 8. We give a proof for x bigger than or equal to 10^21 via an explicit approach based on their work. Together with their data for the remaining x, this results in a full proof of the conjecture. Our method consists of techniques from Analytic Number Theory, such as Partial Summation and cancellations with sums over primes with different remainders. We also rely on classical estimates for prime counting functions, as well as on very recent explicit improvements by Bennet, Martin, O’Bryant and Rechnitzer, which have wide applications in essentially any setting involving estimations of sums over primes.

Bulgaria has always been among the pioneers regarding foundation and/or organization of International Mathematical Competitions. Together with Romania, those are the only two countries that have participated in all 63 editions of the International Mathematical Olympiad (IMO) so far. Up to the moment, Bulgarian students have won 56 IMO golds, 126 IMO silvers, and 115 IMO bronzes, while Bulgaria was twice an organizer – Sofia 1966 and Bourgas 1975.
This talk is devoted to the various stages of the Bulgarian IMO team selection and preparation, as well as the additional activities that the Union of Bulgarian Mathematicians, the Institute of Mathematics and Informatics, and the Leaders of the Bulgarian team became engaged with through the years. For example, Bulgaria was among the key initiators of the foundation of the Balkan Mathematical Olympiad in 1984 in order to prepare the Balkan teams for IMO, and (together with Romania and Greece) has not yet missed a single edition. The same with the Junior Balkan Mathematical Olympiad, the European Girls Mathematical Olympiad, etc. Furthermore, following the good example of IMO, Bulgaria was among the founders and the very first host of both the International Olympiad in Informatics (IOI, Pravetz, 1989) and the International Linguistics Olympiad (IOL, Borovetz, 2003).
One of the key factors for the traditionally solid results of the Bulgarian students is the active role of the Institute of Mathematics and Informatics (IMI-BAS), which provides a priceless bridge between high-school math competitions and academia, as well as between problems of Mathematical research and competitions. For more than 50 years, the Bulgarian IMO leader has always been an employee of IMI-BAS. Most of the authors of national competition problems and lecturers at training camps are renowned Bulgarian mathematicians. And vice versa, the last two Bulgarian IMO leaders are now the director of IMI-BAS, respectively the president of the Union of the Bulgarian Mathematicians. This special collaboration between IMI-BAS and the Bulgarian IMO team will be also analysed in detail in this talk.

The Event is Supported by: