Mathematics is the foundation of science, technology and engineering. At University of Debrecen Faculty of Engineering teachers can experience that the basic studies have difficulties, transition from high school to university mathematics courses is a challenge for many students. According to previous researches, prior mathematical knowledge has a central role in the initial stages of university studies. In the light of the existing literature, this report examined the mathematics level of engineering students at a Hungarian university at the end of first academic year, to investigate the relationship between prior mathematics education in secondary school and academic performance. We report about the effect of high school mathematics knowledge on the university progress of engineering students after the initial stages. We investigated whether the students are able to make up for the prior mathematical knowledge deficiency, or whether it holds them back in university progress even after one year. Our aim was to understand the factors behind of students’ achievement. Based on our survey, we can conclude that at University of Debrecen Faculty of Engineering many engineering students had problems with prior mathematical knowledge deficiency, which affects university progress, significantly correlated with the first practical test, suggesting that the ability to apply knowledge in practice is more closely related to prior knowledge. We hope this paper represents a valuable addition to the literature on academic preparedness and equity in higher education.

Fullerenes are an allotrope of carbon having a hollow, cage-like structure. The atoms in the molecule are arranged in pentagonal and hexagonal rings such that each atom is connected to three other atoms. Simple polyhedra having only pentagonal and hexagonal faces are a mathematical model for fullerenes. We say that a fullerene with n vertices has a magic property if the numbers 1,2,...,n may be assigned to its vertices so that the sums of the numbers on each pentagonal face are equal and the sums of the numbers in each hexagonal face are equal. We show that C8n+4 does not admit such an arrangement for all n, while there are fullerenes, like C24 and C26 that have many nonisomorphic such arrangements.

In this paper the functional equation f(x+y−[x,y])+f([x,y]) = f(x) +f(y) is investigated with the unknown continuous function f : L → Y which satisfies the equation for all x,y ∈ L where L is a finite dimensional normed real vector space equipped with a bilinear, anti-commutative operation [·, ·]: L2 → L, and Y is finite dimensional, normed, real vector space. Some Pexider generalisations of the above equation are also investigated in this paper.

One of the problems that schools or organizers of STEAM (Science, Technology, Engineering, Arts, and Mathematics) camps face to is the balanced distribution of students according to gender, skills, and academic background in a fair manner. In this study, we used a Satisfiability Modulo Theories (SMT) approach to solve the problem of fair team formation. Our implementation of the approach uses the Z3 SMT solver. In our preliminary experiments, we successfully generated fair and balanced teams from 50 students across different scenarios. Using SMT in educational settings saves time and effort for school administrators and organizers of STEAM events, and it also provides an efficient and effective solution to distribute students equitably across teams.

We associate to any point P in a two-dimensional Riemannian manifold (M, g) a cubic curve inspired by the third-order differential equation of geodesics of g. This construction is more simple when the value in P of the Christoffel symbol Γ¹₂₂ of g squares to +1; on this way some special types of points on M are considered. A large part of this note concerns with examples. If Γ¹₂₂(P) = 0 we associate a conic which is discussed directly on examples.

For the purposes of mathematics teacher education, we provide an algebraic and number theoretic explanation of how one can determine, from a and b, whether the decimal expansion of a/b, where gcd(a,b) = 1, contains a pre-period, and if so, how long it is. To that end, we observe that explanation cannot be based solely on group theory because the residue classes of remainders do not form a subgroup of the multiplicative group modulo b. However, the collection of residue classes does form a submonoid of the multiplicative monoid modulo b.

Primary school mathematics education is crucial to building a strong foundation for students’ mathematical knowledge and skills. Students’ attitudes towards mathematics and the teaching habits of their teachers play a significant role in their engagement and achievement. Teachers’ perceptions of primary school mathematics lessons and their understanding of students’ attitudes and teaching habits are critical in designing effective instructional strategies. In our article, we investigated these areas by conducting research among primary school mathematics teachers. The main findings are that mathematics teachers are mostly positive about their students’ attitudes toward mathematics, the atmosphere of their lessons, and their own teaching methods in terms of suitability.