This study aims to examine the levels of mathematical literacy and assessment literacy among prospective mathematics teachers in Kazakhstan, reveal the relationship between these two constructs, and identify profile differences among prospective teachers. A quantitative research design was used in the study, and data were collected from 335 teacher candidates (196 female, 135 male) from seven universities via an online survey. A scale developed based on a literature review and the PISA framework was used for mathematical literacy, while the Assessment Literacy Standards Version 6.0 scale was adapted into Kazakh for assessment literacy. A Bayesian statistical approach was adopted for data analysis, Kendall tau-b correlations were calculated, and latent profile analysis (LPA) was applied. The findings showed that teacher candidates had high perceived competence levels in all seven dimensions of both mathematical literacy and assessment literacy. Overall equality was observed in terms of the gender variable. Moderately strong positive relationships were found between all dimensions of mathematical literacy and assessment literacy. Math anxiety, however, did not show any meaningful relationship with any construct. Latent profile analysis identified three distinct groups: Assessment Experts, Assessment Practitioners, and Assessment Novices. While there were significant differences between the groups in terms of mathematical literacy, math anxiety remained similar. The study offers empirical evidence on the correlation between mathematical literacy and assessment literacy, while also uncovering the diverse composition among teacher candidates. The results show that teacher education programs need to include these two domains of literacy in a way that is connected and provide multiple ways to educate based on individual profiles.

In this article, we obtain some cohomology of classical Lie algebras over an algebraically closed field of characteristic $p>h,$ where $h$ is a Coxeter number, with coefficients in simple modules. We assume that these classical Lie algebras are Lie algebras of semisimple and simply connected algebraic groups. To describe the cohomology of simple modules, we will use the properties of the connections between ordinary and restricted cohomology of restricted Lie algebras.

The strategic organization of independent student endeavors in the professional development of mathematics educators represents a critical element of the pedagogical framework, fostering the acquisition of professional proficiencies, the refinement of critical faculties, and the cultivation of self-directed learning. This article addresses the theoretical underpinnings and methodological approaches to the organization of independent study, surveys the historical landscape of research pertaining to this area, and posits recommendations for the optimization of its deployment within contemporary educational paradigms. The importance of independent work is especially evident in the preparation of future educators, as it fosters the development of skills such as analysis, planning, and the application of innovative educational technologies. The research is based on the analysis of scientific literature, student surveys, and the development of recommendations to improve organizational approaches. The results of a survey among second-year students in the 6В01510 - «Mathematics» program revealed the need for improved communication with instructors, better use of digital technologies, and the addition of supplementary educational resources. The article also suggests creating an electronic educational environment to support independent work, which will include courses, materials, tests, video lessons, and feedback systems to enhance the learning process.

The article considers the harmonic analysis of periodic non-sinusoidal oscillations by Fourier series expansion. The features of decomposition of even and odd functions are revealed. Based on the symbolic method, the Fourier series was presented in a complex form. Examples are presented to provide clarity of the steps of the procedures for decomposing a function into a Fourier series. Examples of Fourier series decomposition of periodic non-sinusoidal electric currents or signals using the Mathcad application software package are considered. Graphical, numerical, and analytical solutions of non-sinusoidal periodic currents or signals have been obtained using computational experiments. Methods for calculating the sum of the terms of the Fourier series for non-sinusoidal periodic signals, which consist of several stages, are presented. It has been proven that complex even and odd functions describing periodic currents that are not sinusoidal (or cosine-shaped) consist of the sum of simple harmonic electrical oscillations. These fluctuations make up the frequency spectrum of these currents. The results of the approximation of periodic signals are presented as a Fourier series over the interval (p, p). Electrical signals are classified into a Fourier series, and the sum of the first two and four terms of this series is obtained. It has been shown that the more members of the signals classified in a row, these members more accurately describe the signal under study.