Computer Tools in Education

On methods for studying dynamic systems

2024-06-25T22:09:55+00:00

Wide application of dynamical systems resulted in designing many various methods for investigations, both analytical and computer-oriented ones. In this paper we consider methods based on ideas of symbolic dynamics, and discuss the application of dynamical systems for solving identification and prognosis problems.
The representation of the system dynamics by an oriented graph constructed in accordance with the system and a finite partition of the phase space gives a possibility to matchtrajectories paths on the graph. By this method one may construct approximation to invariant sets and invariant measures, and the Morse spectrum as well.
Using dynamical systems in identification problems is consideredon examples of probability chainsfor the modeling social and economic resource distribution, and the method of nonlinear dynamics for reconstruction of an attractor on a given time series.

Computing of tropical sequences associated with Somos sequences in the Gfan package

2024-06-29T23:12:01+00:00

This paper examines tropical recurrent sequences associated with Somos sequences. The classical Somos sequences have applications in the theory of elliptic curves. Due to the Laurent character of the classical sequences, a pattern can be inferred between the classical sequences and their tropical counterparts.

The greatest interest is the increase in the dimension of the solution space of tropical sequences depending on the length of the final sequence. For a set of tropical sequences described by tropical recurrence relations, D.Yu.Grigoriev put forward a hypothesis about the stabilization of the maximum dimensions of the components of the corresponding tropical prevarieties. This hypothesis has been proven for tropical linear recurrent sequences. As part of this work, for tropical recurrent sequences associated with the sequences Somos-4 and Somos-5, the corresponding tropical prevarieties were investigated using the Gfan package in order to test Grigoriev's hypothesis.

Exploring the Effectiveness of Prompt Engineering and Quantized Large Language Models in in the Development of Academic Courses

2024-06-25T22:03:50+00:00

This article presents the outcomes of an experiment employing large language models (LLMs) in the development of university course structures. Various prompt engineering methods, including zero-shot, few-shot, chain-of-thought, and tree-of-thought, were employed to formulate queries to LLMs. Primarily, quantized models such as mistral-7b-instruct, mixtral-8x7b-instruct, openchat_3.5, saiga2_13b, starling-lm-7b-alpha, tinyllama, among others, were utilized for the experiment. The generated course structures were compared with data obtained from ChatGPT-4. Models openchat_3.5.q5_k_m and starling-lm-7b-alpha.q5_k_m demonstrated comparable quality in generating educational program structures to ChatGPT-4. The experiment underscores the potential applications of LLMs in the field of education and highlights promising directions for further research.

Web-based system for processing medical research data

2024-06-29T23:43:37+00:00

The issues associated with processing of large amount of medical data are discussed in the article. The limitations of using existing medical information systems in individual research are noted. To simplify medical research processes, web-based system has been developed. The system introduces such features as research design, collaboration, data input, access control, audit of database changes, regular backup, data analysis, and exporting data as sheets and plots. The designed system was deployed to production and received positive feedback from users. The certificate of state registration of a computer program was obtained.

Method of generating unique variants for mathematical problems

2024-06-25T22:24:04+00:00

The article poses the problem of creating generators for unique multivariate mathematical problems. Types of methods of obtaining random numbers are considered. A comparative analysis of the standard generator used by developers with the generator providing the possibility to create sets of numbers occurring once among the required range of values is carried out. A specific example is provided that requires the application of unique problem sets and parameters. The examples are accompanied by formulas in general form, listings of the proposed algorithms of functions in JavaScript, a brief verbal description of the result of the functions. Attention is paid to the generation of numbers without zero, to the peculiarities of development, taking into account the choice of the best interval for a wide range of values of generated numbers, excluding the use of loops and reducing risks. The article explains a method of description of the result of generation of numbers in JSON format, which can be used when transferring the obtained sets between different programming languages.

Should we teach Python at universities?

2024-06-25T22:26:28+00:00

Various measures of popularity of programming languages in different scopes are discussed in the paper, with Python being the main point of interest. Well-known drawbacks of Python as a language and as an ecosystem (not inherent to other popular languages) are listed. The usefullness of Python in carreer is considered overrated, while in education Python often does more harm than good.