Mathematics (e-books)

E-book

Ľubomír Šnajder a kol.

The publication is dedicated to teachers and future teachers of informatics, mathematics and science subjects. The publication presents activities that move students from the role of passive users of digital technologies to that of curious researchers, creative creators and critical thinkers. In the first chapter, we introduce educational strategies and practices to actively engage students in learning. In the second chapter, we briefly describe selected digital technologies that can be an aid to exploring the world around us and creating useful products. In the third chapter, we provide specific ideas for STEAM exploration and projects in which students search answers to real-world questions and solutions to real-world problems. Subject didacticians, experts from different fields and teachers worked closely together to develop ideas for the methodologies.

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E-book

Peter Fedoročko (ed.)

From June 13 to June 16, 2023, the 9th annual Spring School for Doctoral Students at Pavol Jozef Šafárik University in Košice will take place in Stará Lesná. The scientific program of the spring school will comprise 3 plenary lectures by leading scientific experts and 1 workshop.

Doctoral students will present their research papers in two sections: 24 doctoral students of Faculty of Public Administration, Faculty of Law and Faculty of Arts, and 24 doctoral students of Faculty of Medicine and Faculty of Science. The scientific programme of the spring school will also include a panel discussion with the management of Pavol Jozef Šafárik University in Košice.

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E-book

Marián Kireš  (ed.)

Proceedings of Abstracts from the Student Scientific Conference of the Faculty of Science, Pavol Jozef Šafárik University in Košice

The Student Scientific Conference (SSC) represents the culmination of long-term and intensive work on a selected topic, collaboration with a supervisor, or a broader team at the workplace. In practice, however, it often marks the beginning of scientific research, focusing on a chosen subject, field, or close cooperation with a future supervisor of a bachelor's, master's, or doctoral thesis.

This year, the Student Scientific Conference took place on April 19, 2023, featuring 14 sections, a programming competition, and the IHRA contest. Bachelor’s and master’s students presented 101 contributions. Additionally, 8 high school students participated non-competitively, presenting their SOČ projects; 14 students took part in the programming competition, and 3 students competed in the IHRA contest.

We believe that the proceedings of abstracts and related documents serve not only as an archive but also as a dignified presentation of scientific activities at our faculty for the wider public.

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E-book

Ondrej Hutník

The concept of the integral is one of the most significant concepts in mathematics as a whole. In its most primitive form, it was already used by the ancient Greeks in the creation of Euclidean geometry. However, it was only after Descartes' work on analytical geometry in 1637 that mathematicians could begin to consider the integral as a subject of analysis. Descartes' work laid the groundwork for the discovery of infinitesimal calculus by Leibniz and Newton around 1665. At that time, a great dispute arose over the priority of this discovery, dividing scholars of Germany and England into two opposing camps, each favoring their own champion. Today, we know that Newton's work on fluxions and fluents was somewhat earlier, but Leibniz's notation and approach have gained more acceptance in the mathematical world, and the symbols ∫ ∫ and d d are still used today. A brief overview of the history of the integral will be presented in Chapter 1.

Today, there is a plethora of scripts, textbooks, and books dedicated to explaining the concept of the integral. Therefore, every potential author faces the initial question of whether to write another text on this topic. Our affirmative answer to this question was driven by the students' request to find the subject matter of a part of the winter semester of the second year presented in a coherent form. The second motivation is a slightly different approach to the topic. If we consider the methods typically used in solving problems and gaining routine with a certain integral, it mainly involves the Newton-Leibniz formula, and often there is little time left to compute the definite (Riemann) integral using its definition. Therefore, we included a discussion of the Newton integral in Chapter 2, which reflects this fact and is directly related to the indefinite integral, whose various calculation methods receive relatively much attention in the previous semester. Only after that, in Chapter 3, do we build the theory of the Riemann integral, present criteria for its existence, classes of integrable functions, basic properties, and finally its relationship with the Newton integral. Questions primarily concerning geometric applications are addressed in Chapter 4, and in the final chapter, we focus on extending the Riemann integral to unbounded functions and unbounded intervals.

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Vladimír Zeleňák (ed.)

Proceedings of Abstracts of the Student Scientific Conference of the Faculty of Science, Pavol Jozef Šafárik University in Košice

A characteristic feature of education at high-quality universities — among which the Faculty of Science at Pavol Jozef Šafárik University (UPJŠ) in Košice proudly belongs — is the close connection between education and scientific research. Students gain knowledge in their field of study not only through theoretical coursework in individual disciplines, but also through active involvement in solving specific scientific tasks as part of research teams. This can occur during the development of final theses or through participation in the Student Research Assistant Program (ŠPVS), which was revitalized at the faculty in 2015.

The Student Scientific Conference (ŠVK) is one of the faculty’s traditional events, organized during the Faculty’s Science Days as part of Sciencefest. By its very nature, it fits seamlessly into the aforementioned framework of combining education with research, and it has long enjoyed great popularity and student interest. In 2016, the conference featured presentations by 125 students of the Faculty of Science at UPJŠ in Košice, across 16 thematic sections. This collection of abstracts provides an overview of the focus and goals of the student projects. We believe it will serve as inspiration for other potential participants of future conferences and will also be of interest to the broader public, offering additional insight into the faculty's activities.

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E-book

Vladimír Zeleňák(ed.)

The proceedings contain abstracts of contributions from participants of the Student Scientific Conference of the Faculty of Science, Pavol Jozef Šafárik University in Košice, which took place on April 22, 2015.

The Student Scientific Conference (SSC) enjoys long-term popularity among the faculty's students and teachers, and we are pleased that this was no different this year, with 128 contributions submitted to the SSC.

The contributions were organized into 19 sections, additionally complemented by an open programming competition and the final of the IHRA contest. For many students, presenting at the SSC is one of the first opportunities to gain experience in presenting their results before a professional audience. Considering the number of submitted contributions, along with the members of the expert juries from the faculty's teaching staff and the audience who came to support their classmates' presentations, the SSC is an event where a large part of the student and academic community of the faculty meets at one place and time. Many abstracts presented in this proceedings were developed as part of students' work on partial tasks that are components of research projects at the departments of the Faculty of Science, Pavol Jozef Šafárik University.

The abstracts represent, in a way, an overview of research topics at the individual workplaces of the faculty. The SSC proceedings thus serve as a useful tool that students and faculty teachers can use to present the faculty externally to partners, employers, and potential collaborators. Partners from practice have shown interest in cooperating in organizing the SSC for a long time. Since 2005, the association of IT companies has awarded a Prize for the Most Original Work and a Prize for the Work with the Best Prospects for Practical Application.

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E-book

Stanislav Lukáč - Ľubomír Šnajder - Ján Guniš - Zuzana Ješková

The publication is intended for researchers in didactics and teachers of mathematics and computer science. Our aim is to provide readers with a basic orientation in the issue of inquiry-based teaching, to explain and demonstrate several levels of student inquiry through examples, and to offer a classification of inquiry skills.

The core part of the publication consists of methodologies for inquiry-based teaching of specific topics from school mathematics and computer science. We present ideas for implementing inquiry activities, active work with information in solving various types of problems, and the application of modern digital technologies in exploring and discovering patterns.

The publication includes seven methodologies for teaching mathematics and eight methodologies for teaching computer science in the 1st and 2nd years of secondary school.

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