Elementárna teória čísel 1. časť

E-publication

Soňa Király

The Book of Abstracts of The 9th International Conference on Novel Materials Fundamentals and Applications, NFA 2025, contains 46 contributions from the participants of this conference. This congress is primarily focused on novel materials, ranging from theory to practical applications, with the aim of demonstrating how fundamental discoveries can lead to innovative implementations. All contributions are inspiring and professionally prepared.

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Ľubomír Antoni-Stanislav Krajči

An important part of theoretical computer science is the problem of Turing machines. This computational model has two basic properties: like any other computational program, the software of a Turing machine is composed of instructions, but in its case they are all of a single type. Every other (so far known) computer program can be transformed into a Turing machine program without loss of information. While the second feature reduces the question of what a calculator cannot do to the question of what a Turing machine cannot do, the first feature allows a much simpler investigation of such a question. Using this computational model, we can thus find concrete problems that no automaton can ever deal with (perhaps the most famous is the problem of the Turing machine stopping). Their existence demonstrates the fundamental limitations of (not only ideal) computational means, and thus encourages both criticality and humility in our thinking.

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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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Pavol Sokol - Ladislav Bačo - Tomáš Bajtoš

In the university textbook, we present the theoretical foundations and technical details of the activities of a forensic investigator. We describe the identification and provision of digital tracks, file system analysis. analysis of various artifacts of the Windows operating system, analysis of the operating memory. The textbook is also supplemented by a chapter devoted to the analysis of malicious code (malware). University textbooks are intended for students of bachelor's, master's, engineering and doctoral study programs in computer science, but also in non-informatics fields.

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Beáta Valkay ed.
Ivana Slepáková-Lenka Maliničová a kol.

EFFUSE - A Guide for Students is an interactive educational resource for primary and secondary school students to help them better understand how their daily activities affect the environment. The handbook was developed within the EFFUSE project (‘Environment for the future by science education’) and motivates young people to take a greater interest in the nature around them. It focuses on practical field activities during which they will explore the ecosystem of the Laborec and Uh rivers, observe and document organisms and work with real samples from nature. At the same time, they will learn about the work of scientists - botanists, zoologists and microbiologists - and learn basic biomonitoring methods. The manual will also guide them through the process of creating a virtual laboratory to display the results of their investigations of an aquatic ecosystem. It will help them understand the importance of sustainable development and encourage them to behave responsibly towards nature. It is their opportunity to learn about their surroundings in a new way, to learn to think scientifically and to become active creators of positive change for their community and future generations.

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Mária Kožurková (ed.)

Book of Abstracts

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Peter Kollár

The textbook Semiconductor Elements was developed gradually over the past years as an aid for second-year master's students in condensed matter physics. It is intended to support students’ understanding of lectures, considering that important texts, mathematical relationships, and illustrations are provided in advance in the form they will be presented during the lecture.

This allows students to supplement individual pages with their own notes during the lecture, either electronically or in printed form. In this way, a study aid is created for the student, which I believe will help with the final review of knowledge gained throughout the semester in preparation for the exam. This textbook is not meant to serve as standalone literature but is designed to assist orientation in the literature, which is abundant in English but mostly written for scientists, researchers, and students for whom this topic is central and not just one of many parts of their education. Therefore, it is not allocated a larger scope in the study program.

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Mária Ganajová-Ivana Sotáková-Petra Letošníková

The conference proceedings FORMATIVE 2025 – Implementing Formative Assessment in Schools Together constitute the output of an online conference organised by the Institute of Chemical Sciences, Faculty of Science, Pavol Jozef Šafárik University in Košice, in cooperation with the National Institute of Education and Youth in Bratislava, within the framework of the KEGA project No. 001UPJŠ-4/2023. These proceedings present current knowledge, experience, and examples of good practice in implementing formative assessment in primary, secondary, and university teaching, with an emphasis on the use of digital tools. The papers address the foundations of formative assessment in the context of curricular changes and the ongoing educational reform, as well as specific didactic procedures for its implementation in the teaching of science and social science subjects, including mathematics, Slovak language, and foreign languages. Particular attention is paid to the development of professional teaching competences, formative assessment strategies, providing targeted feedback, and promoting students’ active participation in the assessment process. These proceedings also present the Digilib digital library, a tool developed to support the creation and management of formative assessment processes within the school environment. This publication is intended for experts in pedagogy and didactics, teachers at all levels of education, student teachers, digital coordinators, and all those interested in educational innovation and in improving the quality of teaching through formative assessment.

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Mariana Budovská

The aim of writing the university textbook "Selected Heterocyclic Compounds" was to create a study aid for students of the Organic Chemistry program, which provides essential information in a clear format for the subject of Heterocyclic Compounds. In selecting the content of the textbook, the goal was to present basic information about the chemistry of the most significant heterocycles. Given that the summary of chemical knowledge about heterocycles is vast, it was not possible to include all heterocyclic compounds in the content.

The intention was for readers to orient themselves in the field of heterocyclic compounds. Separate chapters included in the content address the nomenclature of heterocycles, basic chemical properties of individual heterocycles, their synthesis and reactions, the occurrence of heterocycles in nature, and their practical applications (medications, dyes, pesticides, detergents, etc.).

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Mária Ganajová - Jozef Hanč - Ivana Sotáková - Petra Letošníková (eds.)

The International Conference on Research in Didactics of the Science – DidSci+ 2022, continues in the educational legacy of the successful series of the previous DidSci conferences held from 2004 in Krakow, Prague, Brno, or Trnava. The DidSci+ conferences present a platform for enduring international cooperation, focusing on the frontiers and current challenges in science education research. This special edition of DidSci conferences, celebrating its 10th anniversary, was held in Košice, at the Faculty of Science of Pavol Jozef Šafárik University, from June 26 to 29, 2022. The careful double-blind review process has led to two major publications offering a comprehensive look at the latest advances in STEM and science subjects education. The first volume of selected papers is published as the IOP Conference Series proceedings, Vol. 3037 with open access at https://iopscience.iop.org/issue/1742-6596/3037/1, and is primarily devoted to STEM education, assessment, evaluation, feedback strategies, and teacher development. The second volume of selected papers, published by ŠafárikPress, focuses more on curriculum development, educational innovation, and digital technologies, primarily in chemistry and biology. Both publications are intended for a wide audience, including in-service and pre-service teachers of science subjects, university students in scientific disciplines, researchers in science education, professionals in pedagogical and methodological centers, curriculum developers, and textbook authors.

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Marián Kulla – Ladislav Novotný – Petra Dávidová – Anton Uhrin (eds.)

Danišovce 16. – 18. 10. 2024

Zborník abstraktov, ktorý máte pred sebou, obsahuje príspevky prezentované na X. Medzinárodnom geografickom kolokviu v Danišovciach. Ústav geografie na Prírodovedeckej fakulte UPJŠ v Košiciach toto podujatie organizuje už od svojho vzniku ako platformu na výmenu vedeckých poznatkov, primárne medzi geografmi zo Slovenska a Česka. Aktuálny jubilejný ročník spoluorganizovali Prírodovedecká fakulta UPJŠ v Košiciach, Slovenská geografická spoločnosť pri SAV v Bratislave v zastúpení jej Košickej pobočky a spoločnosť UMBRA Solutions Košice.

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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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Nataša Tomášková

Selected tasks and problems from biochemistry – metabolism follow biochemistry lectures on metabolism and individual metabolic pathways for students of the second and third year of the bachelor’s degree in the fields of chemistry, biology and their combinations with other fields. Scripts provide an opportunity to better understand the lectured subject matter of metabolism through the solution of tasks and problems as serve as a basis for one-hour exercises. The scripts are divided thematically into eleven chapters, and each chapter contains 10 tasks and 7 problems. At the beginning of the chapters there is a short description and explanation of the given metabolic pathway. However, when solving the tasks, the student must focus mainly on the curriculum that was presented on the given topic in the lecture. Subsequently, at the end of chapter, answers to problems are also presented. These scripts are intentionally accessible only in electronic form. The reason is the effort to continuously update and modernize individual tasks.

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Adriana Zeleňáková - Jozef Bednarčík

Peer-reviewed Proceedings of the Scientific Conference NANOVIR

The main objective of the scientific conference NANOVIR was the presentation of scientific results obtained during the implementation of the NANOVIR project – Nanoparticles for solving diagnostic and therapeutic problems with COVID-19, co-financed by the European Regional Development Fund within the Operational Programme Integrated Infrastructure 2014 – 2020, ITMS: 313011AUW7.

The project was carried out from January 1, 2021, to June 30, 2023, and was supported with a sum of EUR 1,916,004.79. Three co-investigating organizations participated in the project: Pavol Jozef Šafárik University in Košice as the main investigator, the University of Veterinary Medicine and Pharmacy in Košice as partner no. 1, and the Institute of Experimental Physics of the Slovak Academy of Sciences as partner no. 2.

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Adela Kravčáková - Stanislav Vokál - Janka Vrláková 

The presented “General Physics IV, Part 1: Atomic Physics” is intended as a basic study material for lectures from General Physics IV in the second year of bachelor-level study of physics and interdisciplinary study in combination with physics at the Faculty of Science, P. J. Šafárik University in Košice. The content covers the first part of the given course of physics, devoted to atomic physics.

The aim of the course is to obtain basic information about the structure of the atom and the electron shell of the atom.

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Monika Balogová - Viktória Vargová - Kristián Gulyás - Natália Pipová - Dalibor Uhrovič -Marcel Uhrin

A peer-reviewed publication dealing with the biology and ecology of the European green toad, bringing new findings through scientific research on the roosting ecology, spatial activity and dispersal of this protected species in urban environments. The subject matter of this publication is highly topical, as amphibians represent the most threatened vertebrate group in the world. This work is suitable not only for university students interested in batrachology, amphibian ecology, and vertebrate zoology, but also for conservation workers, municipalities, and specialists directly involved in the reconstruction of urban areas with green toads. Last but not least, this publication is suitable for enthusiasts with an interest in nature and its conservation.

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