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Tento učebný text je určený poslucháčom medziodborového štúdia v kombináciách s matematikou, jednoodborového štúdia matematiky ako aj rozširujúceho štúdia matematiky. Je za-meraný na kvadratické kongruencie a niektoré diofantovské rovnice.
Autor
Učebný text je určený poslucháčom medziodborového štúdia v kombinácii s matematikou, jednoodborového štúdia matematiky ako aj rozširujúceho štúdia matematiky. Je zameraný na základné poznatky o deliteľnosti celých čísel, kongruenciách a aritmetických funkciách.
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Ondrej Hutník a kol.
Zbierka úloh z matematickej analýzy III. je pokračovaním predchádzajúcich dvoch vydaných zbierok autorov Kulcsár a Kulcsárová. Táto časť obsahuje príklady na zopakovanie a precvičenie učiva stredných škôl, ako aj časti prvého semestra kurzu matematická analýza určeného pre študentov matematiky, fyziky, informatiky a učiteľského štúdia v kombinácii s matematikou. Zbierka môže tiež pomôcť všetkým učiteľom, ktorí chcú použiť rôzne úlohy vo svojom vyučovaní. Zbierka zahŕňa oblasť postupností reálnych čísel: aritmetické a geometrické postupnosti, všeobecne a rekurentne zadané postupnosti, nachádzajú sa tu úlohy na vyšetrovanie vlastností postupností (monotónnosť, ohraničenosť, konvergencia) a výpočet rôznych typov limít. Všetky zadané úlohy sú vyriešené na konci každej kapitoly s podrobným komentárom.
Autori
Danica Studenovská a kol.
Táto zbierka úloh je určená poslucháčom Prírodovedeckej fakulty UPJŠ, ktorí sa v rámci predmetu Matematika I. zoznamujú s pojmami funkcie, limity, derivácie, integrálu a ich aplikáciami. Ide najmä o študentov nematematických odborov a učiteľských kombinácií, avšak táto zbierka je vhodná aj pre iných študentov a záujemcov o základy matematickej analýzy.
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Danica Studenovská - Tomáš Madaras
Táto publikácia je určená pre študentov nematematických odborov na Prírodovedeckej fakulte UPJŠ v Košiciach. Jej obsahom je látka preberaná v prvom semestri v rámci predmetu Matematika I..
Publikácia nadväzuje na učivo stredných škôl a nevyžaduje žiadne predbežné špeciálne znalosti. Môže slúžiť ako základ na ďalšie samostatné štúdium a môže byť užitočná aj pre iných záujemcov o matematiku a jej aplikácie.
Vyriešené príklady v jednotlivých kapitolách majú pomôcť čitateľovi pri zvládnutí štúdia. Tomu napomáhajú aj ilustratívne obrázky.
Autori
Predložený učebný text sa pokúša ilustrovať možné aplikácie Teórie pravdepodobnosti na príkladoch z oblastí (vo fyzike, chémii, biológii, ekonomike, finančníctve, atď.), ktoré sú spestrené o úlohy na hľadanie optimálnej stratégie.
Text je určený predovšetkým poslucháčom Prírodovedeckej fakulty UPJŠ, budúcim učiteľom matematiky, študentom odboru matematika a informatika prípadne iným záujemcom, ktorí budú aplikovať pravdepodobnostné metódy pri riešení reálnych problémov. Obsahom pokrýva prvú časť predmetu "Pravdepodobnosť a štatistika".
Autorka
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Stanislav Lukáč - Ľubomír Šnajder - Ján Guniš - Zuzana Ješková
Publikácia je určená vedeckým pracovníkom v didaktike a učiteľom matematiky a informatiky. Našim zámerom je predstaviť čitateľom základnú orientáciu v problematike bádateľsky orientovaného vyučovania, vysvetliť a na ukážkach demonštrovať viaceré úrovne žiackeho bádania, poskytnúť klasifikáciu bádateľských zručností. Nosnou časťou publikácie sú metodiky pre bádateľsky orientované vyučovanie konkrétnych tém zo školskej matematiky a informatiky. Predkladáme námety na realizáciu bádateľských aktivít, aktívnu prácu s informáciami pri riešení rôznych typov problémov a aplikáciu moderných digitálnych technológií pri skúmaní a objavovaní zákonitostí. Do publikácie sme zaradili sedem metodík pre vyučovanie matematiky a osem metodík pre vyučovanie informatiky v 1. a 2 ročníku strednej školy.
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Vladimír Zeleňák(ed.)
Zborník obsahuje abstrakty príspevky účastníkov Študentskej vedeckej konferencie PF UPJŠ v Košiciach, ktorá sa konala 22. apríla 2015.
Milí študenti, kolegyne a kolegovia! Už po tretí krát vychádza zborník zo Študentskej vedeckej konferencie (ŠVK) na Prírodovedeckej fakulte Univerzity Pavla Jozefa Šafárika v Košiciach, ktorý práve čítate. ŠVK sa teší dlhodobej obľube medzi študentmi a učiteľmi fakulty a teší nás, že ináč to nebolo ani v tomto roku, keď bolo do ŠVK prihlásených 128 príspevkov. Príspevky boli zaradené do 19 sekcií, ktoré navyše dopĺňala otvorená súťaž v programovaní a finále súťaže IHRA. Vystúpenie na ŠVK je pre mnohých študentov aj jednou z prvých príležitostí na získanie skúseností s prezentáciou svojich výsledkov pred odborným publikom. Ak si uvedomíme počet prihlásených príspevkov, pripočítame k nim členov odborných porôt z radov učiteľov fakulty ako aj divákov, ktorí sa prišli podporiť svojich spolužiakov na vystúpeniach, je ŠVK podujatím, keď sa v jednom čase a na jednom mieste stretáva veľká časť študentskej a akademickej obce fakulty. Mnohé abstrakty príspevkov prezentované v tomto zborníku vznikli v rámci práce študentov na čiastkových úlohách, ktoré sú súčasťou výskumných zámerov na ústavoch PF UPJŠ. Abstrakty príspevkov predstavujú svojim spôsobom prehľad výskumných tém na jednotlivých pracoviskách PF UPJŠ. Zborník z ŠVK je tak dobrým nástrojom, ktorý môžu použiť študenti a učitelia fakulty na jej prezentáciu smerom navonok, k partnerom, zamestnávateľom, potenciálnym spolupracovníkom. O spoluprácu pri organizovaní ŠVK už dlhšie prejavujú záujem aj partneri z praxe. Od roku 2005 udeľuje zoskupenie IT spoločností Cenu za najoriginálnejšiu prácu a Cenu za prácu s najlepšími vyhliadkami na praktické využitie. V roku 2015 bola po prvýkrát otvorená sekcia, s názvom „Predstav svoj nápad!“, založená na myšlienke start-up projektov. Do sekcie boli prihlásené tri príspevky, kde študenti predstavili svoje nápady s potenciálnym využitím v praxi. Ich zámery boli hodnotené úspešnými manažérmi zo spoločností GlobalLogic, Košice IT Valley a AmCham, EXIsport, Investeers, KPMG. Vystúpenie študentov pred porotou, jej komentáre a návrhy boli veľkou devízou a skúsenosťou, ktorú naši potenciálni „start-up-isti“ získali. Vyhlásenie výsledkov ŠVK prebieha od roku 2013 v areáli na Šrobárovej ulici a je sprevádzané s ďalšími akciami ScienceFestu ako sú ŠTRK a Karaoke show. Ukazuje sa, že tento formát vyhlásenia výsledkov si nachádza medzi študentmi a učiteľmi čoraz väčšiu obľubu. Na vyhlásení výsledkov boli ocenené príspevky, ktoré odborné poroty vyhodnotili ako v jednotlivých sekciách ako najlepšie. Samozrejme, nie všetci účastníci ŠVK sa mohli dostať medzi laureátov. Avšak všetci účastníci ŠVK sa môžu považovať v istom zmysle za víťazov, lebo urobili niečo pre rozvoj svojej osobnosti, investovali do svojho vzdelania a prispeli k zveľaďovaniu a rozširovaniu poznania v oblasti prírodných vied, matematiky a informatiky.
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Vladimír Zeleňák (ed.)
Zborník abstraktov Študentskej vedeckej konferencie PF UPJŠ
Charakteristickou črtou vzdelávania na kvalitných vysokých školách, ku ktorým Prírodovedecká fakulta UPJŠ v Košiciach patrí, je úzke prepojenie vzdelávania a vedeckého výskumu. Poznatky a vedomosti z odboru štúdia získavajú študenti nielen teoretickým štúdiom jednotlivých disciplín, ale aj aktívnym zapojením sa do riešenia čiastkových vedeckých úloh v rámci výskumných tímov či už pri vypracovávaní záverečných prác alebo formou nástroja Študentských pomocných vedeckých síl (ŠPVS), ktorých činnosť sa na fakulte revitalizovala v roku 2015.
Študentská vedecká konferencia (ŠVK) je jedným z tradičných podujatí fakulty, ktoré je organizované počas Prírodovedeckých dní ako súčasť Sciencefestu. Svojou povahou prirodzene zapadá do spomínaného súkolia prepojenia vzdelávania a vedy a dlhodobo sa teší veľkej popularite a záujmu študentov. V roku 2016 na ŠVK vystúpilo 125 študentov Prírodovedeckej fakulty UPJŠ v Košiciach, v rámci 16 sekcií. Prehľad o zameraní a cieľoch študentských prác podáva tento zborník. Veríme, že bude inšpiráciou pre ďalších potenciálnych záujemcov o vystúpenie na ŠVK, ale bude zaujímavý aj pre širšiu verejnosť, ktorej môže podať doplnkový pohľad na činnosť fakulty.
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The publication lists interim results of qualitative educational research focused on the development and evaluation of programming tasks being carried out by authors since 2005 in the frame of programming competition PALMA junior. The publication consists of three chapters: Computer science competitions in Slovakia, Tasks in computer science education, Selected problems of PALMA junior competition. The first chapter provides an overview of computer science competitions for a primary and secondary schools in Slovakia. The second chapter described the issue of learning tasks - their components, focus, formulation types, and development system of tasks. The third chapter contains the assignments and commented author solutions of selected problems represented focus of PALMA junior competition – programming, algorithms and mathematics. For each problem is mentioned analysis of pupils’ solutions aimed to ways of thinking, typical misconceptions, sets of preparatory and extended problems. The publication is addressed to computer science teacher trainers, authors of programming competitions problems, and computer science teachers.
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Vladimír Zeleňák (ed.)
Zborník obsahuje príspevky účastníkov Študentskej vedeckej konferencie PF UPJŠ v Košiciach, ktorá sa konala 24. apríla 2014
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Vladimír Zeleňák (ed.)
The publication contains abstracts of contributions presented at the Student Scientific Conference of the Faculty of Natural Sciences at UPJŠ in Košice, held on April 25, 2013. The event was marked by the celebration of the 50th anniversary of the Faculty of Natural Sciences at UPJŠ and was part of a series of events called ScienceFest.
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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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Valéria Skřivánková - Martina Hančová
The publication is focused on discrete random processes, primarily on Markov chains, which have wide application in the field of economics and finance.
The textbook is divided into five chapters, the first of which serves as an introduction to random processes and provides definition, properties and classification of random processes in general. The second chapter discusses Markov chains with discrete time, including valuation of transitions between states and their optimal management. The third chapter focuses on special Markov chains with continuous time and emphasizes construction and solution to the system of Kolmogorov differential equations, which describe the dynamics of the process development. The last two chapters illustrate applications of Markov chains using examples of queuing system modeling and renewal theory.
Besides the explanation of basic terms, definitions and theorems with proofs, this textbook also provides number of solved examples to illustrate the discussed theory. Problem assignments are placed at the end of each chapter, so that readers can test their understanding of the content as they progress through the book. Solutions to all the problems and the list of references are provided at the end of the publication.
This textbook is primarily intented for students majoring in Economics and Financial Mathematics at the Faculty of Science of Pavol Jozef Šafárik University in Košice, and it covers content of the course “Random Proceses 1“ thought there. It might however serve also students from other schools in similar progams or professionals interested in this topic.
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Katarína Cechlárová - Eva Pitoňáková (eds.)
Proceedings of Abstracts from Contributions by Participants of the Student Scientific Conference at the Faculty of Science, UPJŠ in Košice, Held on April 26, 2017
This is the fifth edition of the proceedings from the Student Scientific Conference (ŠVK) at the Faculty of Science, Pavol Jozef Šafárik University in Košice. We are pleased that ŠVK has become an integral part of faculty life and a showcase for the quality of education provided. In 2017, ŠVK took place as part of the traditional Science Days on April 26, 2017. 105 students from the Faculty of Science presented their work. Contributions were organized into 15 sections, supplemented by an open programming competition involving 17 students and the final round of the IHRA competition, which included 27 teams from across Slovakia.
The abstracts in this proceedings demonstrate that students at the Faculty of Science, UPJŠ, acquire knowledge and skills in their field not only through theoretical study of disciplines but also through active engagement in solving partial scientific problems aligned with research goals at the faculty’s institutes. These abstracts also provide an overview of the faculty’s scientific activity, which we believe will be of interest to the broader public.
doc. RNDr. Gabriel Semanišin, PhD.
Dean of the Faculty
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Katarína Cechlárová (ed.)
In 2018, the Student Scientific Conference was held on April 18, 2018, in 16 sections covering biology and ecology, chemistry, physics, geography, mathematics, computer science, and their subject didactics. There were 110 registered contributions from bachelor's and master's students. Additionally, eight high school students participated outside of the competition; these students already visit our alma mater at a young age, work in our laboratories, and prepare for further studies under the guidance of our enthusiastic teachers. The day also included a programming competition and the IHRA competition in three categories, where students from PF UPJŠ competed alongside pupils from elementary and secondary schools.
The abstracts of the Student Scientific Conference contributions convincingly demonstrate that PF UPJŠ students study their field not only theoretically but also actively engage in solving partial scientific problems that are part of the research goals at PF UPJŠ institutes. This collection provides an overview of scientific activity at the faculty, which we believe will be interesting for the broader public as well.
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Ondrej Krídlo - Gabriel Semanišin
For computer scientists, the constant challenge is to seek efficient algorithms and various technical and implementation possibilities to improve the computational complexity of currently known algorithms. Partial solutions are offered by approaches such as grid-based methods and parallelization of computation. Quantum computers represent a significant but still unfulfilled promise. From a theoretical perspective, probabilistic and approximation approaches provide very effective solutions, and these are the methods we aim to explore in detail.
These electronic university textbooks serve as supplementary materials for the course Approximation and Probabilistic Algorithms. They were developed from the authors' materials and contributions by Prof. RNDr. Viliam Geffert, DrSc., whom the authors thank for providing the manuscript. Acknowledgments also extend to RNDr. Ján Katrenič, PhD., who prepared the first set of exercises for the course, and Žaneta Semanišinová, who reviewed large portions of the text and contributed suggestions for its improvement.
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Katarína Cechlárová (ed.)
This year, the Student Scientific Conference was held on April 24, 2019, across 17 sections in disciplines such as biology and ecology, chemistry, physics, geography, mathematics, informatics, and their didactics. Bachelor’s and master’s students presented a total of 124 contributions. The most successful participants advanced to national or traditional Czech-Slovak student scientific showcases in fields like physics, chemistry, mathematics, informatics, and mathematics didactics.
In addition to faculty students, 10 high school students participated outside the competition. They were invited based on their achievements in subject-specific Olympiads or because they were already engaged with the faculty under the guidance of dedicated teachers in laboratory work as part of their preparation for future studies. The day also featured a programming competition with 23 participants, an IHRA contest involving 16 teams of high school students and 15 teams from elementary schools, and a new Puzzle section where 72 high school students from the region competed.
The abstracts from the Student Scientific Conference demonstrate that our faculty's students not only absorb theoretical knowledge delivered in lectures but also actively engage in solving partial scientific problems that align with research objectives at the institutes of PF UPJŠ. This collection serves as both a record of scientific activity at the faculty and a dignified presentation for the broader public.
Prof. RNDr. Katarína Cechlárová, DrSc.
Vice-Dean for Education
Doc. RNDr. Gabriel Semanišin, PhD.
Dean of the Faculty
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Adriana Zeleňáková - Zuzana Ješková - Adela Kravčáková et al. (eds.)
The proceedings contain abstracts of contributions from participants of the 10th Czech-Slovak Student Scientific Conference in Physics, which took place on May 2–3, 2019, at the Faculty of Science, Pavol Jozef Šafárik University in Košice.
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Peter Fedoročko (ed.)
Proceedings of the 7th Annual Doctoral Spring School 2020
From November 10 to November 11, 2020, the 7th annual Spring School for Doctoral Students at Pavol Jozef Šafárik University in Košice will take place in Košice in a modified mode in the on-line space. The scientific program of the spring school will comprise 2 plenary lectures by leading scientific experts of Pavol Jozef Šafárik University in Košice. 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 22 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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Statistics is defined as a scientific discipline based on learning from data and on finding, controlling, and presenting uncertainty. In these university textbooks we present the history of statistics, basic concepts of statistical modeling, measurement of dependencies, regression models, analysis of variance. We describe simple sorting, multiple comparisons, assumptions of the ANOVA model, Kruskal-Wallis test.
University textbooks are suitable for students of mathematics and computer science at the first and second level of universities. Study materials are also suitable for students of non-informatics disciplines with a view to improving their knowledge and practical experience in the fields of informatics and provide an opportunity for students to apply in IT companies in solving practical tasks.
Download e-book for free (pdf)
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Božena Mihalíková - Ondrej Hutník - Jozef Kiseľák
The textbook is devoted to the mathematical analysis of infinite series of numbers and functions. It is intended for students of mathematics, physics and computer science, as well as interdisciplinary study of combination with mathematics. It contains a theoretical background for investigating the convergence of infinite series, expanding functions into power and Taylor series, as well as the use of these results in various problems of mathematics, physics, and computer science. Using the historical background the textbook clarifies the motivations and the need to introduce some key concepts and their further development. Basic concepts and statements are demonstrated on a large number of solved exercises, but it contains a number of exercises for independent practice. Several results are supplemented by dynamic animations executable in the electronic version of the textbook.
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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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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.
Download e-book for free (pdf)
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Ondrej Hutník (ed.)
Book of abstract
Uncertainty Modeling 2024 (UM 2024) is organized by Pavol Jozef ˇSaf´arik University in Koˇsice. It is a continuation of the series of colloquia held in Rzesz´ow under the name International Symposium on Fuzzy Sets (ISFS) and in Bratislava under the name Uncertainty Modeling.
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Linear programming belongs to parts of mathematics with the greatest number of real applications. This Slovak-English problem collection provides an overview of basic knowledge in the area, application problems as well as problems to acquire routine in calculations. It is complemented by questions motivating the student to look for further theoretical principles, construct conterexamples and formulate arguments to explain the studied phenomena.
Slovenčina
