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Linear programming via problem solving
E-book
E-book
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.
Uncertainty Modeling 2024
E-book
E-book
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.
Teória vypočítateľnosti
E-book
E-book
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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Pokročilé štatistické metódy
E-book
E-book
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.
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Jarná škola doktorandov 2020
E-book
E-book
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.
Určitý integrál
E-book
E-book
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.
Študentská vedecká konferencia PF UPJŠ 2014
E-book
E-book
Vladimír Zeleňák (ed.)
The proceedings contain contributions from participants of the Student Scientific Conference of the Faculty of Science at UPJŠ in Košice, which took place on April 24, 2014.
Tvorba úloh pre programátorské súťaže
E-book
E-book
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.