Mathematics (e-books)

E-book

Daniel Klein

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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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.

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E-book

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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E-book

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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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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