Cesta k otvorenej vede

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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E-book

Sylvia Dražilová

The Lecture Notes Primary Cholestatic Liver Diseases is intended primarily for undergraduate medical students and provides a comprehensive and up-to-date overview of the diagnosis and management of the major cholestatic liver diseases. The publication focuses primarily on primary biliary cholangitis (PBC) and primary sclerosing cholangitis (PSC). The introductory section covers the physiology of bile formation and transport, the pathophysiological mechanisms underlying cholestasis, and the fundamental diagnostic approach to patients presenting with a cholestatic pattern of liver test abnormalities.

The individual chapters integrate current knowledge of disease pathogenesis and natural history with a practical, clinically oriented approach to patient care. Particular emphasis is placed on the interpretation of laboratory, immunological, imaging, and histological findings; non-invasive assessment of liver fibrosis; risk stratification for disease progression; current therapeutic options; and indications for liver transplantation. 

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E-book

Ján Hreško

This teaching guide is intended for teachers and instructors who are introducing new readers to Dante’s Divine Comedy, in particular the first cantica, Inferno, offering support and a grounding in the cultural background of one of the most important works of European medieval literature. Rather than forming yet another academic contribution to the study of Dante and his work, the guide focuses on using a guided seminar reading method within study groups and fostering meaningful discussions about the central themes and issues of the Inferno. Under the guidance of a teacher, students are encouraged to engage actively with the motifs and moral universe of this classic literary work – a primary source that cannot be replaced by any retelling. The proposed interpretations draw on established scholarly commentaries to deepen the readers’ understanding of the text, and each lesson is accompanied by a selected bibliography. The guide includes thematic introductions presenting Dante Alighieri as both author and protagonist within the Divine Comedy. It also offers carefully selected questions designed to foster textual comprehension and stimulate discussion during seminar readings of selected cantos of the Inferno. In addition, the publication includes special lessons on associated literary and artistic works. The guide features a wealth of original illustrations and an extensive range of visual materials. The course thus builds upon the traditional practice of seminar-based readings of works by the great authors, an approach which continues to form part of the curriculum at many liberal arts colleges, by integrating innovative techniques into this established educational method.

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E-publication

Beáta Valkayed.
Ivana Slepáková-Lenka Maliničová a kol.

The EFFUSE Teacher's Guide is a practical educational material for primary and secondary school teachers who want to develop environmental awareness with their pupils through field-based learning. It is based on the concept of the EFFUSE project (‘Environment for the future by science education’), which aims to link science, research and education with environmental protection. The manual provides teachers with methodological support for planning and implementing outdoor activities aimed at observing and documenting organisms around the Laborec River and the Uh River. It contains instructions for working with real samples, basic biomonitoring procedures and offers the opportunity to participate in the creation of a virtual laboratory that mirrors the state of the local aquatic ecosystem. Through these activities, pupils will learn to understand the links between human activity and the state of the environment, while learning the basics of how scientists work in the fields of biology and ecology. The guide also motivates teachers to become agents of positive change, inspire the younger generation to be active and engage the community in conservation. It is a challenge and an opportunity to create a space for meaningful learning in line with current trends in environmental and digital education.

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