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Cílem diplomové práce je ukázat, jakým způsobem probíhá nejen separace a likvidace tříděného odpadu, ale hlavně systém, jakým probíhá jeho svoz. Na optimalizaci svozu tříděného odpadu je pohlíženo z matematického hlediska. Jsou využity matematické modely a heuristiky, které vedou k vyčíslení trasy, která se bude přibližovat optimální trase sběrných vozů. Za použití reálných dat poskytnutých pražskými svozovými společnostmi je demonstrováno praktické využití optimalizace svozových tras. Součástí diplomové práce je vytvořená aplikace pro výpočet trasy pomocí heuristik.

Současné konkurenční prostředí nutí distribuční firmy zajišťovat bezprostřední obsluhu svých zákazníků. Zatímco statická verze okružních a rozvozních úloh nepřipouští možnost akceptovat dodatečné požadavky zákazníků, dynamická verze umožňuje dispečerovi měnit naplánované trasy vozidel, jakmile se objeví nový požadavek. Pro řešení dynamických úloh jsou navrženy optimalizační matematické modely a heuristické vkládací algoritmy. V některých úlohách jsou zahrnuty podmínky s časovými okny. V práci jsou analyzovány speciální distribuční úlohy: dynamická úloha kurýrní služby, dynamická úloha obchodního cestujícího s apriorní informací a dynamická rozvozní úloha s dělenou dodávkou. Řešení většiny úloh je demonstrováno na vygenerovaných datech za použití programu LINGO jako řešitele a VBA v MS Excel jako uživatelského rozhraní a výstupního prostředí. Jsou prezentovány výsledky počítačových experimentů.

Title: Implementation of Challenging Tasks in Mathematics Education Author: PhDr. Lucie Růžičková Department: Department of Mathematics and Mathematics Education Supervisor: RNDr. Alena Kopáčková, Ph.D. ABSTRACT The thesis deals with practical implementation of challenging tasks in mathematics education. The methodology for examining "the fidelity of implementation of mathematical tasks" is being designed to describe whether the task is used according to the original intention of the teacher or according to the intention of its author. This methodology is employed in the analysis of four experiments to examine mathematical tasks and task environments. Then, based on the experience with the analysis, the methodology is adapted to the needs of both the teaching practice and educational research. The main result of the thesis is the creation of the methodology for examining the fidelity of implementation of mathematical tasks which is based on contrasting the descriptions of four general elements of the mathematical task at different phases of its implementation. KEY WORDS: mathematics education, mathematical task, challenging task, implementation of tasks

This work is concerned with five problems in combinatorics. In Josephus problem, people are standing in a circle or in a row and every q-th is executed until only one person remains. We show how to find the survivor, and discuss the generalization when each person has more lives. In Tower of Hanoi, we study the numbers and properties of moves necessary to transport the tower from one rod to another, where the total number of rods is either three or four. We mention related problems with restrictions on the legal moves. In ménage problem, we calculate the number of seatings of couples around a table such that men and women alternate and nobody sits next to his or her partner. We also discuss permutations with restricted positions and rook polynomials. In ballot problem, we consider two candidates competing against each other and calculate the probability that, throughout the count, the first candidate always had more votes than k times the number of votes of the second one; we also mention the relation to Catalan numbers. In Kirkman's schoolgirl problem, the task is to find a weekly schedule for fifteen girls walking daily out in triads so that no two go together more than once. We also discuss the social golfer problem and Schurig's tables.

The thesis "The Phenomenon of Free Time" focuses mainly on grasping free time as a phenomenon by analyzing the related terms in the work of Karl Marx and in the work of Emmanuel Lévinas. The introductory section is therefore devoted to a selection of philosophical questioning about the nature of time. Then I focus on analyzing the works of Karl Marx, especially in the light of the terms work, working hours and free time. In the chapter "Time in Phenomenology", I focus on the difference between the Aristotle's conception of time and the phenomenological conception of time. In this relation, I come mainly from the ideas of Edmund Husserl, Martin Heidegger, Jan Patočka and Emmanuel Lévinas. In the next section, I analyze the work of Emmanuel Lévinas and focus on the terms existence, time, work and other related terms. In the next chapter, I try to capture the tension of onticity and ontology of Marx and Lévinas and thus reach the phenomenon of free time as an ontological problem. I present this conception of the problem of the phenomenon of free time in the conclusion.

Title: Text properties as a factor in solving word problems with the use of Venn diagrams Author: Bc. Daniela Návarová Department: Department of Mathematics and Mathematical Education Supervisor: doc. RNDr. Jarmila Novotná, CSc. Supervisor's e-mail address: Jarmila.Novotna@pedf.cuni.cz This diploma thesis deals with the word problems where Venn diagrams can be used. The word problems are studied as texts and their specific text properties are scrutinised in the first, theoretical, part of the thesis. The second part describes an experiment that focuses on the importance of text properties of word problems for the problem solvers. The main aims of this diploma thesis are to show the possibility of textual examination of the chosen texts and to unfold some connections between the mathematical and linguistic views on the area of word problems. Keywords: text, word problem, Venn diagram

This diploma thesis deals with the pupil's solving of learning tasks from biology at grammar schools. Five components of learning tasks were compiled on the basis of the Tollinger taxonomy. Each file tests a different category of Tollinger learning tasks. The main aim of the thesis was to find out which types of learning tasks are preferred by students. The aim of the thesis was based on a questionnaire of pupils as well as on an interview with a biology teacher at the grammar school.

Diplomová práce zkoumá logistickou situaci v konkrétní firmě tak, aby optimalizace rozvozní úlohy nebyla jen dílčí optimalizací. Budoucí rozvoj firmy vede k navržení nových regionálních center na základě nejnovějších logistických trendů a zároveň se při rozhodování o umístění centra využije teorie diskrétního vícekriteriálního rozhodování. Samotné vybudování center vychází z teorii řízení projetků. Rozvozní úloha je aplikována na stávající i nová regionální centra s využitím aplikace v MS Excel a programu Lingo.

The new panmictic model of seed orchard scheme for forests trees is described in this thesis. It can be used either alone or in combination with existing designs without losing efficiency. In this case it iscombined with Minimum Inbreeding design. The establishment of seed orchards and importance of achieving panmixy and minimizing inbreeding in the population of seed orchard are described in the theoretical part. The resultant algorithm defines panmictic situation as a situation where close neighborhoods of all possible combinations of clones occur within the seed orchard grid with the same frequency. To achieve this we developed a formula for variance that is minimized as a criterion function. The algorithm has been programmed in R and it was tested for different tasks including balanced or unbalanced numbers of clones and different sizes or shapes (rectangular or non-rectangular shape) of orchard. The model is able to solve all of these situations, and it is very effective especially in the case of balanced numbers of clones. Optimal solution of the given task was often found at the first iteration. To evaluate the relative quality of resulting schemes theoretic proxy to level of maximum panmixy was defined for every specific task- the Theoretical minimum variance. The effectiveness of MI scheme combined with clonal rows was also evaluated. The result is a hybrid scheme with predefined MI clonal rows surrounded by panmictic algorithm, while close neighborhood of clonal rows was also optimized. This scheme will be used for the establishment of Abies fraseriseed orchard in North Carolina under NCSU Christmas Tree Genetics Program. Another possible modifications of the algorithm, such as the inclusion of local separation zones or assortative mating are summarized in conclusions.