This diploma thesis briefly introduces the concept of inquiry based teaching mathematics. In inquiry based teaching, emphasis is placed primarily on the active activity of the pupil, the aim of which is to discover a certain reality. This activity mainly involves solving problems and finding the right paths to achieve the right goal. We can call this path to a goal as a research. The inquiry process involves observing, formulating questions, identifying information, designing possible processes, and verifying them. In this educational method, the role of the teacher is not to pass the facts to the pupils, but to target them and to supervise the correctness of their practices. We can understand the teacher here as a guide, adviser or assistant on the path to the goal (discovery). In the thesis a few examples of mathematics of elementary and secondary schools are given, in which the inquiry based approach is applied. Mathematics in the given examples is not complicated, emphasis is put on the practical use. In the examples interdisciplinary relationships are developed as well, which is an important part of the inquiry based teaching. In each example, additional questions are provided.

The aim of the thesis is to study the pseudonymous letters of Aeschines, all of which purport to give an account of his sojourn in exile. There is a strong consensus among scholars that all the letters are forgeries, and their date of composition tends to be located in the first few centuries CE on linguistic grounds. Embracing a variety of literary forms, these letters were probably composed by multiple hands and may for convenience be divided into three categories: Letters 2, 3, 7, 11, 12 imitate the ‘Demosthenic’ letters in a manner similar to the Hellenistic (and beyond) historical declamations and progymnasmata; Letters 1, 5, 6, 8, 9, 10 come to us with features reminiscent of what German scholars would call Briefromane, or ‘epistolary novels’, and are normally deemed typical of the so-called Second Sophistic; and Letter 4 is a showpiece assuming the form of a Pindaric exegesis. The thesis consists of two parts. The first gives an extensive account of the letters, including their background, history of scholarship, and basic features, to seek to present the ‘forger’ and the text in their proper historical and cultural contexts. The second part, which constitutes the basis for the reflections developed in the first, provides a detailed commentary in thematic sequence. It begins with the ‘Demosthenic’ counterparts (Epp. 2, 3, 7, 11, 12), and stylistic comparisons are made throughout. The analysis of the fictional letters (Epp. 1, 5, 6, 8, 9) pays particular attention to their consistency of narrative and engagement with other literary genres. The commentary on Letter 4 foregrounds the Pindaric elements and completes the thesis. Letter 10 is discussed at sporadic points: it is a later attachment to the corpus and the erotic content is inconsistent with the ‘original’ forgeries. The overall focus of the thesis is on two overlapping aspects of Aeschines’ early reception in antiquity – as ‘the other orator’ beside Demosthenes and as inspiration for later rhetorical education. Existing studies, however, are more concerned with textual criticism and linguistic analysis and have left the letters almost unproductive in these respects: so Drerup (1904), Schwegler (1914), and, most recently, García Ruiz and Hernández Muñoz (2012). In his classic work Goldstein (1968) took the parallel passages in the pseudonymous letters as evidence for authenticating Demosthenes’ letters, and scholars are now able to take advantage of a more reliable reference when studying Ps.-Aeschines. Holzberg (1994), on the other hand, established a set of generic criteria for the Briefromane and has substantially changed the way we read Ps.-Aeschines: it is now possible to appreciate the literary value of the letters without scrutinising their authenticity. Yet both these studies tell us only half the story: while Goldstein left more remarks on the imitative counterparts of Demosthenes’ letters, Holzberg focused on the way the letters reflect the epistolary narrative. Following Rohde (1876/1960), moreover, it seems common sense to characterise the pseudo-historical tale as seen through the letters as a product of the ‘Second Sophistic’, though discoveries of new papyri, e.g. the Ninus romance c. first century BCE, undermined this assumption. My study is built on these investigations in an attempt to form the most extended analysis. The study of the ‘Demosthenic’ counterparts will contribute to a better understanding of Ps.-Aeschines’ intertextual engagement with Demosthenes and his successors, e.g. Ps.-Leosthenes (FGrH 105 F 6 = MP3 2496). It shows that Ps.-Aeschines owes a great deal to the culture of rhetoric and highlights his significance in the Nachleben of Attic oratory. As for the other letters, this thesis argues that they deserve some space in our accounts of the history of exilic, periegetic, and epinician literatures for contextualising a wide range of preexisting literary forms such as the Homeric Odyssey (Ep. 1) and Pindar’s victory odes (Ep. 4). As contingent by-products of the ‘Demosthenic’ counterparts, however, they seem to allow no confident judgement about generic consciousness, esp. the very notion of ‘novel’, and need to be approached as antedating the Imperial exponents. Contrary to the communis opinio, therefore, I attempt to move the date of composition forward to the late Hellenistic period, in which there was already ample encouragement for a sophist, as well as for his students, to write pseudonymous letters. The ‘traitors’ blacklist’ (Ep. 12.8–9) and the term for the Rhodian family of Diagoreans (Ep. 4.4) entertain this possibility inasmuch as both show marked affinities with the Hellenistic sources. Last but not least, the two coexisting, radically opposed interpretations of one’s civic orientation in exile will help us tackle the stability and change in the political cultures of the post-Classical era. My conclusion is that these letters hold a unique position as very early – and very illuminating – examples of how different literary, political trends were interwoven to make, and to remould, a Classic. It is hoped that this study may have done something to reappraise Ps.-Aeschines, who is, in all likelihood, a pre-sophisticated forerunner at a crossroads in the history of Greek literature.

As obras frequentemente consideradas como as mais relevantes para o estudo da filosofia kantiana são as três críticas que apresentam o rigor do pensamento filosófico e marcam uma mudança de perspectiva no pensamento moderno, apontando limites e novos horizontes para o conhecimento humano. Porém, concomitantemente ao desenvolvimento destas obras encontramos outras que também são importantes para a compreensão do projeto filosófico kantiano como um todo. Destaca-se no presente projeto de pesquisa a Antropologia de um ponto de vista pragmático e sua relevância para o estudo da formulação da noção moral a partir da observação das ações humanas e da possibilidade de identificação e formação do cidadão do mundo para Kant. / The works often regarded as the most relevant to the study of Kant\'s philosophy are the three critical presenting the rigor of philosophical thought and mark a change of perspective in modern thought, pointing limits and new horizons to human knowledge. However, concurrently with the development of these works find others that are also important for understanding the Kantian philosophical project as a whole. Stands out in this research project Anthropology from a pragmatic point of view and its relevance to the study of the formulation of the moral sense from the observation of human actions and the possibility of identifying and training the \"world citizen\" to Kant.

A perturbation analysis shows that if a numerically stable procedure is used to compute the matrix sign function, then it is competitive with conventional methods for computing invariant subspaces. Stability analysis of the Newton iteration improves an earlier result of Byers and confirms that ill-conditioned iterates may cause numerical instability. Numerical examples demonstrate the theoretical results.

The aim of the thesis is to gain knowledge concerning what pupils aged 8 and 9 need to learn to become familiar with negative numbers. The framework used in this research, variation theory, impliesthat students' problems in learning what was intended may have to do with the fact that some critical aspects of the studied object have not yet been discerned by the student. To get the pupils to understand the idea behind each critical aspect, carefully constructed examples were used. According to variation theory it is necessary to experience differences before you experience similarities. To answer the research question data was collected by using the learning study model. It is characterized by an iterative design where I as a researcher collaborate with teachers to try to find and orchestrate the critical aspects. The method is interventionist, which means that interventions are done in teaching. In the learning study I have cooperated with two primary school teachers and 64 pupils in four different classes. The data consists of video-recordings of lessons, pre- and posttests, interviews with pupils and notes from the meetings of the learning study group. When planning lessons as well as analyzing data, concepts relating to the theory of variation have been used as analytical tools. This thesis contributes to research by investigating in detail what aspects students need to differentiate in order to become familiar with negative numbers. The results show that the pupils needed not only to discern, but also to differentiate three different critical aspects: To differentiate the values of two negative numbers. To differentiate the function of the minuend versus the function of the subtrahend in a subtraction. To differentiate the minus sign for negative numbers versus the minus sign for subtraction.

Large scale datasets collected using non-expert labelers are prone to labeling errors. Errors in the given labels or label noise affect the classifier performance, classifier complexity, class proportions, etc. It may be that a relatively small, but important class needs to have all its examples identified. Typical solutions to the label noise problem involve creating classifiers that are robust or tolerant to errors in the labels, or removing the suspected examples using machine learning algorithms. Finding the label noise examples through a manual review process is largely unexplored due to the cost and time factors involved. Nevertheless, we believe it is the only way to create a label noise free dataset. This dissertation proposes a solution exploiting the characteristics of the Support Vector Machine (SVM) classifier and the sparsity of its solution representation to identify uniform random label noise examples in a dataset. Application of this method is illustrated with problems involving two real-world large scale datasets. This dissertation also presents results for datasets that contain adversarial label noise. A simple extension of this method to a semi-supervised learning approach is also presented. The results show that most mislabels are quickly and effectively identified by the approaches developed in this dissertation.

The thesis focuses on the discriminatory treatments in the Czech tax law. The aim is to analyze the Czech Income Tax Act and the Value Added Tax Act to identify possible tax discriminations. The thesis studies infringement procedures leaded by the European Commission and it also studies cases of the European Commission against the Czech Republic on this matter and cases that can have impact on the Czech Republic because non discrimination is one of the primary principles of EU law. The identified discriminations should be removed in such a way that the Czech tax legislation does not discriminate against any group of taxpayers

In the thesis, we explore the prospects of creating adversarial examples using various generative models. We design two algorithms to create unrestricted adversarial examples by perturbing the vectors of latent representation and exploiting the target classifier's decision boundary properties. The first algorithm uses linear interpolation combined with bisection to extract candidate samples near the decision boundary of the targeted classifier. The second algorithm applies the idea behind the FGSM algorithm on vectors of latent representation and uses additional information from gradients to obtain better candidate samples. In an empirical study on MNIST, SVHN and CIFAR10 datasets, we show that the candidate samples contain adversarial examples, samples that look like some class to humans but are classified as a different class by machines. Additionally, we show that standard defence techniques are vulnerable to our attacks.

This thesis examines adversarial examples in machine learning, specifically in the im- age classification domain. State-of-the-art deep learning models are able to recognize patterns better than humans. However, we can significantly reduce the model's accu- racy by adding imperceptible, yet intentionally harmful noise. This work investigates various methods of creating adversarial images as well as techniques that aim to defend deep learning models against these malicious inputs. We choose one of the contemporary defenses and design an attack that utilizes evolutionary algorithms to deceive it. Our experiments show an interesting difference between adversarial images created by evolu- tion and images created with the knowledge of gradients. Last but not least, we test the transferability of our created samples between various deep learning models. 1

Improved metacognitive thinking can impact student’s success. A novel homework method called Solved Problem Analysis (SPA) was developed with the intent to foster metacognitive thinking. It was hypothesized that supporting metacognition would lead to increased performance on in-class exams and the ACS final exam. Results showed SPA was effective at increasing performance on both. In order to more directly measure student’s metacognitive thinking, a knowledge survey was implemented to measure the difference between student’s perceived understanding of the material and their actual performance. These knowledge surveys showed students were able to predict how much of the material they understood. Monitoring one’s thinking is an important part of metacognition. This cognitive monitoring can be mimicked in study group interactions. The effect of self-assembled study groups on student exam performance was also examined, where it was found that self-assembled study groups did not effectively increase exam performance.