Calculus at the university level is taken by thousands of undergraduate students each year. However, a significant number of students struggle with the subject, resulting in poor problem solving, low achievement, and high failure rates in the calculus courses overall (e.g., Kaput, 1994; Szydlik, 2000; Tall, 1985; Tall & Ramos, 2004; White & Mitchelmore, 1996). This is cause for concern as the lack of success in university calculus creates further barriers for students who require the course for their programs of study. This study examines this issue from the perspective of Tall’s Three Worlds of Mathematics (Tall, 2004a, 2004b, 2008), a theory of mathematics and mathematical cognitive development. A fundamental argument of Tall’s theory suggests that connecting between the different mathematical worlds, named the Embodied-Conceptual, Symbolic-Proceptual, and Formal-Axiomatic worlds, is essential for full cognitive development and understanding of mathematical concepts. Working from this perspective, this research examined, through the use of calculus task questions and semi-structured interviews, how fifteen undergraduate calculus students made connections between the different mathematical worlds for the calculus topics of limits and derivatives. The analysis of the findings suggests that how the students make connections can be described by eight different Response Categories. The study also found that how the participants made connections between mathematical worlds might be influenced by the type of questions that are asked and their experience in calculus courses. I infer that these Response Categories have significance for this study and offer potential for further study and educational practice. I conclude by identifying areas of further research in regards to calculus achievement, the Response Categories, and other findings such as a more detailed study of the influence of experience.

Representations of the Other in Contemporary Australia is a thesis consisting of a novel, Brother Nation, and an exegesis in a separate volume. Brother Nation is set in Australia at the beginning of the twenty-first century, a time of great political and social change. The novel explores ambiguities in issues of race, crime and moral justice through the eyes of an adolescent who comes of age amidst a chain of disturbing events. Omar Assaf is a sensitive sixteen-year-old with a problem—he needs to lose his virginity. However, like most boys his age, he is anxious and naive about matters of sex and love. When a young female friend, Belle, rejects his romantic overtures, Omar is crushed. He rapidly falls under the corrupting influence of his older brother, Sam, and Sam’s motley band of miscreant friends. Fuelled by drugs, alcohol and pornography, the boys roam the migrant suburbs of southwest Sydney, alleviating their boredom and frustration by flirting with crime, cruising in cars and pursuing girls. However, Omar soon learns that being involved with Sam and the boys has dangerous consequences. In compensating for his sense of emasculation, Omar finds himself taking part in a series of attacks, including a betrayal of Belle. Though ambivalent about and at times sickened by his complicity, Omar realises much too late that he and his brother have entered a theatre where their fate will be determined by broader, more powerful forces than he could ever have imagined. The exegesis charts the creation of Brother Nation via the author’s movement from a mode of autopoiesis to allopoiesis, through the practice of narrative research. That is, the essay is structured to illustrate how the process of researching the novel resulted in the production of knowledge external to the creative work itself. In doing this I discuss the genesis of the idea to write the novel, the basis and modes of my narrative research, the style of the finished work in relation to the genre of the ‘faction’ or ‘non-fiction novel’, and the internal and external conflicts that arose in relation to the representation of demonised Arabic Other characters in the story. I also contextualise the work in relation to other relevant fiction and non-fiction texts that address similar subject matter, and make a case for holding a non-essentialised notion of cultural identity regarding my own speaking position. In particular, this exegesis investigates problematic questions in relation to representations of contemporary characters with an immigrant Other background; and, via the framework of Bakhtinian theories of dialogism and heteroglossia, considers the extent to which seemingly incompatible moral viewpoints can be coherently instantiated in fiction through a multiplicity of characters’ voices. / v. 1 [Novel]: Brother Nation -- v. 2 [Exegesis]: Representations of the Other in contemporary Australia. / Thesis (Ph.D.) -- University of Adelaide, School of Humanities, 2007

This thesis addresses the problem of investigating the properties and abilities of a variety of computer vision representations with respect to spatial geometric transformations. Our approach is to employ machine learning methods for finding the behaviour of existing image representations empirically and to apply deep learning to new computer vision tasks where the underlying spatial information is of importance. The results help to further the understanding of modern computer vision representations, such as convolutional neural networks (CNNs) in image classification and object detection and to enable their application to new domains such as local feature detection. Because our theoretical understanding of CNNs remains limited, we investigate two key mathematical properties of representations: equivariance (how transformations of the input image are encoded) and equivalence (how two representations, for example two different parameterizations, layers or architectures share the same visual information). A number of methods to establish these properties empirically are proposed. These methods reveal interesting aspects of their structure, including clarifying at which layers in a CNN geometric invariances are achieved and how various CNN architectures differ. We identify several predictors of geometric and architectural compatibility. Direct applications to structured-output regression are demonstrated as well. Local covariant feature detection has been difficult to approach with machine learning techniques. We propose the first fully general formulation for learning local covariant feature detectors which casts detection as a regression problem, enabling the use of powerful regressors such as deep neural networks. The derived covariance constraint can be used to automatically learn which visual structures provide stable anchors for local feature detection. We support these ideas theoretically, and show that existing detectors can be derived in this framework. Additionally, in cooperation with Imperial College London, we introduce a novel large-scale dataset for evaluation of local detectors and descriptors. It is suitable for training and testing modern local features, together with strictly defined evaluation protocols for descriptors in several tasks such as matching, retrieval and verification. The importance of pixel-wise image geometry for object detection is unknown as the best results used to be obtained with combination of CNNs with cues from image segmentation. We propose a detector which uses constant region proposals and, while it approximates objects poorly, we show that a bounding box regressor using intermediate convolutional features can recover sufficiently accurate bounding boxes, demonstrating that the required geometric information is contained in the CNN itself. Combined with other improvements, we obtain an excellent and fast detector that processes an image only with the CNN.

O processo de abertura a outros universos culturais decorrente do estreitamento das relações entre as sociedades fez emergir mais fortemente a necessidade de reflexão sobre as noções de cultura e de representação. Tais noções tornam-se, no campo da Didática das Línguas Estrangeiras, de fundamental importância uma vez que o conhecimento das línguas representa o vínculo de aproximação entre as diferentes comunidades culturais, e favorece a compreensão das diversas formas de ver e de viver o mundo. O processo de ensino-aprendizagem de uma língua estrangeira deve, deste modo, buscar favorecer a reflexão sobre o diverso com vistas ao despertar do aprendiz a essa diversidade, evitando, sempre que possível, a folclorização das culturas. Através da análise do corpus extraído da imprensa francesa e cujo objeto do discurso é o Brasil, buscamos demonstrar objetivamente uma das vias de reflexão sobre o diverso, uma vez que nos vemos representados no e pelo discurso dos artigos selecionados. Isto nos parece enriquecedor, pois nos coloca, enquanto brasileiros, frente às representações do Outro sobre a nossa sociedade, e nos faz perceber e refletir sobre a existência de um processo inverso de construção de representações de uma outra cultura, onde nos encontramos como agentes. O objetivo é favorecer, através da objetivação dos fatos apresentados, a reflexão sobre a diversidade cultural, sobre a importância da relativização e sobre os perigos da generalização / The opening process to other cultural universes generated through more closeness between societies as created needs for a new thinking approach on culture and representation. These concepts are now put in the field of Foreign Language Didactic at a very important place because the understanding of languages is an essential element in the relationship between various cultural communities and therefore help the understanding of the diverse forms to see and living the world. The teaching-learning of a foreign language must also stimulate the reflection on the diversity of cultural facts therefore stimulating the awareness of the learning person that excessive folklorisation could damage badly the reality of theses cultures. Through the analysis of the French Press elements about Brazil, we have been looking for an objective approach on how to demonstrate possible diversities, after having acknowledged the manner we have been seen through the selected articles. That has been very interesting because, as Brazilian, we have been in front of how the Other sees our society and therefore how we should conduct our representation analysis of the Other. The final aim is to support, through a better objectivity of the given facts, a thinking process on cultural diversity, on the importance of relativism and on the danger of excessive generalisation

Calculus at the university level is taken by thousands of undergraduate students each year. However, a significant number of students struggle with the subject, resulting in poor problem solving, low achievement, and high failure rates in the calculus courses overall (e.g., Kaput, 1994; Szydlik, 2000; Tall, 1985; Tall & Ramos, 2004; White & Mitchelmore, 1996). This is cause for concern as the lack of success in university calculus creates further barriers for students who require the course for their programs of study. This study examines this issue from the perspective of Tall’s Three Worlds of Mathematics (Tall, 2004a, 2004b, 2008), a theory of mathematics and mathematical cognitive development. A fundamental argument of Tall’s theory suggests that connecting between the different mathematical worlds, named the Embodied-Conceptual, Symbolic-Proceptual, and Formal-Axiomatic worlds, is essential for full cognitive development and understanding of mathematical concepts. Working from this perspective, this research examined, through the use of calculus task questions and semi-structured interviews, how fifteen undergraduate calculus students made connections between the different mathematical worlds for the calculus topics of limits and derivatives. The analysis of the findings suggests that how the students make connections can be described by eight different Response Categories. The study also found that how the participants made connections between mathematical worlds might be influenced by the type of questions that are asked and their experience in calculus courses. I infer that these Response Categories have significance for this study and offer potential for further study and educational practice. I conclude by identifying areas of further research in regards to calculus achievement, the Response Categories, and other findings such as a more detailed study of the influence of experience.

Orientadores: Dharam Vir Ahluwalia, Pedro Cunha de Holanda / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-27T16:17:02Z (GMT). No. of bitstreams: 1 Souza_GustavoSalinasde_M.pdf: 1015499 bytes, checksum: c37e17dd874ddddc3fa8389ff81fc905 (MD5) Previous issue date: 2015 / Resumo: O presente trabalho é dedicado a um estudo sistemático das representações dos grupos HOM(2) e SIM(2), que são subgrupos do grupo de Lorentz. É sabido que teorias cujas simetrias são descritas por tais subgrupos preservam a constância da velocidade da luz, esse fato sendo referido como Very Special Relativity. É mostrado que existem representa ções de HOM(2) e SIM(2) redutíveis e de dimensão nita, que portanto não podem ser obtidas inteiramente de representações irredutíveis. Estas são obtidas diretamente das representações das álgebras de Lie hom(2) e sim(2), usando o conhecimento dos grupos de cobertura universal de HOM(2) e SIM(2), que também são apresentados no texto / Abstract: The present work is devoted to a systematic study of the representations of the groups HOM(2) and SIM(2), which are subgroups of the Lorentz group. Theories with symmetries given by these subgroups are known to preserve the constancy of the speed of light, this fact being referred as Very Special Relativity. It is shown that there are nitedimensional reducible representations of HOM(2) and SIM(2) that are not completely reducible, and thus cannot be obtained entirely from irreducible representations. These are obtained directly from the representations of the Lie algebras hom(2) and sim(2), using the knowledge of the universal covering groups of HOM(2) and SIM(2), which are also presented in the text / Mestrado / Física / Mestre em Física

Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.

The aim of this thesis is to provide new insights and add to existing knowledge regarding how news media represents female politicians. Previous studies across the world have shown that throughout decades and still today, women tend to be underrepresented in political news or be heard only in regard to ‘feminine’ issues like education or family. Additionally, when it comes to female politicians, the focus is more often on their physical appearance, than it is with their male colleagues. In this thesis the focus is turned to Finland and the election of the country’s current Prime Minister, 34-year-old Sanna Marin. By conducting a thematic analysis, informed by the perspective of framing and representation theory, of news articles published around Marin’s election, this thesis explores the re-occurring themes regarding her representation in these articles and places these themes in a wider context of the media representation of female politicians. Framing theory helps to highlight the role media has in constructing reality whereas representation theory adds to the understanding of how people interpret the world, in this case the news, and helps to further argue why these presented representations matter. The analysis shows that the performance of a young female politician might seem accepted at first glance and doubtfulness is only found after one takes a look under the surface. Even though Finland can be considered a fairly gender equal country, gender stereotypes are still subtly reinforced by the media. Ultimately, it is not about how someone is represented, but rather what is left out. All this indicates that gender representations continue to be a salient issue and that female politicians like Sanna Marin still need to constantly prove their ability and competence as political subjects.

Our cultural values and socio-political perspectives are perhaps most clearly reflected in our material environment. When this environment is subjected to drastic change, the effects on these values and perspectives are likely to be profound. This dissertation considers the wide-ranging socio-cultural effects of material change through a close reading of three literary texts, each of which presents a portrait of a particular city in transition. The three texts which form the basis of this study are Orhan Pamuk's Istanbul: Memories and the City, William Dalrymple's City of Djinns: A Year in Delhi, and Ivan Vladislavic's Portrait with Keys: The City of Johannesburg Unlocked. In my reading of the effects of material change as depicted in these texts, I draw on architectural theorist Fred Scott's three possible approaches to existing material and cultural infrastructure, namely demolition, preservation and re-appropriation. Using this framework, and extending it in several ways, I discuss the ways in which processes of demolition/destruction, preservation, and adaptation/re-appropriation are inscribed in these texts. In Pamuk's Istanbul, the founding of the modern nation state of Turkey is shown to have stimulated two opposing responses, namely Mustafa Kemal's discourse of Turkification, concerned with development and modernity, and a reactionary melancholy yearning for the past, called hüzün. Dalrymple's City of Djinns highlights the various forms of socio-cultural destruction which accompanied Partition while also documenting the many examples of accidental preservation within the rapidly modernising city; also important in City of Djinns are descriptions of material and cultural re-appropriation, highlighted in depictions of urban resilience and the formation of new heterogeneous communities capable of transcending former divisions. Vladislavic's Johannesburg is also concerned with three possible responses to change in the urban environment after the abolition of apartheid: the urge to demolish and emigrate, the contrary need to preserve and fortify, as well as the compromise offered by the decision to re-appropriate and adapt. / Orhan Pamuk / Dissertation (MA)--University of Pretoria, 2017. / English / MA / Unrestricted

In this paper linear representations of finite groups are introduced, and the associated character theory with it. Some work of linear representations of the dihedral group $D_n$ and the symmetric group $S_n$ is presented. \\We also take a look at the finite matrix groups $\textbf{GL}(\mathbb{F}_q)$ and $\textbf{SL}(\mathbb{F}_q)$. The character table for $\textbf{SL}(\mathbb{F}_4)$ and its representation spaces in an implicit form are calculated. We define the standard representation $\varphi $ of $\textbf{SL}(\mathbb{F}_q)$ and prove that it is irreducible for an arbitrary finite field $\mathbb{F}_q$.