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This paper is a study of continue and related metric spaces, Chapter I is an introductory chapter. Irreducible continua and noncut points are the main topics in Chapter II. The third chapter begins with a few results on locally connected spaces. These results are then used to prove results in locally connected continua. Decomposable and indecomposable continua are dealt with in Chapter IV. Totally disconnected metric spaces are studied in the beginning of Chapter V. Then we see that every compact metric space is a continuous image of the Cantor set. A continuous map from the Cantor set onto [0,1] is constructed. Also, a continuous map from [0,1] onto [0,1]x[0,1] is built, Then an order preserving homeomorphism is constructed from a metric arc onto [0,1],

Number perception, its neural basis and its relationship to how numerical stimuli are presented have been challenging research topics in cognitive neuroscience for many years. A primary question that has been addressed is whether the perception of the quantity of a visually presented number stimulus is dissociable from its early visual perception. The present study examined the possible influence of visual quality judgment on quantity judgments of numbers. To address this issue, volunteer adult subjects performed a mental number comparison task in which two-digit stimulus numbers (Arabic number format), among the numbers between 31 and 99 were mentally compared to a memorized reference number, 65. Reaction times (RTs) and neurophysiological (i.e. electroencephalographic (EEG) data) responses were acquired simultaneously during performance of the two-digit number comparison task. In this particular quantity comparison task, the number stimuli were classified into three distance factors. That is, numbers were a close, medium or far distance from the reference number (i.e., 65). In order to evaluate the relationship between numerical stimulus quantity and quality, the number stimuli were embedded in varying degrees of a typical visual noise form, known as "salt and pepper noise" (e.g., the visual noise one perceives when viewing a photograph taken with a dusty camera lens). In this manner, the visual noise permitted visual quality to be manipulated across three levels: no noise, medium noise (approximately 60% degraded visual quality from nonoise), and dense noise (75% degraded visual quality from no-noise). / The RTs provided the information about the overt responses; however, the temporal relationship of visual quality (starts earlier than quantity perception) and quantity were examined using eventrelated potentials (ERPs) extracted from continuous EEG recordings. The analysis of the RTs revealed that the judgment of number quantity is dependent upon visual number quality. In addition, the same effect was observed over the ERP components occurring between 100 ms and 300 ms after stimulus onset time over the posterior electrodes. Principal components analysis (PCA) and independent component analysis (ICA) methods were used to further analyze the ERP data. The consistent results of the PCA and ICA were used to represent the spatial brain dynamics, as well as to obtain temporal dynamics. The overall conclusion of the present study is that ERPs, ICs and PCs along with RTs suggested a strategy of quantitative perception (i.e., number comparison) based on the qualitative attributes of the stimuli highlighting the importance of the design of the task and the methodology / by Meltem Ballan. / Thesis (Ph.D.)--Florida Atlantic University, 2010. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2010. Mode of access: World Wide Web.

My thesis examines Thomas Hobbes's attempt to develop a mathematical account of nature. I argue that Hobbes's conception of how we should think quantitatively about the world was deeply indebted to the ideas of his ancient and medieval predecessors. These ideas were often amenable to Hobbes's vision of a demonstrative, geometrically-based science. However, he was forced to adapt the ancient and medieval models to the demands of his own thoroughgoing materialism. This hybrid resulted in a distinctive, if only partially successful, approach to the problems of the new mechanical philosophy.

Orientador: Antonio Carlos Carrera de Souza / Banca: Margareth Aparecida Sacramento Rotondo / Banca: César Donizetti Pereira Leite / Resumo: O primeiro movimento desta pesquisa visa cartografar os processos: educador/educando e as possibilidades da relação dialógica entre estes, em situação de sala de aula. Como elemento constitutivo, deste movimento, foram utilizadas estratégias didáticas que enfatizaram o argumento e a construção conjunta de conhecimento incentivando, assim, ambientes criativos e heurísticos de aprendizagem. Desenharam-se oficinas em Geometria, olhando-as como um dispositivo acionador e de intervenção dentro da sala de aula para trabalhar com estudantes da Educação de Jovens e Adultos (EJA). Analisaram-se, assim, os processos, inerentes na relação dialógica, contextualizados nos estudos de Paulo Freire e nas relações de poder, como propostas por Michel Foucault. Foram exploradas situações problemáticas do entorno que conseguiram corresponder aos aspectos criativos como: a arte, a música e a exploração do meio. Espera-se que os resultados da investigação iluminem o tipo de relação argumentativa que ocorre em sala de aula. Ao utilizar estratégias didáticas, previamente desenhadas, como disparadoras do desenvolvimento das oficinas espera-se alterar, ao menos localmente, as relações de poder que travam as possibilidades dialógicas em sala de aula / Abstract: The first movement of this research aims to map the processes: teacher / student relationship and the possibilities of dialogue between them in the classroom situation. As a constitutive element, this movement used teaching strategies that emphasize the argument and the joint construction of knowledge by encouraging thus creative environments and heuristic learning. Were designed and conducted geometry workshops, that were observed as a driver and intervention device within the classroom to work with students of Youth and Adults (EJA). We analyzed the inherent processes in the dialogic relationship, contextualized in the studies of Paulo Freire and power relationships, as proposed by Michel Foucault. Surrounding situation issues that can match the creative aspects such as art, music and exploration of the environment were explored. The research findings elucidated the argumentative type of relationship that occur in the classroom. By using teaching strategies, previously designed as triggering of the development of the workshops, there was a change, at least locally, in the relations of power that keep dialogical possibilities in the classroom / Mestre

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Made available in DSpace on 2015-12-10T14:24:12Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-05-15. Added 1 bitstream(s) on 2015-12-10T14:30:21Z : No. of bitstreams: 1 000853981.pdf: 780858 bytes, checksum: 5ceb1d5a7d209ea636278ac985213d40 (MD5) / O presente trabalho exibe um estudo de caso sobre o desenvolvimento conceitual e metodológico da Matemática, por meio do exame e comparação das concepções de função de Gottlob Frege e Bertrand Russell. Em particular, são discutidos: a extensão fregiana da ideia matemática de função, a noção russelliana de função proposicional, os seus pressupostos filosóficos e as suas implicações. O presente estudo baseia-se em análises dos livros que os dois autores publicaram sobre os fundamentos da Matemática, e também de alguns outros escritos de sua autoria, entre eles, manuscritos que foram publicados postumamente. Conclui-se a partir dessas análises que a concepção compreensiva de função de Frege e a função proposicional de Russell são generalizações de uma importante aquisição do pensamento matemático, qual seja, a ideia de função, e que a conceitografia e as teorias dos tipos e das descrições, por sua vez, constituem a exploração metódica daquilo que essas generalizações acarretam. Conclui-se, finalmente, que embora existam diferenças expressivas entre as concepções de função de Frege e Russell, um padrão de rigor associado a reflexões mais amplas sobre a natureza do significado emerge em meio às investigações que empreenderam sobre a noção de função: a função fregiana e a função proposicional são as entidades que participam de suas respectivas relações de significado e cuja natureza é precisada no âmbito dessas relações / This work presents a case study about the conceptual and methodological development of Mathematics by the examination and comparison of function conceptions in the thinking of Gottlob Frege and Bertrand Russell. Particularly, we discuss the fregean extension of mathematical idea of function, the russellian notion of propositional function and their philosophical assumptions and implications. The basis for this study is a analisys of the authors' books on the foundations of Mathematics and some other authors' writings, included among these some posthumous publications. From this analisys we conclude that the comprehensive function concept of Frege and the Russell's propositional function are both generalizations of an important acquisition of mathematical thought, namely the idea of function, and that the conceptography, the type theory and the theory of descriptions, in turn, constitute the methodical exploration of what these generalizations imply. Finally, we conclude that, though there are expressives differences between the function conceptions of Frege and Russell, a pattern of rigour associated with more wide reflections on the nature of meaning emerges from their investigations of the concept of function: the fregian function and the propositional function are the entities that participate of their respective meaning relations and whose nature is explained by these relations

Made available in DSpace on 2015-06-17T19:34:45Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-21. Added 1 bitstream(s) on 2015-06-18T12:47:07Z : No. of bitstreams: 1 000831902.pdf: 2366966 bytes, checksum: 4543defc3a2094cda6bb6c2f79efc5a1 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O conceito de foreground se refere a como uma pessoa vê seu próprio futuro. Envolve seus desejos, sonhos, intenções, expectativas, esperanças, medos e obstáculos. Este conceito é discutido em uma perspectiva social e inclui o contexto social, político e econômico do indivíduo. Os motivos para alguém aprender são formados em seu foreground e, consequentemente, alunos com foregrounds arruinados, sem perspectivas atraentes de futuro, têm poucos motivos para aprender. Apesar de haver pesquisas que apresentam importantes contribuições para as relações entre o foreground de um indivíduo e seu engajamento em atividades educativas, elas não discutem o que pode ser feito quando o foreground de um estudante não oferece motivos para a aprendizagem. Isso remete à minha pergunta de pesquisa: como reelaborar foregrounds em ambientes educacionais? Para investigar o pretendido, optei por desenvolver um conjunto de atividades em um ambiente educacional com um grupo de jovens em idade escolar para entender de que forma tais atividades poderiam contribuir para a reelaboração de seus foregrounds. Este cenário da coleta de dados foi configurado em uma instituição social de semiabrigo e intitulado Projeto Futebol. Esse tema foi explorado tendo como foco o desejo de muitas crianças de se tornarem jogadores de futebol. As atividades desenvolvidas foram baseadas na proposta de trabalho com projetos e envolveram jogos, conversas com profissionais convidados, entrevistas, produção de maquete, gravação e edição de vídeo. Entrevistas realizadas com os jovens participantes e episódios ocorridos durante o Projeto Futebol foram analisados para identificar possíveis reelaborações em suas perspectivas de futuro e para discutir o próprio conceito de foreground. A análise dos dados levou em conta o seguinte objetivo de pesquisa: investigar os foregrounds de estudantes em um ambiente educacional baseado na proposta pedagógica de trabalho com... / The concept of foreground relates to how individuals see their future, including their wishes, dreams, intentions, expectations, hopes, fears, and obstacles. The concept of foreground is usually discussed from a social perspective, and includes the social, political and economic context of a person. The reasons that students have for learning are formed from their foregrounds therefore, students with ruined foregrounds feel they have no real prospects for the future and no reason to learn. Although there are studies that discuss the relation between the foreground of individuals and their engagement in educational activities, this research does not discuss what to do when a student's foreground does not offer any real reasons for learning. This leads to my research question: how to reform foregrounds in educational settings? To investigate this subject, I chose to develop a set of activities with a group of school children in an educational setting, which would allow me to understand how such activities could contribute to reforming their foregrounds. This data collection was set in a social institution that shelters economically poor children and adolescents in an after-school center. The theme of this project was Soccer Project, which focused on the natural desire of many children to become soccer players. Included, were activities based on the project work proposal, which included games, chats with professional guests, interviews, acting, and recording and editing video. Interviews with youth participants and episodes from the Soccer Project were analyzed to identify possible reforms in their future, as well as to discuss the concept of foreground in general. The data analysis took into account the following research objective: to investigate the student's foregrounds in an educational setting based on project work proposals, in order to discuss the foreground reforms. This research will contribute in the following ways: to the...

Made available in DSpace on 2014-08-13T14:50:59Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-03-20Bitstream added on 2014-08-13T17:59:45Z : No. of bitstreams: 1 000773957.pdf: 1468912 bytes, checksum: 082ae3b4f43830614c3238fd212a4786 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo dessa tese é investigar a relação entre matemática e filosofia em três obras de Platão: o Mênon, o Fédon e A República. Busca-se com isso esclarecer, primeiramente, a influência da matemática no desenvolvimento da filosofia, e, depois, o efeito desta na evolução metodológica daquela, principalmente no que diz respeito ao método analítico, ou hipotético. A pesquisa é norteada pelos testemunhos de Proclus em seus Comentários ao Livro I dos Elementos de Euclides, onde o nome de Platão é associado ao método. Em seguida, verifica-se a descrição dos métodos da análise e síntese feita por Pappus de Alexandria em sua Coleção matemática, a partir da qual são procurados nos diálogos os elementos precursores. A interpretação dos trechos matemáticos dos textos platônicos apoiase nos testemunhos e fragmentos de Hipócrates de Quios, Filolau de Crotona e Árquitas de Tarento, elaborando assim um quadro geral do estado da arte das ciências matemáticas nos séculos V-VI a.C. O seu intuito foi o de contextualizar as principais questões da matemática que teriam atraído o interesse de Platão, levando-o a valer-se da matemática como paradigma metodológico e heurístico a ser adaptado à filosofia. Apresentando uma inovação didática envolta por problemas da imprecisão da linguagem, Platão reformula as doutrinas présocráticas combinadas ao pensamento matemático, cujos desdobramentos são essenciais à organização aristotélica e à formalização Euclidiana / The objective of this thesis is to investigate the relationship between mathematics and philosophy in three Plato‟s work: the Meno, the Phaedo and the Republic. Searching with this to clarify, first, the influence of mathematics in the philosophy‟s development, and then, the effect of this one on the methodological development of that, especially with regard to the analytical or hypothetical method. The research is guided by the Proclus testimony in his Commentary On The First Book of Euclid’s Element, where the name of Plato is associated with the method. Hereupon, is checked the description of the methods of analysis and synthesis made by Pappus of Alexandria in his Mathematical Collection, from which is searched the precursor elements on the dialogues. The interpretation of the mathematical passages of the Platonic texts are based on testimonies and fragments of Hippocrates of Chios, Philolaus of Croton, and Archytas of Tarentum, thus elaborating a general picture of the mathematical sciences state of the art in the centuries V-VI BC. Its scope was to contextualize the main issues of the mathematics that have attracted the Plato‟s interest and that led him to avail himself of that science as a methodological and heuristic paradigm to be adapted to the philosophy. Featuring a didactic innovation surrounded by the imprecision of language problems, Plato reformulates the pre-Socratic doctrines combined to the mathematical thinking, whose developments are essential to Aristotelian organization and Euclidean formalization

Orientador: Ole Skovsmose / Banca: Otávio Roberto Jacobini / Banca: Maria do Carmo de Sousa / Banca: César Donizetti Pereira Leite / Banca: Antonio Vicente Marafioti Garnica / Resumo: O conceito de foreground se refere a como uma pessoa vê seu próprio futuro. Envolve seus desejos, sonhos, intenções, expectativas, esperanças, medos e obstáculos. Este conceito é discutido em uma perspectiva social e inclui o contexto social, político e econômico do indivíduo. Os motivos para alguém aprender são formados em seu foreground e, consequentemente, alunos com foregrounds arruinados, sem perspectivas atraentes de futuro, têm poucos motivos para aprender. Apesar de haver pesquisas que apresentam importantes contribuições para as relações entre o foreground de um indivíduo e seu engajamento em atividades educativas, elas não discutem o que pode ser feito quando o foreground de um estudante não oferece motivos para a aprendizagem. Isso remete à minha pergunta de pesquisa: como reelaborar foregrounds em ambientes educacionais? Para investigar o pretendido, optei por desenvolver um conjunto de atividades em um ambiente educacional com um grupo de jovens em idade escolar para entender de que forma tais atividades poderiam contribuir para a reelaboração de seus foregrounds. Este cenário da coleta de dados foi configurado em uma instituição social de semiabrigo e intitulado Projeto Futebol. Esse tema foi explorado tendo como foco o desejo de muitas crianças de se tornarem jogadores de futebol. As atividades desenvolvidas foram baseadas na proposta de trabalho com projetos e envolveram jogos, conversas com profissionais convidados, entrevistas, produção de maquete, gravação e edição de vídeo. Entrevistas realizadas com os jovens participantes e episódios ocorridos durante o Projeto Futebol foram analisados para identificar possíveis reelaborações em suas perspectivas de futuro e para discutir o próprio conceito de foreground. A análise dos dados levou em conta o seguinte objetivo de pesquisa: investigar os foregrounds de estudantes em um ambiente educacional baseado na proposta pedagógica de trabalho com... / Abstract: The concept of foreground relates to how individuals see their future, including their wishes, dreams, intentions, expectations, hopes, fears, and obstacles. The concept of foreground is usually discussed from a social perspective, and includes the social, political and economic context of a person. The reasons that students have for learning are formed from their foregrounds therefore, students with ruined foregrounds feel they have no real prospects for the future and no reason to learn. Although there are studies that discuss the relation between the foreground of individuals and their engagement in educational activities, this research does not discuss what to do when a student's foreground does not offer any real reasons for learning. This leads to my research question: how to reform foregrounds in educational settings? To investigate this subject, I chose to develop a set of activities with a group of school children in an educational setting, which would allow me to understand how such activities could contribute to reforming their foregrounds. This data collection was set in a social institution that shelters economically poor children and adolescents in an after-school center. The theme of this project was "Soccer Project", which focused on the natural desire of many children to become soccer players. Included, were activities based on the project work proposal, which included games, chats with professional guests, interviews, acting, and recording and editing video. Interviews with youth participants and episodes from the Soccer Project were analyzed to identify possible reforms in their future, as well as to discuss the concept of foreground in general. The data analysis took into account the following research objective: to investigate the student's foregrounds in an educational setting based on project work proposals, in order to discuss the foreground reforms. This research will contribute in the following ways: to the... / Doutor