Type 1 Diabetes (T1D) is an autoimmune disease where the pancreas produces little to no insulin, which is a hormone that regulates blood glucose levels. This happens because the immune system attacks (and kills) the beta cells of the pancreas, which are responsible for insulin production. Higher levels of glucose in the blood could have very negative, long term effects such as organ damage and blindness. To date, T1D does not have a defined cause nor cure, and research for this disease is slow and difficult due to the invasive nature of T1D experimentation. Mathematical modeling provides an alternative approach for treatment development and can greatly advance T1D research. This thesis describes both a single-compartment and multi-compartment model for Type 1 Diabetes.

This research is primarily concerned with the on-going development of the secondary mathematics curriculum in The Bahamas. In order to determine whether pupils assimilated mathematical ideas into a schematic structure, and could retrieve and use them as final behaviours outlined in the syllabuses, data from two diagnostic tests administered to pupils of 13+ and 15+ years respectively, were analysed. For the former age range, 377 pupils completed an Objective Test containing 50 items and for the latter age range 241 pupils attempted a Choice-Type Test with the instruction to choose any 10 of the total of 14 questions [continued]…

Submitted by Daniele Amaral (daniee_ni@hotmail.com) on 2016-09-15T16:05:03Z No. of bitstreams: 1 DissWCCJ.pdf: 1969639 bytes, checksum: cbe6746c0279668ba7ff3b8de72d8caf (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-16T19:51:53Z (GMT) No. of bitstreams: 1 DissWCCJ.pdf: 1969639 bytes, checksum: cbe6746c0279668ba7ff3b8de72d8caf (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-16T19:51:57Z (GMT) No. of bitstreams: 1 DissWCCJ.pdf: 1969639 bytes, checksum: cbe6746c0279668ba7ff3b8de72d8caf (MD5) / Made available in DSpace on 2016-09-16T19:52:02Z (GMT). No. of bitstreams: 1 DissWCCJ.pdf: 1969639 bytes, checksum: cbe6746c0279668ba7ff3b8de72d8caf (MD5) Previous issue date: 2015-08-21 / Não recebi financiamento / Cryptography is a fascinating topic, concerning the practical point of view, and it is useful to access bank accounts, e-mails and social networks. According to this perspective, this study aimed to show how simple it may be to make use of cryptography. It was proved, through the work performed, that it is possible for students from elementary and high school to encrypt and decrypt messages using R.S.A. Cryptography, which involves the concept of creating public keys and private keys for the encryption of messages. A simple but powerful activity on the utility view was assigned to show students from the 9th grade of elementary school and from the 1st and 2nd years of high school from a private school in São Paulo State how interesting and pleasurable the use of Mathematics can be. Such activities are not usually present in the traditional didactic materials. The theoretical tools, containing theorem and corollaries, as well as their demonstrations, which mathematically justify the validity of techniques and the algorithm used on R.S.A. Cryptography will be presented. The activities do not assume sophisticated prerequisites and can be applied in the classroom, in real situations, so that the students can appreciate the beauty of Mathematics. / A criptografia é um assunto fascinante do ponto de vista prático; é útil para acessar contas bancárias, e-mails e redes sociais. Segundo esta perspectiva, esta dissertação baseou-se em mostrar o quão simples pode ser a utilização da criptografia. No trabalho realizado foi mostrado que é possível, para alunos do Ensino Fundamental e Médio, codificar e decifrar mensagens utilizando a criptografia - RSA, a qual envolve o conceito da criação de chaves públicas e chaves privadas para a codificação de mensagens. Uma atividade simples, porém importante do ponto de vista utilitário, foi aplicada para mostrar aos alunos do 9º ano do Ensino Fundamental, da 1ª e 2ª séries do Ensino Médio de uma escola particular do interior paulista para mostrar o quão interessante e prazerosa pode ser a utilização da Matemática. Tais atividades não constam usualmente nos materiais didáticos tradicionais. Nesta dissertação será apresentado o ferramental teórico, contendo teoremas e corolários, assim como suas demonstrações, os quais justificam, matematicamente, a validade das técnicas e do algoritmo utilizados na criptografia – RSA. As atividades não pressupõem pré-requisitos sofisticados, podendo ser aplicadas em sala de aula, em situações reais, para que os alunos apreciem a beleza da Matemática.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2017-08-29T19:44:39Z No. of bitstreams: 1 2016 - Renan Lu?s da Silva.pdf: 4060423 bytes, checksum: a0c47ab6b30233ec990b5b29cf0b6a69 (MD5) / Made available in DSpace on 2017-08-29T19:44:39Z (GMT). No. of bitstreams: 1 2016 - Renan Lu?s da Silva.pdf: 4060423 bytes, checksum: a0c47ab6b30233ec990b5b29cf0b6a69 (MD5) Previous issue date: 2016-08-31 / CAPES / In the midst of the information age, it is necessary to approach and adapt the didactics and methodology in the classroom with the possibilities of placement through the use of the so-called Information and Communication Technologies (ICTs) that emerged at the end of the XX century, And are still at peak of use and possibilities these days. Regarding the elevation of Mathematics Education or the teaching of school mathematics are many as tools that enable a constructivist learning process (the student is the focus of learning and constructs his knowledge alone, with only a brief teacher's mediation) and that On the realization of an effective practice. Thus, the present study was developed in order to clarify and explain understandings of some of the main Information and Communication Technologies that can be implemented to make mathematics teaching feasible and also in a test of classroom experience and the benefits of using the tools of Information and Communication. / Em meio ? era informacional se fazem necess?rias a aproxima??o e a adequa??o da did?tica e da metodologia em sala de aula com as possibilidades colocadas pelo uso das chamadas Tecnologias de Informa??o e Comunica??o (TIC?s) que emergiram ainda no final do s?culo XX, muito timidamente, e ainda se encontram em apogeu de utiliza??o e possibilidades nos dias atuais. No que diz respeito ? eleva??o da Educa??o Matem?tica ou do ensino de matem?tica escolar s?o muitas as ferramentas que possibilitam um processo de aprendizagem construtivista (o aluno ? o foco da aprendizagem e constr?i seus conhecimentos sozinho, apenas com a breve media??o do docente) e que esteja longe de direcionamentos pragm?ticos, que conduzem a uma educa??o apenas para a efetiva??o pr?tica. Assim, o presente estudo se desenvolve no sentido de esclarecer e explicitar entendimentos acerca de algumas das principais Tecnologias de Informa??o e Comunica??o que podem ser efetivadas para viabilizar o ensino de matem?tica e, tamb?m, na realiza??o de uma experi?ncia em sala de aula, compreender os benef?cios impetrados pelo uso das ferramentas de Tecnologia da Informa??o e da Comunica??o.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-12-22T12:20:23Z No. of bitstreams: 1 Dissertação - Gilmar José do Nascimento - 2014.pdf: 3342644 bytes, checksum: 6d59b125cab769363607e1d9dfce31f4 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-01-26T13:24:20Z (GMT) No. of bitstreams: 1 Dissertação - Gilmar José do Nascimento - 2014.pdf: 3342644 bytes, checksum: 6d59b125cab769363607e1d9dfce31f4 (MD5) / Made available in DSpace on 2015-01-26T13:24:20Z (GMT). No. of bitstreams: 1 Dissertação - Gilmar José do Nascimento - 2014.pdf: 3342644 bytes, checksum: 6d59b125cab769363607e1d9dfce31f4 (MD5) Previous issue date: 2014-02-03 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / This work aims to enable the understanding of physics conceptions utilizing basic foundations of mathematics. In this regard, the aim is to highlight both those the phenomena that occur in nature as the phenomena which occur in laboratory manipulations. A extensive research is made about mathematical concepts that will subsequently be applied to several types of problems, being possible understand fundamental aspects involving physical quantities. With the goal to experience the in practice applications, robotic prototypes using LEGO MINDSTORMS kits, simulating real situations of nature and confronting of the computations with classical theoretical results are built. / Este trabalho tem como objetivo principal possibilitar a compreensão de conceitos físicos utilizando fundamentos básicos de matemática. Neste sentido, pretende-se evidenciar tanto os fenômenos que ocorrem na natureza quanto os fenômenos que ocorrem em manipulações de laboratórios. No presente estudo, é possível perceber que a matemática é de fundamental importância no estudo dos fenômenos físicos. Um vasto estudo é feito acerca de conceitos matemáticos que, em seguida, serão aplicados à vários tipos de problemas, sendo possível compreender aspectos fundamentais envolvendo grandezas físicas. Com o objetivo de vivenciar as aplicações na prática, são construídos protótipos robóticos utilizando os kits LEGO MINDSTORMS, simulando situações reais da natureza e confrontando os cálculos com resultados teóricos clássicos.

There is an increasing concern for the impact of humans on the environment. Traditionally, ecological models consider human influence as a constant or linearly varying parameter, whereas socioeconomic models and frameworks tend to oversimplify the ecological system. But tackling complex environmental challenges faced by our societies requires interdisciplinary approaches due to the intricate feedbacks between the socioeconomic and ecological systems involved. Thus, models of social-ecological systems couple an ecological system with a socioeconomic system to investigate their interaction in the integrated dynamical system. We define this coupling formally and apply the social-ecological approach to three ecological cases. Indeed, we focus on eutrophication in shallow freshwater lakes, which is a well-known system showing bistability between a clear water state and a turbid polluted state. We also study a model accounting for an aquifer (water stock) and a model accounting for a biotic population exhibiting bistability through an Allee effect. The socioeconomic dynamics is driven by the incentive that agents feel to act in a desirable or undesirable way. This incentive can be represented by a difference in utility, or in payoff, between two strategies that each agent can adopt: agents can cooperate and act in an environment-friendly way, or they can defect and act in an ecologically undesirable way. The agents' motivation includes such factors as the economic cost of their choice, the concern they feel for the environment and conformism to the collective attitude of the human group. Thus, the incentive to cooperate responds to the state of the ecological system and to the agents' collective opinion, and this response can be linear, nonlinear and monotonic, or non-monotonic. When investigating the mathematical form of this response, we find that monotonic non-linear responses may result in additional equilibria, cycles and basins of attraction compared to the linear case. Non-monotonic responses, such as resignation effects, may produce much more complicated nullclines such as a closed nullcline and weaken our ability to anticipate the dynamics of a social-ecological system. Regarding the modelling of the socioeconomic subsystem, the replicator dynamics and the logit best-response dynamics are widely used mathematical formulations from evolutionary game theory. There seems to be little awareness about the impact of choosing one or the other. The replicator dynamics assumes that the socioeconomic subsystem is stationary when all agents adopt the same behaviour, whereas the best-response dynamics assumes that this situation is not stationary. The replicator dynamics has formal game theoretical foundations, whereas best-response dynamics comes from psychology. Recent experiments found that the best-response dynamics explains empirical data better. We find that the two dynamics can produce a different number of equilibria as well as differences in their stability. The replicator dynamics is a limit case of the logit best-response dynamics when agents have an infinite rationality. We show that even generic social-ecological models can show multistability. In many cases, multistability allows for counterintuitive equilibria to emerge, where ecological desirability and socioeconomic desirability are not correlated. This makes generic management recommendations difficult to find and several policies with and without socioeconomic impact should be considered. Even in cases where there is a unique equilibrium, it can lose stability and give rise to sustained oscillations. We can interpret these oscillations in a way similar to the cycles found in classical predator-prey systems. In the lake pollution social-ecological model for instance, the agents' defection increases the lake pollution, which makes agents feel concerned and convince the majority to cooperate. Then, the ecological concern decreases because the lake is not polluted and the incentive to cooperate plummets, so that it becomes more advantageous for the agents to defect again. We show that the oscillations obtained when using the replicator dynamics tend to produce a make-or-break dynamics, where a random perturbation could shift the system to either full cooperation or full defection depending on its timing along the cycle. Management measures may shift the location of the social-ecological system at equilibrium, but also make attractors appear or disappear in the phase plane or change the resilience of stable steady states. The resilience of equilibria relates to basins of attraction and is especially important in the face of potential regime shifts. Sources of uncertainty that should be taken into account for the management of social-ecological systems include multistability and the possibility of counterintuitive equilibria, the wide range of possible policy measures with or without socioeconomic interventions, and the behaviour of human collectives involved, which may be described by different dynamics. Yet, uncertainty coming from the collective behaviour of agents is mitigated if they do not give up or rely on the other agents' efforts, which allows modelling to better inform decision makers.