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1
Gallo, Andrea. "The Kolmogorov Operator and its Applications in Finance". Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13815/.
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Nella tesi parliamo di una classe di operatori differenziali alle derivate parziali. In particolar modo dell'operatore di Kolmogorov, operatore degenere ma, grazie al celebre Teorema di Hormander, ipoellittico. Nei primi tre capitoli presentiamo una beve introduzione alla teoria dei gruppi di Lie stratificati, mostrandone alcune proprietà, in cui rientrano anche i K-gruppi dove incontriamo l'operatore di Kolmogorov. Nel quarto capitolo grande spazio è dato all'applicazione finanziaria del lavoro: la soluzione di un problema di Cauchy con l'equazione di Kolmogorov è il prezzo d'arbitraggio di un'opzione asiatica con media geometrica. Nella parte finale della tesi mostriamo una formula di rappresentazione delle soluzioni dell'equazione di Kolmogorov usando la soluzione fondamentale.
2
Shibalovich, Paul. "Fundamental theorem of algebra". CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2203.
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The fundamental theorem of algebra (FTA) is an important theorem in algebra. This theorem asserts that the complex field is algebracially closed. This thesis will include historical research of proofs of the fundamental theorem of algebra and provide information about the first proof given by Gauss of the theorem and the time when it was proved.
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Singh, Jesper. "On the fundamental theorem of calculus". Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-103809.
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The Riemann integral has many flaws, some that becomes visible in the fundamental theorem of calculus. The main point of this essay is to introduce the gauge integral, and prove a much more suitable version of that theorem.Riemannintegralen har många brister. Vissa utav dessa ser man i integralkalkylens huvudsats. Huvudmålet med denna uppsats är att introducera gauge integralen och visa en mer lämplig version av huvudsatsen.
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Backwell, Alex. "Recovery theorem: expounded and applied". Master's thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/8531.
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Includes bibliographical references.This dissertation is concerned with Ross' (2011) Recovery Theorem. It is generally held that a forward-looking probability distribution is unobtainable from derivative prices, because the market's risk-preferences are conceptually inextricable from the implied real-world distribution. Ross' result recovers this distribution without making the strong preference assumptions assumed necessary under the conventional paradigm. This dissertation aims to give the reader a thorough understanding of Ross Recovery, both from a theoretical and practical point of view. This starts with a formal delineation of the model and proof of the central result, motivated by the informal nature of Ross' working paper. This dissertation relaxes one of Ross' assumptions and arrives at the equivalent conclusion. This is followed by a critique of the model and assumptions. An a priori discussion only goes so far, but potentially problematic assumptions are identified, chief amongst which being time additive preferences of a representative agent. Attention is then turned to practical application of the theorem. The author identifies a number of obstacles to applying the result { some of which are somewhat atypical and have not been directly addressed in the literature { and suggests potential solutions. A salient obstacle is calibrating a state price matrix. This leads to an implementation of Ross Recovery on the FTSE/JSE Top40. The suggested approach is found to be workable, though certainly not the final word on the matter. A testing framework for the model is discussed and the dissertation is concluded with a consideration of the findings and the theorem's applicability.
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McCallum, Rupert Gordon Mathematics & Statistics Faculty of Science UNSW. "Generalisations of the fundamental theorem of projective geometry". Publisher:University of New South Wales. Mathematics & Statistics, 2009. http://handle.unsw.edu.au/1959.4/43385.
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The fundamental theorem of projective geometry states that a mapping from a projective space to itself whose range has a sufficient number of points in general position is a projective transformation possibly combined with a self-homomorphism of the underlying field. We obtain generalisations of this in many directions, dealing with the case where the mapping is only defined on an open subset of the underlying space, or a subset of positive measure, and dealing with many different spaces over many different rings.
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Cohen, Jeremy S. (Jeremy Stein) 1975. "Implementation and application of the fundamental theorem of probability". Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/46277.
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Thesis (M.Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (leaves 64-65).
The "RIK" (Reasoning with Incomplete Knowledge) algorithm, a mathematical programming based algorithm for performing probabilistic inference on (possibly) incompletely specified systems of discrete events is reviewed and implemented. Developed by Myers, Freund, and Kaufman, it is a tractable reformulation of the computational approach implicit to the Fundamental Theorem of Probability as stated by De Finetti and extended by Lad, Dickey and Rahman. Enhancements to the original algorithm are presented and several applications of the algorithm to real-world systems including fault trees and belief networks are explored. The system is solved successfully for moderately large problems, providing practical information for system designers coping with uncertainty.
by Jeremy S. Cohen.
M.Eng.and S.B.
7
Hayes, Mark Gerard. "Investment and finance under fundamental uncertainty". Thesis, University of Sunderland, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275518.
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Delbaen, Freddy y Walter Schachermayer. "The fundamental theorem of asset pricing for unbounded stochastic processes". SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 1999. http://epub.wu.ac.at/850/1/document.pdf.
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The Fundamental Theorem of Asset Pricing states - roughly speaking - that the absence of arbitrage possibilities for a stochastic process S is equivalent to the existence of an equivalent martingale measure for S. It turns out that it is quite hard to give precise and sharp versions of this theorem in proper generality, if one insists on modifying the concept of "no arbitrage" as little as possible. It was shown in [DS94] that for a locally bounded R^d-valued semi-martingale S the condition of No Free Lunch with Vanishing Risk is equivalent to the existence of an equivalent local martingale measure for the process S. It was asked whether the local boundedness assumption on S may be dropped. In the present paper we show that if we drop in this theorem the local boundedness assumption on S the theorem remains true if we replace the term equivalent local martingale measure by the term equivalent sigma-martingale measure. The concept of sigma-martingales was introduced by Chou and Emery - under the name of "semimartingales de la classe (Sigma_m)". We provide an example which shows that for the validity of the theorem in the non locally bounded case it is indeed necessary to pass to the concept of sigma-martingales. On the other hand, we also observe that for the applications in Mathematical Finance the notion of sigma-martingales provides a natural framework when working with non locally bounded processes S. The duality results which we obtained earlier are also extended to the non locally bounded case. As an application we characterize the hedgeable elements. (author's abstract)Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Bartolini, Gabriel. "On Poicarés Uniformization Theorem". Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-7968.
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A compact Riemann surface can be realized as a quotient space $\mathcal{U}/\Gamma$, where $\mathcal{U}$ is the sphere $\Sigma$, the euclidian plane $\mathbb{C}$ or the hyperbolic plane $\mathcal{H}$ and $\Gamma$ is a discrete group of automorphisms. This induces a covering $p:\mathcal{U}\rightarrow\mathcal{U}/\Gamma$.
For each $\Gamma$ acting on $\mathcal{H}$ we have a polygon $P$ such that $\mathcal{H}$ is tesselated by $P$ under the actions of the elements of $\Gamma$. On the other hand if $P$ is a hyperbolic polygon with a side pairing satisfying certain conditions, then the group $\Gamma$ generated by the side pairing is discrete and $P$ tesselates $\mathcal{H}$ under $\Gamma$.
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Lacaussade, Charles-Thierry. "Evaluation d'actifs financiers et frictions de marché". Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. http://www.theses.fr/2024UPSLD021.
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Cette thèse vise à fournir des méthodes théoriques et empiriques innovantes dans le cadre de l'évaluation des actifs financiers aux chercheurs en économie, aux teneurs de marché et aux différents acteurs de marché, dont les courtiers, les négociants, les gestionnaires d'actifs et les régulateurs. Nous proposons une extension du théorème fondamental de l'évaluation des actifs (FTAP) adaptée aux marchés présentant des frictions financières. Par conséquent, nos méthodes d'évaluation des actifs permettent d'obtenir un système de prix présentant des bid-ask spreads (écarts entre le prix d’achat et de vente), tels qu'ils sont observés sur les marchés financiers ce qui les rendent plus facilement interprétables. Dans le premier chapitre, nous introduisons deux théorèmes de représentation pour l'évaluation des actifs financiers sur les marchés à deux dates, en tenant compte d'une variété de frictions financières (coûts de transaction, taxes, frais de commission). Ce résultat repose sur une nouvelle condition d'absence d'arbitrage adaptée au marché avec frictions financières, qui prend en compte les stratégies potentielles d'achat et de vente. En outre, ces modèles d'évaluation des actifs reposent tous deux sur des mesures de probabilité non additives. Le premier modèle est une règle de prix de Choquet, pour laquelle nous proposons un cas particulier adapté à la calibration, et le second est une règle d'évaluation à priors multiples. Dans le deuxième chapitre, en vue de généraliser nos modèles d'évaluation des actifs, nous fournissons les conditions nécessaires et suffisantes pour des règles de prix de Choquet en multi-périodes caractérisées notamment par l’existence des bid-ask spreads. Nous montrons qu'il est possible de modéliser un problème de tarification dynamique sur plusieurs périodes par un problème de tarification sur une période lorsque la filtration est sans friction, ce qui est équivalent à supposer la propriété de martingale, qui est équivalente à supposer la cohérence des prix. Enfin, dans le troisième chapitre, nous présentons l'axiomatisation d'une classe particulière de règles de prix de Choquet, à savoir les règles de tarification dépendantes du rang qui supposent aussi l'absence d'arbitrage et la parité put-call (entre les options de vente et les options d'achat). Les règles de prix dépendantes du rang ont l'avantage d'être facilement calibrées car la mesure de probabilité non additive prend la forme de la probabilité objective distordue. Nous proposons donc une étude empirique de ces règles de prix dépendantes du rang par le biais d'une calibration paramétrique sur des données de marché afin d'explorer l'impact des frictions financières sur les prix. Nous étudions également la validité empirique de la parité put-call. En outre, nous étudions l'impact du délai d'expiration (valeur temps) et de la moneyness (valeur intrinsèque) sur la forme de la fonction de distorsion. Nous trouvons que les règles de prix dépendantes du rang qui en résultent sont toujours plus précises que la règle de référence (FTAP). Enfin, nous établissons un lien entre les frictions du marché et l'aversion au risque du marchéThis thesis aims to provide innovative theoretical and empirical methods for valuing securities to economics researchers, market makers, and participants, including brokers, dealers, asset managers, and regulators. We propose an extension of the Fundamental Theorem of Asset Pricing (FTAP) tailored to markets with financial frictions. Hence, our asset pricing methodologies allow for more tractable bid and ask prices, as observed in the financial market. This thesis provides both theoretical models and an empirical application of the pricing rule with bid-ask spreads.In our first chapter, we introduce two straightforward closed-form pricing expressions for securities in two-date markets, encompassing a variety of frictions (transaction cost, taxes, commission fees). This result relies on a novel absence of arbitrage condition tailored to the market with frictions considering potential buy and sell strategies. Furthermore, these asset pricing models both rely on non-additive probability measures. The first is a Choquet pricing rule, for which we offer a particular case adapted for calibration, and the second is a Multiple Priors pricing rule.In the second chapter, as a step toward generalizing our asset pricing models, we provide the necessary and sufficient conditions for multi-period pricing rules characterized by bid-ask spreads. We extend the multi-period version of the Fundamental Theorem of Asset Pricing by assuming the existence of market frictions. We show that it is possible to model a dynamic multi-period pricing problem with a one-stage pricing problem when the filtration is frictionless, which is equivalent to assuming the martingale property, which is equivalent to assuming price consistency.Finally, in the third chapter, we give the axiomatization of a particular class of Choquet pricing rule, namely Rank-Dependent pricing rules assuming the absence of arbitrage and put-call parity. Rank-dependent pricing rules have the appealing feature of being easily calibrated because the non-additive probability measure takes the form of a distorted objective probability. Therefore, we offer an empirical study of these Rank-Dependent pricing rules through a parametric calibration on market data to explore the impact of market frictions on prices. We also study the empirical validity of the put-call parity. Furthermore, we investigate the impact of time to expiration (time value) and moneyness (intrinsic value) on the shape of the distortion function. The resulting rank-dependent pricing rules always exhibit a greater accuracy than the benchmark (FTAP). Finally, we relate the market frictions to the market's risk aversion
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Zhang, Guangfeng. "Exchange rates : macro and micro fundamentals". Thesis, University of Glasgow, 2009. http://theses.gla.ac.uk/933/.
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This thesis aims to examine a number of issues related to exchange rate movements at different time horizons: long-run, in terms of investigating equilibrium real exchange rates; medium-run, in terms of investigating predictability of exchange rates in out-of-sample forecasting contexts; and short-run, in terms of studying high-frequency exchange rate dynamics in the actual foreign exchange trading. Specifically, we reassess four topics concerning exchange rate movements through macroeconomic fundamental analysis and microstructure approaches to exchange rates. With macro approaches, our study demonstrates, in a panel data setting, the link between real exchange rates and net foreign asset could be through the association between real exchange rates and trade balance. The panel study indicates the heterogeneity, in terms of the association between real exchange rates and trade balance, between the OECD economies and less mature economies. Our study on the monetary exchange rate model indicates the monetary model can describe the long-run behaviour of nominal exchange rates. Furthermore, we find the short-term exchange rate deviation adjustments to equilibrium and nonlinearities involved in the association between exchange rates and monetary fundamentals. With micro approaches, our study demonstrates, in short run, order flow has a significant impact on the contemporaneous exchange rate dynamics. However, we observe the prediction of order flow on the future exchange rate is quite weak. Our study also finds the weak interaction between macro news and private information in the exchange rate volatility study.
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Schachermayer, Walter. "The fundamental theorem of asset pricing under proportional transaction costs in finite discrete time". SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 2002. http://epub.wu.ac.at/1512/1/document.pdf.
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We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's approach to foreign exchange markets under transaction costs. The financial market is modelled by a d x d matrix-valued stochastic process Sigma_t_t=0^T specifying the mutual bid and ask prices between d assets. We introduce the notion of ``robust no arbitrage", which is a version of the no arbitrage concept, robust with respect to small changes of the bid ask spreads of Sigma_t_t=0^T. Dually, we interpret a concept used by Kabanov and his co-authors as "strictly consistent price systems". We show that this concept extends the notion of equivalent martingale measures, playing a well-known role in the frictionless case, to the present setting of bid-ask processes Sigma_t_t=0^T. The main theorem states that the bid-ask process Sigma_t_t=0^T satisfies the robust no arbitrage condition if it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Dalang-Morton-Willinger to the present setting, and also generalizes previous results obtained by Kabanov, Rasonyi and Stricker. An example of a 5-times-5-dimensional process Sigma_t_t=0^2 shows that, in this theorem, the robust no arbitrage condition cannot be replaced by the so-called strict no arbitrage condition, thus answering negatively a question raised by Kabanov, Rasonyi and Stricker. (author's abstract)Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Klisińska, Anna. "The fundamental theorem of calculus : a case study into the didactic transposition of proof /". Luleå : Luleå Tekniska Universitet, 2009. http://pure.ltu.se/ws/fbspretrieve/2732706.
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Mathew, Panakkal J. "Three Topics in Analysis: (I) The Fundamental Theorem of Calculus Implies that of Algebra, (II) Mini Sums for the Riesz Representing Measure, and (III) Holomorphic Domination and Complex Banach Manifolds Similar to Stein Manifolds". Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_diss/2.
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We look at three distinct topics in analysis. In the first we give a direct and easy proof that the usual Newton-Leibniz rule implies the fundamental theorem of algebra that any nonconstant complex polynomial of one complex variable has a complex root. Next, we look at the Riesz representation theorem and show that the Riesz representing measure often can be given in the form of mini sums just like in the case of the usual Lebesgue measure on a cube. Lastly, we look at the idea of holomorphic domination and use it to define a class of complex Banach manifolds that is similar in nature and definition to the class of Stein manifolds.
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Myers, Tracy S. (Tracy Scott). "Reasoning with incomplete probabilistic knowledge : the RIP algorithm for de Finetti's fundamental theorem of probability". Thesis, Massachusetts Institute of Technology, 1995. http://hdl.handle.net/1721.1/11885.
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Rocha, Vitail José. "Números complexos e o teorema fundamental da álgebra". Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/3683.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The objective of this work is to tell a little bit about the emergence and development of the Fundamental Theorem of Algebra, having as plot the historical context and the formalization of Complex Numbers, which mixes with this theorem. Considering the mathematical rigor in the construction of this subject, which o ered structure for the consolidation of this theorem. This work aims to achieve a more accessible demonstration, due to their necessary presence in high school, but in an axiomatic form.
O objetivo deste trabalho é contar um pouco sobre o surgimento e desenvolvimento do Teorema Fundamental da Álgebra, tendo como enredo o contexto histórico e formaliza ção dos Números Complexos, que se mistura com este teorema. Levando em consideração o rigor matemático na construção deste corpo, o qual ofereceu estrutura para a consolidação deste teorema. Este trabalho busca alcançar uma demonstração mais acessível, devido a sua presença necessária no Ensino Médio, mas de forma axiom ática .
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Majaya, Thomas Bongani. "The fundamental determinants of the South African real exchange rate from 1995 to 2014". Master's thesis, University of Cape Town, 2017. http://hdl.handle.net/11427/25332.
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In a connected world, the foreign exchange rate for any country ensures that exports are competitive, imports are affordable, and there exists an economic environment conducive for sustainable growth of the economy. South Africa as an emerging country is no exception. Many stakeholders including, the South African Reserve Bank (SARB) as the monetary authority of the country are interested in understanding the key factors that influence the South African exchange rate and how these factors may be managed effectively to ensure sustainable economic growth for the South African economy. This research studies the fundamental determinants of the real exchange rate (RER) for South Africa under a market driven floating exchange rate arrangement from March 1995 to December 2014. The research investigates the effects of the fundamental determinants of the RER on the South African rand using Johansen's method and a Vector Error Correction Model (VECM). The results of the research show that five fundamental variables drove the RER for the 20 years from 1995 to 2014 mainly commodity prices, interest rate differential, net foreign assets, terms of trade, openness and productivity. The most significant of these determinants were commodity prices, openness and productivity. The interaction of commodity prices and the RER point to the fact that South Africa does not suffer from the Dutch Disease. The research also supports the Balassa-Samuelson effect where an increase in productivity causes RER appreciation. In terms of policy, the research recommends that South Africa should continue to strengthen the manufacturing export led strategy as well as diversifying the economy. This entails growing the manufacturing sector, diversifying the export markets to reduce reliance on China and the Euro Zone. South Africa should continue with the inflation targeting policy of the SARB, implemented through the interest rate instrument, which only affects the domestic economy and has no major effect on the RER.
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Segadas, Vianna Claudia Coelho de. "Students' understanding of the fundamental theorem of calculus : an exploration of definitions, theorems and visual imagery". Thesis, University College London (University of London), 1998. http://discovery.ucl.ac.uk/10020309/.
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The aim of this research was to investigate students' understanding of the Fundamental Theorem of Calculus (FTC). The FTC was chosen as the basis of this research because it is one of the most important topics taught in calculus, establishing the link between the concepts of differentiation and integration. Data was collected from first year undergraduate students at the Federal University of Rio de Janeiro, in Brazil. The sample comprised students from three areas: mathematics, computer sciences and engineering. A pilot study was applied in 1994 and the main study in 1995 and 1996. Questionnaire, interviews based on responses to the questionnaire and computer-task based interviews were used. The data were analysed using both quantitative and qualitative methods. The results show that some of the students' obstacles to understanding the FTC are related to difficulties with the concepts of function, continuity, derivative and integral. The definitions of these concepts were not clear in their minds and they frequently made use of images that contained only partial aspects of the definitions or were based on some particular examples. This hampered the students when they met new examples that did not fit with their pre-formed images. It was also found that definitions and theorems were so fragmented in the students' minds that there was no way they could appreciate a proof, exemplified by the proof of the FTC. Their conceptions of proof reflected the fact that they were not used to thinking of proving as fundamental to generalising a proposition, and in examining a proof, it was difficult for them to see the central ideas behind it. These results are closely associated with students' habits: they tend not to pay attention to theoretical aspects, memorising algorithmic procedures without reflecting on their applicability.
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Scucuglia, Ricardo. "A investigação do teorema fundamental do cálculo com calculadoras gráficas /". Rio Claro : [s.n.], 2006. http://hdl.handle.net/11449/91065.
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Orientador: Marcelo de Carvalho BorbaBanca: Mônica E. Villarreal
Banca: Telma de S. Gracias
Resumo: A informática vem gerando discussões sobre fundamentos da Matemática e reorganizando dinâmicas em Educação Matemática. Baseado nessa idéia, e em meu engajamento como pesquisador participante do GPIMEM, estruturei uma pesquisa onde discuto como Estudantes-com-Calculadoras-Gráficas investigam o Teorema Fundamental do Cálculo (TFC). Apoiado na perspectiva epistemológica Seres-Humanos-com-Mídias, que evidencia o papel das tecnologias no processo de produção de conhecimento, realizei experimentos de ensino com duplas de estudantes do primeiro ano da graduação em matemática, UNESP, Rio Claro, SP. A partir da análise de vídeos da primeira sessão de Experimentos de Ensino notei que a utilização de programas e comandos da Calculadora Gráfica TI-83 condicionou o pensamento das estudantes na investigação dos conceitos de Soma de Riemann e Integração (conceitos intrinsecamente inerentes ao TFC). Na segunda sessão, explorando exemplos de funções polinomiais com o comando de integração definida da Calculadora Gráfica, os coletivos pensantes formados por Estudantes-com-Calculadoras- Gráficas-Lápis-e-Papel estabeleceram conjecturas sobre o TFC. No processo de demonstração deste Teorema, foram utilizadas noções intuitivas e notações simplificadas, antes que fosse usada a simbologia padronizada pela Matemática Acadêmica. Essa abordagem possibilitou o engajamento gradativo das estudantes em discussões matemáticas dedutivas a partir dos resultados obtidos experimentalmente com as atividades propostas na pesquisa.
Abstract: Information technology has been generating discussion regarding the foundations of mathematics, and reorganizing dynamics in mathematics education. Based on this idea, and on my engagement as a researcher participating in GPIMEM, I designed a study in which I discuss how students-with-graphing-calculators investigate the Fundamental Theorem of Calculus (FTC). Based on the epistemological perspective of humans-with-media, which emphasizes the role of technology in the process of knowledge production, I conducted teaching experiments with pairs of students enrolled in the first year of the mathematics program at the State University of São Paulo (UNESP), Rio Claro campus. Based on analysis of video-tapes of the first teaching experiments session, I noted that the use of programs and commands of the TI-83 graphing calculator conditioned the students thinking in the inquiry into the concepts Riemann Sums and Integration (concepts intrinsically inherent to the FTC). In the second session, exploring examples of polynomial functions with the definite integration command by the graphing calculator, the thinking collectives composed of students-withgraphing- calculators-paper-and-pencil established conjectures regarding the FTC. In the process of demonstrating this theorem, intuitive notions and simplified notations were used before using the standardized symbology of academic mathematics. This approach made it possible for the students to become gradually engaged in deductive mathematical discussions based on the results obtained experimentally through the activities proposed in the study.
Mestre
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Costa, Allan Inocêncio de Souza. "Uma demonstração do teorema fundamental da álgebra". Universidade Federal de São Carlos, 2016. https://repositorio.ufscar.br/handle/ufscar/8723.
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In this work we explain an elegant and accessible proof of the Fundamental Theorem of Algebra using the Lagrange Multipliers method. We believe this will be a valuable resource not only to Mathematics students, but also to students in related areas, as the Lagrange Multipliers method that lies at the heart of the proof is widely taught.
Neste trabalho expomos uma demonstração acessível e elegante do Teorema Fundamental da Álgebra utilizando o método dos multiplicadores de Lagrange. Acreditamos que este trabalho seria uma fonte valiosa não são para estudantes de Matemática, mas também para estudantes de áreas relacionadas, uma vez que o método dos multiplicadores de Lagrange é amplamente ensinado em cursos de exatas.
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Beirami, Ahmad. "Network compression via network memory: fundamental performance limits". Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/53448.
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The amount of information that is churned out daily around the world is staggering, and hence, future technological advancements are contingent upon development of scalable acquisition, inference, and communication mechanisms for this massive data. This Ph.D. dissertation draws upon mathematical tools from information theory and statistics to understand the fundamental performance limits of universal compression of this massive data at the packet level using universal compression just above layer 3 of the network when the intermediate network nodes are enabled with the capability of memorizing the previous traffic. Universality of compression imposes an inevitable redundancy (overhead) to the compression performance of universal codes, which is due to the learning of the unknown source statistics. In this work, the previous asymptotic results about the redundancy of universal compression are generalized to consider the performance of universal compression at the finite-length regime (that is applicable to small network packets). Further, network compression via memory is proposed as a compression-based solution for the compression of relatively small network packets whenever the network nodes (i.e., the encoder and the decoder) are equipped with memory and have access to massive amounts of previous communication. In a nutshell, network compression via memory learns the patterns and statistics of the payloads of the packets and uses it for compression and reduction of the traffic. Network compression via memory, with the cost of increasing the computational overhead in the network nodes, significantly reduces the transmission cost in the network. This leads to huge performance improvement as the cost of transmitting one bit is by far greater than the cost of processing it.
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CIBELLI, Gennaro. "Sharp Estimates for Fundamental Solutions of some degenerate Kolmogorov equations arising in Finance". Doctoral thesis, Università degli studi di Ferrara, 2017. http://hdl.handle.net/11392/2488066.
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The thesis is devoted to the study of a degenerate parabolic partial differential equation which arises in models for the pricing of Arithmetic Average Asian Options in Finance in the framework introduced by Black, Scholes and Merton.
The aim of the work is to prove optimal estimates for the fundamental solution of the related operator.
The interest in this result is in that an expression of the fundamental solution is not available, whereas explicit information on its asymptotic behaviour are provided in the work.
The problem of proving upper and lower estimates for the fundamental solution of a second order partial evolution operator has long history and it has been considered by many authors in the study of PDE's.
The methodology used involves several techniques belonging to the theory of Partial Differential Equations, Stochastic Processes and Optimal Control Theory, and can be applied to several different problems.
In particular, the proof of the lower bound relies on the repeated application of the Harnack inequality for positive solution of along a suitable chain of points, combined with an optimization procedure. Such procedure lead us to naturally consider an optimal control problem which will be explicitly solved.
For the upper bound, we combine analytical results with elementary tools belonging to Optimal Control Theory. In particular we use an analogous results to the Moser iteration and the Hamilton-Jacobi-Bellman equation for the value function related to a relevant optimal control problem.La tesi è dedicata allo studio di una equazione differenziale alle derivate parziali parabolica degenere che interviene in modelli per il pricing di Opzioni asiatiche a media aritmetica in Finanza nel setting introdotto da Black, Scholes e Merton. Lo scopo del lavoro è quello di ricavare stime ottimali per la soluzione fondamentale del relativo operatore. L'interesse in questo risultato risiede nel fatto che un' espressione della soluzione fondamentale non è disponibile, mentre informazioni esplicite sul suo comportamento asintotico sono fornite nel lavoro di Tesi. Il problema di dimostrare stime ottimali dall'alto e dal basso per la soluzione fondamentale di un operatore di evoluzione del secondo ordine ha lunga storia ed è stato considerato da molti autori nello studio delle PDE's. La metodologia utilizzata coinvonlge diverse tecniche appartenenti all' Analisi Matematica, Processi stocastici e Teoria del controllo ottimo e può essere applicata a diversi problemi. In particolare, la prova del limite inferiore si basa sulla ripetuta applicazione della disuguaglianza di Harnack per soluzioni positive lungo un'opportuna catena di punti, combinata con una procedura di ottimizzazione. Tale procedura ci conduce a considerare naturalmente un problema di controllo ottimo che sarà risolto in modo esplicito. Per il limite superiore, si combinano alcuni risultati di PDE con strumenti elementari appartenenti alla teoria del controllo ottimo. In particolare, si usano risultati analoghi all' iterazione Moser e l'equazione di Hamilton-Jacobi-Bellman per la funzione valore relativo ad un pertinente problema di controllo ottimo.
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Santos, Admilson Alves dos. "Trigonometria Hiperbólica: uma abordagem elementar". Universidade Federal de Roraima, 2014. http://www.bdtd.ufrr.br/tde_busca/arquivo.php?codArquivo=263.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorA meta principal desta dissertação é apresentar uma construção da trigonometria hiperbólica e um estudo das funções trigonométricas hiperbólicas de forma que alunos de iniciacão científica e professores do Ensino Médio tenham melhor acesso à referida teoria. A construção da trigonometria hiperbólica será feita priorizando a aplicação de conceitos elementares da matemática. Será utilizado o ramo direito da hiperbóle x2-y2 = 1, fazendo uma comparação com a construção da trigonometria circular e tomando como ponto de partida um setor hiperbolico. Sera necessario calcular a area desse setor hiperbólico, o que poderia ser feito através de uma integral denida, porem outros recursos elementares serão adotados, atendendo ao objetivo principal deste trabalho. Apresentar-se-á também uma conexão entre a trigonometria hiperbólica e a trigonometria circular, que é extendida num momento posterior para funções trigonométricas circulares e trigonométricas hiperbolicas. As funções trigonométricas hiperbólicas e suas funções inversas serão estudadas analítica e graficamente. O estudo analítico seguirá de forma completamente elementar, porém o estudo gráfico será feito utilizando alguns elementos da teoria dos limites de funções Algumas aplicações da trigonometria hiperbólica serão mostradas. Para analizar, é apresentada a trigonometria hiperbólica no conjunto dos números complexos.
The main goal of this dissertation is to present a construction of hyperbolic trigonometry, and a study of hyperbolic trigonometric functions so that undergraduate students and high school teachers have better access to that theory. The construction of hyperbolic trigonometry will be prioritizing the application of elementary concepts of math. Will be used the right branch of the hyperbola x2 y2 = 1, making a comparison with the construction of circular trigonometry and taking as starting point a hyperbolic trigonometry sector. Will need calculate the area of this hyperbolic sector, which could be done through of a denite integral, but other basic features will be adopted, answering to main objective of this work. Also present a connection between circular trigonometry and hyperbolic trigonometry, which is extended after for circular trigonometric functions and hyperbolic trigonometric functions. The hyperbolic trigonometric functions and their inverse functions will be studied analytically and graphically. The analytical study will follow so completely elementary, however the graphic study will be done using some elements of the theory of limits of functions. Some application of hyperbolic trigonometry are displayed. Finally, the hyperbolic trigonometry is presented in the set of complex numbers.
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CUNEO, Alejandro Javier. "Math for freedom. An original proof of the fundamental theorem of algebra within the ambit of real numbers". Doctoral thesis, Università degli studi di Bergamo, 2013. http://hdl.handle.net/10446/28645.
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At the beginning of my work there’s a description of a particular philosophy of mathematics, the mathematics for freedom, which is used to ultimately justify thoughts and positions about the didactics of mathematics. The main remark is that didactics of mathematics won’t be incisive by remaining on general considerations and thus avoiding the specific features of each topic to be learned. The origin of the didactic hints relative to specific topics can only derive from a profound mathematical study of these topics. The last observation is naturally followed by an explanation and a classification of what a profound mathematical study of a topic is. For many elementary topics in mathematics there is not enough mathematical research already performed at high levels of profundity, and this causes a serious didactic difficulty. For this reason, didactical concerns can motivate mathematical research. This is the case of the fundamental theorem of algebra in the ambit of real numbers. The existing proofs of this result make use of the complex numbers. The use of complex numbers causes that the fundamental ideas on which the proofs rely become very difficult to be identified. This motivates the development of an original proof of this result that avoids the use of complex numbers. As expected the proof I developed enlightens on the fundamental ideas on which the result rests. The zero-level curves that correspond to the remainder of the division between a generic even-degree polynomial and a quadratic polynomial present an interweaved pattern in a region far away enough from the origin, and this implies the existence of an intersection of these zero-level curves and therefore also the existence of a quadratic polynomial dividing the given even-degree polynomial. The proof makes extensive use of the recursive properties of the algebraic expression of the remainder and of continuity.
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Holanda, Felipe D'Angelo. "Introduction to differential geometry of plane curves". Universidade Federal do CearÃ, 2015. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=15052.
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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel SuperiorA intenÃÃo desse trabalho serà de abordar de forma bÃsica e introdutÃria o estudo da Geometria Diferencial, que por sua vez tem seus estudos iniciados com as Curvas Planas. Serà necessÃrio um conhecimento de CÃlculo Diferencial, Integral e Geometria AnalÃtica para melhor compreensÃo desse trabalho, pois como seu prÃprio nome nos transparece Geometria Diferencial vem de uma junÃÃo do estudo da Geometria envolvendo CÃlculo. Assim abordaremos subtemas como curvas suaves, vetor tangente, comprimento de arco passando por fÃrmulas de Frenet, curvas evolutas e involutas e finalizaremos com alguns teoremas importantes, como o teorema fundamental das curvas planas, teorema de Jordan e o teorema dos quatro vÃrtices. O que, basicamente representa, o capÃtulo 1, 4 e 6 do livro IntroduÃÃo Ãs Curvas Planas de HilÃrio Alencar e Walcy Santos.
The intention of this work is to address in basic form and introductory study of Differential Geometry, which in turn has started his studies with Planas curves. It will require a knowledge of Differential Calculus, Integral and Analytic Geometry for better understanding of this work, because as its name says in Differential Geometry comes from the joint study of geometry involving Calculation. So we discuss sub-themes as smooth curves, tangent vector, arc length through formulas of Frenet, evolutas curves and involute and conclude with some important theorems, as the fundamental theorem of plane curves, Jordan 's theorem and the theorem of four vertices. What basically is, Chapter 1, 4 and 6 of the book Introduction to Plane Curves HilÃrio Alencar and Walcy Santos.
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Scucuglia, Ricardo [UNESP]. "A investigação do teorema fundamental do cálculo com calculadoras gráficas". Universidade Estadual Paulista (UNESP), 2006. http://hdl.handle.net/11449/91065.
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A informática vem gerando discussões sobre fundamentos da Matemática e reorganizando dinâmicas em Educação Matemática. Baseado nessa idéia, e em meu engajamento como pesquisador participante do GPIMEM, estruturei uma pesquisa onde discuto como Estudantes-com-Calculadoras-Gráficas investigam o Teorema Fundamental do Cálculo (TFC). Apoiado na perspectiva epistemológica Seres-Humanos-com-Mídias, que evidencia o papel das tecnologias no processo de produção de conhecimento, realizei experimentos de ensino com duplas de estudantes do primeiro ano da graduação em matemática, UNESP, Rio Claro, SP. A partir da análise de vídeos da primeira sessão de Experimentos de Ensino notei que a utilização de programas e comandos da Calculadora Gráfica TI-83 condicionou o pensamento das estudantes na investigação dos conceitos de Soma de Riemann e Integração (conceitos intrinsecamente inerentes ao TFC). Na segunda sessão, explorando exemplos de funções polinomiais com o comando de integração definida da Calculadora Gráfica, os coletivos pensantes formados por Estudantes-com-Calculadoras- Gráficas-Lápis-e-Papel estabeleceram conjecturas sobre o TFC. No processo de demonstração deste Teorema, foram utilizadas noções intuitivas e notações simplificadas, antes que fosse usada a simbologia padronizada pela Matemática Acadêmica. Essa abordagem possibilitou o engajamento gradativo das estudantes em discussões matemáticas dedutivas a partir dos resultados obtidos experimentalmente com as atividades propostas na pesquisa.
Information technology has been generating discussion regarding the foundations of mathematics, and reorganizing dynamics in mathematics education. Based on this idea, and on my engagement as a researcher participating in GPIMEM, I designed a study in which I discuss how students-with-graphing-calculators investigate the Fundamental Theorem of Calculus (FTC). Based on the epistemological perspective of humans-with-media, which emphasizes the role of technology in the process of knowledge production, I conducted teaching experiments with pairs of students enrolled in the first year of the mathematics program at the State University of São Paulo (UNESP), Rio Claro campus. Based on analysis of video-tapes of the first teaching experiments session, I noted that the use of programs and commands of the TI-83 graphing calculator conditioned the students thinking in the inquiry into the concepts Riemann Sums and Integration (concepts intrinsically inherent to the FTC). In the second session, exploring examples of polynomial functions with the definite integration command by the graphing calculator, the thinking collectives composed of students-withgraphing- calculators-paper-and-pencil established conjectures regarding the FTC. In the process of demonstrating this theorem, intuitive notions and simplified notations were used before using the standardized symbology of academic mathematics. This approach made it possible for the students to become gradually engaged in deductive mathematical discussions based on the results obtained experimentally through the activities proposed in the study.
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Selli, Luis Fernando. "GeoGebra, recurso computacional a favor da aprendizagem matemática no ensino fundamental II". Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/5958.
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Previous issue date: 2014-03-21Financiadora de Estudos e Projetos
This paper is related to the application of GeoGebra software in the following topics: Ratio, Proportion, Thales Theorem, Similarities, Similarity of Triangles, Pythagorean Theorem, Trigonometric Ratios in the Triangle Rectangle, Number and circumference. Initially all the contents were thought by traditional method, board and chalk. Therefore the GeoGebra software was applied. It was developed to teachers and students (9th grade) of an elementary school involved in these activities. Positive and negative results were showed but there is a perspective of improvement. All the stages are separately related to help the understanding. The object is the analyses about the importance and relevancy of using computerized mathematical tools during the learning process.
Este trabalho trata da aplicação do software GeoGebra nos seguintes temas: Razão, Proporção, Teorema de Tales, Semelhança, Semelhança de Triângulos, Teorema de Pitágoras, Razões Trigonométricas no Triângulo Retângulo, o número e a Circunferência. Cada conteúdo foi trabalhado inicialmente do modo tradicional, giz e lousa, e posteriormente com o uso do GeoGebra. Desenvolvido de modo inédito para o professor e para os alunos de 8ª série (9° ano) envolvidos nas atividades, mostra resultados positivos e negativos com perspectiva de melhoras. Todas as etapas estão relatadas separadamente e o desenvolvimento foi feito de modo a favorecer uma compreensão adequada sobre o trabalho com o objetivo de propiciar a análise sobre a importância e relevância do uso de ferramentas matemáticas informatizadas no auxílio da aprendizagem.
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Ysusi, Mendoza Carla Mariana. "Estimation of the variation of prices using high-frequency financial data". Thesis, University of Oxford, 2005. http://ora.ox.ac.uk/objects/uuid:1b520271-2a63-428d-b5a0-e7e9c4afdc66.
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When high-frequency data is available, realised variance and realised absolute variation can be calculated from intra-day prices. In the context of a stochastic volatility model, realised variance and realised absolute variation can estimate the integrated variance and the integrated spot volatility respectively. A central limit theory enables us to do filtering and smoothing using model-based and model-free approaches in order to improve the precision of these estimators. When the log-price process involves a finite activity jump process, realised variance estimates the quadratic variation of both continuous and jump components. Other consistent estimators of integrated variance can be constructed on the basis of realised multipower variation, i.e., realised bipower, tripower and quadpower variation. These objects are robust to jumps in the log-price process. Therefore, given adequate asymptotic assumptions, the difference between realised multipower variation and realised variance can provide a tool to test for jumps in the process. Realised variance becomes biased in the presence of market microstructure effect, meanwhile realised bipower, tripower and quadpower variation are more robust in such a situation. Nevertheless there is always a trade-off between bias and variance; bias is due to market microstructure noise when sampling at high frequencies and variance is due to the asymptotic assumptions when sampling at low frequencies. By subsampling and averaging realised multipower variation this effect can be reduced, thereby allowing for calculations with higher frequencies.
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Barbosa, Gabriela dos Santos. "O teorema fundamental da aritmética: jogos e problemas com alunos do sexto ano do ensino fundamental". Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11358.
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Previous issue date: 2008-12-16Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The present thesis has the purpose of carrying out an interventionist study for the introduction of the Fundamental Theorem of Arithmetic (FTA) and main concepts associated to it to students of the 6th Grade of Basic Education. In the research we intend to answer the following question: What are the arguments used by students in the significance process of the Fundamental Theorem of Arithmetic? For that purpose, we carried out a study with 22 students of a private school situated in the north zone of Rio de Janeiro. The group had already been in touch, according to the school s formal point of view, with the concepts related to the Fundamental Theorem of Arithmetic: multiples, divisors, prime and compound numbers and prime factors decomposition. The research has as theoretical fundamental, the Conceptual Fields Theory proposed by Vergnaud (1983, 2001) and the ideas of Campbell and Zazquis (2002) related to the learning process of concepts associated with the Basic Number Theory, which TFA belongs to. The method used a study divided into three stages. The first stage was the collective use of an initial evaluation. The second addressed the intervention stage, which was divided into three activity groups, and inserted into them, there were two intermediary evaluations. And, at last, the third corresponds to the use, also collective, of a final evaluation, with the same questions as the initial evaluation. Data was analysed from two perspectives, one directed to quantitative analysis, where we tried to relate the percentages of rights, with the help of the statistic package SPSS (Statistical Package for Social Sciences). The second perspective was data analysis from the qualitative point of view, aiming at identifying the type of mistakes made by students, as well as their strategies to solve problem-situations. The results showed that students had developed their own scheme to deal with concepts in construction. In this process, even if implicitly, a series of mathematic concepts present in students actions; is the teacher s function to create favourable conditions for the students to explain them
A presente tese teve por objetivo realizar um estudo intervencionista para a introdução do Teorema Fundamental da Aritmética (TFA) e dos principais conceitos associados a ele com alunos do 6º ano do Ensino Fundamental. Na pesquisa, propomo-nos a responder a seguinte questão: De que argumentos os alunos se valem no processo de significação do Teorema Fundamental da Aritmética? Para tanto, realizamos um estudo com 22 alunos, advindos de uma turma de uma escola particular da zona norte do Rio de Janeiro. O grupo já havia tido contato, do ponto de vista formal da escola, com conceitos associados ao Teorema Fundamental da Aritmética: múltiplo, divisor, números primos e compostos e decomposição em fatores primos. A fundamentação teórica da pesquisa contou com a Teoria dos Campos Conceituais proposta por Vergnaud (1983, 2001) e as idéias de Campbell e Zazquis (2002) com relação à aprendizagem dos conceitos associados à Teoria Elementar dos Números, de que o TFA é parte integrante. O método constou de um estudo dividido em três etapas. A primeira referiu-se a aplicação coletiva de uma avaliação inicial. A segunda voltou-se para a fase de intervenção, que foi divida em três grupos de atividades intercalados por duas avaliações intermediárias. E, por fim, a terceira corresponde à aplicação, também coletiva, de uma avaliação final, com as mesmas questões da avaliação inicial. Os dados foram analisados em duas perspectivas: uma voltada à análise quantitativa, em que se buscou relacionar os percentuais de acerto, com a ajuda do pacote estatístico SPSS (Statistical Package for Social Science). A segunda perspectiva referiu-se à análise dos dados do ponto de vista qualitativo, visando identificar os tipos de erros cometidos pelos alunos, bem como suas estratégias na resolução de situações-problema. Os resultados mostraram que os alunos desenvolvem esquemas próprios para lidar com os conceitos em construção. Nesse processo, uma série de conceitos matemáticos está presente, ainda que implicitamente, em suas ações. É função do professor criar condições que favoreçam aos alunos explicitá-los
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Takaendesa, Peter. "The behaviour and fundamental determinants of the real exchange rate in South Africa". Thesis, Rhodes University, 2006. http://eprints.ru.ac.za/516/.
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De, Scheemaekere Xavier. "Essays in mathematical finance and in the epistemology of finance". Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209938.
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The goal of this thesis in finance is to combine the use of advanced mathematical methods with a return to foundational economic issues. In that perspective, I study generalized rational expectations and asset pricing in Chapter 2, and a converse comparison principle for backward stochastic differential equations with jumps in Chapter 3. Since the use of stochastic methods in finance is an interesting and complex issue in itself - if only to clarify the difference between the use of mathematical models in finance and in physics or biology - I also present a philosophical reflection on the interpretation of mathematical models in finance (Chapter 4). In Chapter 5, I conclude the thesis with an essay on the history and interpretation of mathematical probability - to be read while keeping in mind the fundamental role of mathematical probability in financial models.Doctorat en Sciences économiques et de gestion
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Silva, Daniel Ferreira da. "Uma introdução à integral de Riemann contextualizada ao ensino médio /". São José do Rio Preto, 2019. http://hdl.handle.net/11449/191105.
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Orientador: Fabiano Borges da SilvaResumo: Neste trabalho apresentamos a definição da integral de Riemann por meio de somatórios de retângulos que aproximam pela falta e pelo excesso a região sob uma curva definida por uma função. Posteriormente mostramos que as funções contínuas definidas num intervalo fechado e limitado [a, b] são integráveis e fornecemos um exemplo de função não integrável. Finalmente apresentamos o Teorema Fundamental do Cálculo e uma abordagem para a teoria de integração que pode ser aplicada no contexto do Ensino Médio.
Abstract: ln this work we present the definition of the Riemann integral by summing rectangles that approximate the region under a curve defined by a function due to lack and excess. Then we show that continuous functions defined in a closed and limited interval [a, b] are integrable, and after we provide an example of an unintegrable function. Finally we present the Fundamental Calculus Theorem and an approach to integration theory that can be applied in the High School context.
Mestre
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Cruz, Flávio Pereira da. "Argumentação e prova no ensino fundamental: análise de uma coleção didática de matemática". Pontifícia Universidade Católica de São Paulo, 2008. https://tede2.pucsp.br/handle/handle/11291.
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Previous issue date: 2008-02-15Secretaria da Educação do Estado de São Paulo
This dissertation aims to analyze how the collection Mathematics and Reality approaches argumentation and proof when it refers to the Fundamental Theorem of Arithmetic and the Theorem of Pythagoras. It s inserted in the Project AProvaME (Argumentation and Proof in School Mathematics) that proposes the investigation of conceptions of argumentation and proof in the teaching of mathematics in schools in the state of São Paulo and to form a group of researchers to elaborate situations of learning involving arguments and proof to be investigated in the classroom. The analysis of the collection, in our research, is based on the work done by BALACHEFF et. al. (2001) which presents possible activities that may involve argumentation and proof classifying them into various types and levels. We have used this classification, when it refers to the Fundamental Theorem of Arithmetic and the Theorem of Pythagoras, to consider the theoretical text and the respective exercises presented in the collection that are related to argumentation and proof. We have noticed that the proposed activities may basically be classified as "tasks of initiation to proof." We conclude, in our analysis, that the collection is not designed to work with argumentation and proof to develop such skills in students when presenting the Fundamental Theorem of Arithmetic and the Theorem of Pythagoras, and also when proposing its activities. We propose, at the end of our work, dynamic activities that may complement those that are present in the collection, aiming to help in the development of new approaches on argumentation and proof in the classroom
Este trabalho tem o objetivo de analisar como a coleção Matemática e Realidade aborda argumentação e prova quando trata do Teorema Fundamental da Aritmética e do Teorema de Pitágoras. Ele está inserido no projeto AProvaME - (Argumentação e Prova na Matemática Escolar) que propõe a investigação de concepções de argumentação e prova no ensino de matemática em escolas do estado de São Paulo e formar grupo de pesquisadores para elaborar situações de aprendizagem envolvendo argumentação e prova para serem investigadas em sala de aula. A análise da coleção, em nossa pesquisa, tem como fundamento o trabalho desenvolvido por BALACHEFF et. al. (2001) que apresenta possíveis atividades que possam envolver argumentação e prova classificando-as em vários tipos e níveis. Utilizamos esta classificação para analisar, quando trata do Teorema Fundamental da Aritmética e do Teorema de Pitágoras, o texto teórico e os respectivos exercícios apresentados na coleção e que estejam relacionados com argumentação e prova. Constatamos que são propostas basicamente atividades que podem ser classificadas como de tarefas de iniciação a prova . Concluímos, em nossa análise, que a coleção não visa o trabalho com argumentação e prova para desenvolver tais competências nos alunos quando apresenta os temas Teorema Fundamental da Aritmética e Teorema de Pitágoras e também quando propõe as respectivas atividades. Propomos ao final de nosso trabalho, atividades dinâmicas que podem complementar as que estão presentes na coleção, com o propósito de contribuir na elaboração de novas abordagens sobre argumentação e prova em sala de aula
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Grande, André Lúcio. "Um estudo epistemológico do Teorema Fundamental do Cálculo voltado ao seu ensino". Pontifícia Universidade Católica de São Paulo, 2013. https://tede2.pucsp.br/handle/handle/10979.
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Previous issue date: 2013-12-05Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The Fundamental Theorem of Calculus (FTC) occupies a prominent position in the study of Differential and Integral Calculus (DIC) as it establishes a relationship which exists between the operations of integration and differentiation as inverse to each other in addition to its use in the calculation of definite integrals, especially in solving problems which involve area, volume and arc length, amongst others. However, in the context of Mathematics Education, regarding the teaching and learning of Calculus, researches conducted in Brazil and other countries like France, England and the United States, have shown misunderstanding on the part of the students regarding the lack of connection between the concepts of Integral and Derivatives in the study of FTC. Facing this scenario, this thesis aimed at conducting a didactic and epistemological study of FTC, presenting, as its result, the elaboration and analysis of teaching intervention of which main aim was to reveal and bring up the relationship between the operations of derivation and integration and under which conditions this relationship is established as this constitutes the essence of the theorem. As a theoretical frame of reference, one has used the ideas connected to the use of intuition and rigor in the construction of mathematical knowledge according to Henri Poincaré (1995) as well as the categorizations of intuition and the interrelations between its components: the formal, algorithmic and intuitive components in mathematical activities according to Efraim Fischbein (1991). The research presented is qualitative, presenting, as methodological procedures, the development of a teaching intervention as wells as the analysis of the solutions to questions proposed by fourteen students from a technological course in a public college in the state of São Paulo with the help of Geogebra Software. In order to analyze the resolutions, besides the already mentioned theoretical frame of reference, one has also adopted the works of Tall (1991) on the role of visualization of the teaching of Calculus and the interrelationships with intuition and rigor. As results, one highlights that exploring the concepts of integral, initially by the idea of accumulation and working simultaneously with the question related to the variation of this accumulation, has shown to be a suitable strategy so that students could understand the mutual relationship between integration and derivation as operations inverse to each other, as well as it allowed them to internalize such relationship as in the genesis of FTC which came after the study of these operations. Furthermore, one can conclude that the concept of function constituted the conducting principle which guided students on the understanding of FTC. Nevertheless, difficulties in understanding the continuity of a function, one of the central points of the theorem, was also an issue which came up in the results of the teaching intervention. Analysis has shown better results on students dealing with mathematical activities when the axis of interactions among formal, algorithmic and intuitive components is dealt with the axis regarding the question of visualization in the process of teaching and learning Calculus. At the end of tasks, one has observed that students have begun to show indications of concern in order to relate intuition with rigor in the building of mathematical knowledge
O Teorema Fundamental do Cálculo (TFC) ocupa uma posição de destaque no estudo do Cálculo Diferencial e Integral (CDI), pois estabelece a relação existente entre as operações de integração e derivação como inversas entre si, além da sua utilização no cálculo de integrais definidas, em especial na resolução de problemas envolvendo área, volume e comprimento de arco, entre outras. Entretanto, no âmbito da Educação Matemática, quanto ao ensino e aprendizagem do Cálculo, pesquisas realizadas no Brasil e em outros países, tais como França, Inglaterra e Estados Unidos evidenciaram a incompreensão dos alunos no tocante à falta de ligação existente entre os conceitos de integral e derivada no estudo do TFC em um curso de Cálculo. Diante desse panorama, esta tese teve por objetivo realizar um estudo didático e epistemológico do TFC, apresentando como resultado a elaboração e análise de uma intervenção de ensino que procurou fazer emergir a relação entre as operações de integração e derivação e sob quais condições essa relação se estabelece, o que constitui a essência do teorema. Como referencial teórico foram utilizadas as ideias ligadas ao uso da intuição e do rigor na construção do conhecimento matemático, segundo Henri Poincaré (1995), bem como as categorizações da intuição e as inter-relações entre os componentes: formal, algorítmico e intuitivo nas atividades matemáticas, de acordo com Efraim Fischbein (1991). A pesquisa é qualitativa, apresentando como procedimentos metodológicos a elaboração de uma intervenção de ensino, bem como a análise das resoluções das questões efetuadas por 14 estudantes do curso de Tecnologia de uma faculdade pública do Estado de São Paulo com o auxílio do software GeoGebra. Para análise das resoluções, além do referencial teórico citado, foram adotados os trabalhos de Tall (1991) sobre o papel da visualização no ensino do Cálculo e as inter-relações com a intuição e o rigor. Como resultados, destaca-se que explorar os conceitos de integral inicialmente por meio da ideia de acumulação, simultaneamente trabalhando-se com a questão da variação dessa acumulação, mostrou-se uma estratégia pertinente para que os estudantes compreendessem a relação mútua entre integração e derivação como operações inversas uma da outra, assim como permitiu que os estudantes interiorizassem que tal relação, como ocorreu na gênese do TFC, realizou-se posteriormente ao estudo dessas operações. Além disso, pode-se concluir que o conceito de função constituiu-se na linha condutora que norteou o entendimento dos estudantes sobre o TFC. Não obstante, as dificuldades da compreensão de continuidade de uma função, um dos pontos centrais do teorema, também foi uma questão que emergiu dos resultados da intervenção de ensino. A análise mostrou melhores resultados por parte dos estudantes nas atividades matemáticas, quando o eixo das interações entre os componentes algorítmico, formal e intuitivo é trabalhado em conjunto com o eixo relacionado à questão da visualização no ensino e aprendizagem do Cálculo. No final das tarefas, observou-se que os estudantes começaram a mostrar indícios da preocupação de relacionar a intuição com o rigor na construção do conhecimento matemático
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Stegani, Ozilde Peter. "O teorema de Pitágoras no oitavo ano do ensino fundamental". Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/5961.
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Previous issue date: 2014-05-23Financiadora de Estudos e Projetos
In this paper we reflect on a group of eight lessons applied in the eighth year of elementary school. In these classes, we treat the Pythagorean Theorem, seeking to justify this outcome appropriate to the student s eighth grade elementary school mode. We were interested in seeking justifications with historical content, to rescue, to the extent possible, a part of the history of the Pythagorean Theorem. We take care to seek a mathematical justification for each procedure adopted to develop pedagogical activities. Throughout the text brushing been several suggestions for improving the finished product, though it kept almost entirely in Appendix 1. Also critical to our work interweave throughout the text, seeking both personal growth as offering the opportunity for a better match of the final product to whom this is of interest. At the end we suggest some current applications of the Pythagorean Theorem. Finished the job in the classroom involving the class with the game of dominoes, adapted to the content studied, trying to leave a better final impression on the students. We describe the construction of pedagogical object, the math worked during such construction and finally its application in the classroom. We make four appendices. In the first present the final product. In the second we seek to exemplify the student s work. In the third and fourth work building Pythagorean triangles.
Neste trabalho procuramos refletir sobre um grupo de oito aulas aplicadas no oitavo ano do Ensino Fundamental. Nestas aulas, tratamos do Teorema de Pitágoras, buscando justificar este resultado de modo adequado ao aluno do oitavo ano do Ensino Fundamental. Foi de nosso interesse buscar justificativas com um teor histórico, de modo a resgatar, na medida do possível, uma parte da história do Teorema de Pitágoras. Tomamos o cuidado de buscar uma justificativa matemática para o cada procedimento pedagógico adotado ao desenvolver as atividades. Durante todo o texto fomos pincelando várias sugestões para melhorar o produto final, se bem que o mantivemos quase que totalmente no Apêndice 1. Também entremeamos críticas ao nosso trabalho durante todo o texto, buscando tanto um crescimento pessoal quanto ofertando a oportunidade de uma melhor adequação do produto final a quem este for de interesse. Ao final sugerimos algumas aplicações atuais do Teorema de Pitágoras. Terminamos o trabalho em sala de aula envolvendo a classe com o jogo de dominó, adaptado ao conteúdo estudado, buscando deixar uma melhor impressão final nos alunos. Descrevemos a construção deste objeto pedagógico, a matemática trabalhada durante tal construção e por último sua aplicação com em aula. Confeccionamos quatro apêndices. No primeiro apresentamos o produto final. No segundo buscamos exemplificar os trabalhos dos alunos. No terceiro e quarto trabalhamos a construção de triângulos pitagóricos.
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Anacleto, Grácia Maria Catelli. "Uma investigação sobre a aprendizagem do teorema fundamental do cálculo". Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11280.
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Previous issue date: 2007-10-09This study aims to investigate the knowledge mobilized by students who have already studied the Fundamental Theorem of Calculus (FTC) regarding the concepts of differentiation and integration and its relationship. The FTC is one of the most important topic in any Calculus course according to Segadas (1998). The intention of the study is to evaluate if the mobilization of these concepts occurred in the proper manner for specific questions resolution where necessarily they have to be applied. The research was based on Douady s (1987) theoretical beliefs of the tool-object dialectic and change of frameworks. As support the study was carried through Segadas (1998) research on the understanding of the FTC by students at the end of the course of Calculus. A pilot-questionnaire was applied to students of a Computer Science course in a private University of São Paulo city. In this first inquiry we perceive the participant students had not received the FTC related content in the deep required for our research in this course. Thus we have decide restructure the questionnaire and apply it to a different group of students in the Mathematics Bachelors course where the FTC content was teach deeper due to greater teaching load in the same university. The research found the majority of the students have found difficulties to solve problems where the simple visualization of graphs would solve it without developing extensive algorithms. This findings shows the students obstacles to understand the FTC are related to an incomplete mobilization of differentiation, integration and continuity concepts since to solve the given questions they have only partially used these knowledge. Such fact is probably associated the students habits who do not tend to focus their attention to the conceptual aspects of the theorem but only memorizing the procedures algorithm without reflecting on its applicability. The theoretical fundamentals used revealed an efficient tool in the analysis of the protocols who led us to these conclusions
Este estudo teve por objetivo investigar os conhecimentos mobilizados por alunos que já haviam estudado o Teorema Fundamental do Cálculo (TFC) relativamente aos conceitos de derivada e integral e sua interelação. O TFC, segundo Segadas (1998), é um dos tópicos mais importantes em qualquer curso de Cálculo. Pretendemos com o trabalho avaliar se a mobilização desses conceitos se deu de forma adequada na resolução de questões específicas em que a aplicação desses conceitos era necessária. A pesquisa fundamentou-se nos pressupostos teóricos da dialética ferramenta-objeto e jogos de quadros de Douady (1987). Teve como base a pesquisa realizada por Segadas (1998) sobre a compreensão do TFC pelos alunos ao final do curso de Cálculo. Foi aplicado um questionáriopiloto a alunos do curso da Ciência da Computação de uma universidade particular da cidade de São Paulo. Percebemos nessa primeira investigação que alunos que participaram do estudo piloto não haviam recebido o conteúdo relativo ao TFC com a profundidade requerida pela nossa pesquisa. Reestruturamos o questionário e reaplicamos a um grupo alunos do curso de Licenciatura em Matemática desta mesma universidade, onde esta disciplina é ministrada com maior carga horária. Verificamos que a maioria dos alunos encontrou dificuldades para solucionar problemas em que a simples visualização de gráficos faria com que não necessitassem desenvolver longos algoritmos. Este resultado demonstra que os obstáculos dos estudantes para compreender o TFC estão relacionados com uma incompleta mobilização das noções de derivada, integral e continuidade, uma vez que utilizaram apenas parcialmente esses conhecimentos para a solução das questões apresentadas. Tal fato está provavelmente associado aos hábitos dos estudantes, que tendem a não focar atenção aos aspectos conceituais do teorema, apenas memorizando o algoritmo dos procedimentos sem refletir sobre a sua aplicabilidade. A fundamentação teórica mostrou-se uma ferramenta eficaz na análise dos protocolos que nos conduziram a essas conclusões
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Toledo, André Ferraz de. "Teorema fundamental da álgebra : uma abordagem visual para o Ensino Médio". reponame:Repositório Institucional da UFABC, 2016.
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Orientadora: Profa. Dra. Ana Carolina BoeroDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Mestrado Profissional em Matemática em Rede Nacional, 2016.
O Teorema Fundamental da Álgebra é um tópico de grande relevância para a Matemática, com o qual o aluno toma contato na 3a série do Ensino Médio. Talvez porque todas as demonstrações conhecidas desse resultado utilizem argumentos que não podem ser apresentados de modo preciso nessa etapa de ensino, sua abordagem em diversos livros didáticos resume-se, basicamente, a destacar algumas de suas consequências e aplicações. O propósito deste trabalho é fornecer um material que possa ser utilizado por professores da Educação Básica no intuito de explorar esse fascinante resultado. Para atingirmos esse objetivo, apresentamos uma breve contextualizaçãohistória do Teorema Fundamental da Álgebra, que serve tanto para apontar sua utilidade em outros ramos da Matemática como também para observar a evolução de certos conceitos matemáticos. Em seguida, apresentamos uma prova rigorosa desse resultado, com o menor nível de complexidade possível, além de duas abordagens alternativas com apelo visual que podem ser utilizadas para apresentar uma justificativa de sua validade aos alunos do Ensino Médio.
The Fundamental Theorem of Algebra is a topic of great relevance to Mathematics, with which the student makes contact in the 3rd grade of High School. Perhaps because all known demonstrations of this result use arguments that can not be accurately presented at this stage of teaching, its approach in several textbooks basically boils down to highlighting some of its consequences and applications. The purpose of this work is to provide a material that can be used by teachers of Basic Education in order to explore this fascinating result. To reach this goal, we present a brief history of the Fundamental Theorem of Algebra, which serves both to point out its usefulness in other branches of mathematics and also to observe the evolution of certain mathematical concepts. Next, we present a rigorous proof of this result, with the lowest level of complexity possible, as well as two alternative approaches with visual appeal that can be used to present a justification of its validity to high school students.
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Diniz, Josedilton Alves. "Eficiência das transferências intergovernamentais para a educação fundamental de municípios brasileiros". Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/12/12136/tde-26072012-113928/.
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Existe um consenso na literatura segundo o qual as habilidades, os conhecimentos e a capacidade dos indivíduos produzem um aumento no nível de capital humano, que é elemento-chave para o progresso econômico de um país e de sua qualidade de vida. O Estado procura, de maneira geral, criar formas de potencializar os investimentos destinados à educação. A forma como esses recursos são alocados e distribuídos vai determinar a eficiência do gasto público. A eficiência da educação pode ser expressa por indicadores que refletem a qualidade da atividade educacional, comparados com os recursos aplicados. A definição dessa eficiência depende de vários fatores. Alguns deles são controlados pelo gestor; outros não, tais como: background familiar, característica do aluno e dos professores. Além desses aspectos, há também aqueles de natureza política que podem influenciar a estrutura de todas as relações intergovernamentais de um país, principalmente aquelas referentes ao financiamento dos serviços de educação. As relações definidas no pacto federativo têm implicações nos resultados da educação, na medida em que se efetivam as bases de negociação. Na educação brasileira, há alguns problemas intergovernamentais na definição de diretrizes, principalmente nas transferências de recursos. Muitas vezes, as decisões são tomadas unilateralmente pelo governo central, que intervém no montante de recursos a serem transferidos e na forma como eles devem ser aplicados, diminuindo a autonomia do município, bem como desconsiderando o conhecimento do gestor acerca das reais necessidades da comunidade e as especificidades locais. O objetivo desta pesquisa é mensurar a eficiência da aplicação dos gastos em educação e procurar identificar relações empíricas que validem a tese de que as transferências condicionais da educação fundamental são desfavoráveis à eficiência da aplicação de recursos. A fundamentação teórica para esta tese teve na teoria do federalismo fiscal sua principal ancoragem. Subsidiariamente, a teoria econômica da educação ajudou na compreensão da problemática e na definição das variáveis utilizadas para mensurar a eficiência da educação fundamental. Na parte empírica da pesquisa, mensurou-se a eficiência utilizando a técnica da Análise Envoltória de Dados em painel, denominada de DEA dinâmica DSBM (Dinamic Slacks Based Model), com dados do período de 2004 a 2009, referentes a 3.013 municípios brasileiros. Essa fase foi desenvolvida em dois estágios. No primeiro, utilizaram-se os insumos controlados pelo gestor (custo por aluno) e o Índice de Desenvolvimento da Educação Básica - IDEB, como produto da educação. No segundo, ajustaram-se os escores de eficiência obtidos no primeiro estágio, acrescentando ao modelo as variáveis não-controladas pelo gestor, mas que influenciavam a eficiência. A partir desses ajustamentos no poder discricionário dos escores de eficiência técnica, foi feita uma regressão GEE (Generalized Estimating Equations), tendo como variáveis explicativas da eficiência as transferências condicionais da educação fundamental, tais como: o Fundo de Manutenção e Desenvolvimento da Educação Básica (FUNDEB) e o Fundo Nacional de Desenvolvimento da Educação (FNDE). Os resultados revelaram que, de forma geral, as transferências intergovernamentais condicionais direcionadas à educação afetam negativamente a eficiência dos gastos públicos no ensino fundamental, confirmando a tese proposta. Destaque-se, ainda, que a autonomia financeira tem um efeito positivo na eficiência da educação. Por fim, há evidências empíricas para afirmar que os municípios considerados mais eficientes têm maior custo por aluno, maiores índices de desenvolvimento da educação básica e maior número de alunos matriculados. Acredita-se que esta pesquisa possa proporcionar uma reflexão acerca da estrutura de financiamento da educação, especialmente no que diz respeito às condicionalidades de recursos específicos ao ensino fundamental.There is a consensus in the literature that skills, knowledge and ability of individuals produce an increased level of human capital that is the key to the economic progress of a country and the quality of life. The State seeks, in general, to create ways to leverage investments to education. The way these resources are allocated and distributed will determine the efficiency of public spending. The efficiency of education can be expressed by indicators that reflect the quality of the educational activity, compared to the resources applied. The definition of this efficiency depends on several factors, some of them are controlled by the manager and others not, such as family background, characteristics of students and teachers. Besides these aspects, there are also those of political nature that may influence the structure of all intergovernmental relations of a country, especially those relating to financing of education services. The relations defined in the federal pact have implications for the results of education to the extent that accomplishes the basis for negotiation. In Brazilian education, there are some intergovernmental problems in the definition of guidelines, especially in resource transfers. Often, the decisions are made unilaterally by the central government that intervenes in the amount of resources to be transferred and the way these resources should be applied, decreasing the municipal autonomy as well as ignoring the manager\'s knowledge about the real needs of the community and local specificity. The objective of this research is to measure the efficiency of the application of spending on education and seek to identify empirical relations that validate the thesis that the conditional transfer of basic education are unfavorable to the efficient use of resources. The theoretical basis for this thesis had on the theory of fiscal federalism its main anchor. Alternatively, the economic theory of education has helped in understanding the problem and definition of variables used to measure the efficiency of education. In the empirical part of this research, the efficiency was measured using Data Envelopment Analysis in panel, called Dynamic DEA DSBM (Slacks Based Dynamic Model) with data for the period 2004 to 2009, relating to 3013 municipalities. This phase was conducted in two stages. At first stage, we used the inputs controlled by the manager (cost per student) and the Index of Development of Basic Education - IDEB, as a product of education. In the second stage, we adjusted the scores obtained in the first stage adding to the model uncontrollable variables by the manager, but that affected the efficiency. From these adjustments at the discretion of the technical efficiency scores, was made a regression GEE (Generalized Estimating Equations), having as explanatory variables of the efficiency the conditional transfer of basic education such as the Fund for the Development of Basic Education (FUNDEB) and the Fund for the National Education Development (FNDE). The results revealed that, in general, that conditionals transfers to education negatively affect the efficiency of public spending in basic education, confirmed the thesis proposed. Also, it should be noted that financial autonomy has a positive effect on the efficiency of education. Finally, there is empirical evidence to argue that municipalities considered more efficient have higher cost per student, larger IDEB and larger number of students enrolled. We believed that this research can provide a reflection on the structure of education funding, especially with regard to the conditionalities of specific resources to basic education.
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Barros, Jéssica Laís Calado de. "O teorema da aplicação de Riemann: uma prova livre de integração". Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-13122017-161946/.
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Neste trabalho, seguindo a abordagem de Weierstrass, temos o objetivo de responder a seguinte questão: conhecida a equivalência entre holomorfia e analiticidade no caso complexo, quais propriedades das funções analíticas podem ser obtidas sem assumir tal equivalência? Analisando esta situação, resultados interessantes serão obtidos sem o uso de qualquer teorema de integração complexa e, para alcançar tal objetivo, nossas principais ferramentas serão a teoria de somas não ordenadas de famílias em C e propriedades do índice de caminhos fechados. Entre os resultados apresentados estão os conhecidos Teorema Fundamental da Álgebra, Lema de Schwarz, Teorema de Montel, Teorema da Série Dupla de Weierstrass, Princípio do Argumento, Teorema de Rouché, Teorema da Fatoração de Weierstrass, Pequeno Teorema de Picard e o Teorema da Aplicação de Riemann.In this work, following the Weierstrass\'s approach, we aim to answer the following question: knowing the equivalence between holomorphy and analyticity in the complex case, which properties of analytic functions can be obtained without assuming such equivalence? Through analyzing this situation, interesting results will be obtained without employing of any complex integration theorem and in order to achieve this goal, our main tools will be the theory of unordered sums in C and properties of winding numbers of closed paths. Among the proven results are the well known Fundamental Theorem of Algebra, Schwarz\'s Lemma, Montel\'s Theorem, Weierstrass\'s Double Series Theorem, Argument Principle, Rouché\'s Theorem, Weierstrass\'s Factorization Theorem, Picard\'s Little Theorem and the Riemann\'s Mapping Theorem.
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Moreira, Charles dos Anjos [UNESP]. "Linguagem de categorias e o Teorema de van Kampen". Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/152195.
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Esse trabalho trata de elementos da Topologia Algébrica, a qual tem como fundamental aplicação abordar questões acerca de Espaços Topológicos sob o ponto de vista algébrico. Uma das questões é tentar responder se dois espaços topológicos X e Y são homeomorfos. Neste sentido, o grupo fundamental é uma ferramenta algébrica útil por se tratar de um invariante topológico. Além disso, apresentamos o Teorema de van Kampen do ponto de vista da Linguagem de Categorias e Funtores.
This work treats of elements of the Algebraic Topology, which has as fundamental application to approach subjects concerning Topological Spaces under the algebraic point of view. One of the subjects is to try to answer if two topological spaces X and Y are homeomorphics. In this sense, the fundamental group is an useful algebraic tool for treating of an topological invariant. In addition, we presented the van Kampen's Theorem of the point of view of the language of Categories and Functors.
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Meilstrup, Mark H. "Wild Low-Dimensional Topology and Dynamics". BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2203.
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In this dissertation we discuss various results for spaces that are wild, i.e. not locally simply connected. We first discuss periodic properties of maps from a given space to itself, similar to Sharkovskii's Theorem for interval maps. We study many non-locally connected spaces and show that some have periodic structure either identical or related to Sharkovskii's result, while others have essentially no restrictions on the periodic structure. We next consider embeddings of solenoids together with their complements in three space. We differentiate solenoid complements via both algebraic and geometric means, and show that every solenoid has an unknotted embedding with Abelian fundamental group, as well as infinitely many inequivalent knotted embeddings with non-Abelian fundamental group. We end by discussing Peano continua, particularly considering subsets where the space is or is not locally simply connected. We present reduced forms for homotopy types of Peano continua, and provide a few applications of these results.
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Nicacio, Nilson Herminio. "Uma justificava da validade do teorema fundamental da ?lgebra para o ensino m?dio". Universidade Federal do Rio Grande do Norte, 2013. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18666.
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Previous issue date: 2013-08-14Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics
Dentre os v?rios teoremas que s?o ensinados na educa??o b?sica, alguns podem ser demonstrados em sala de aula e outros n?o, devido o grau de dificuldade de sua prova formal. Um exemplo cl?ssico e o Teorema Fundamental da Alg?bra, que n?o ? demonstrado, pois ? necess?rio conhecimentos em Matem?tica de n?vel superior. Neste trabalho, justicamos intuitivamente a validade do Teorema Fundamental da Algebra usando o software Geogebra. E, baseados em [2], apresentamos uma clara demonstra??o formal desse teorema que est? endere?ada aos professores do ensino b?sico e alunos de licenciatura em Matem?tica
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Coulon, Michael. "Modelling price dynamics through fundamental relationships in electricity and other energy markets". Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:ddc11641-920f-461f-85cd-a9e6351d9104.
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Energy markets feature a wide range of unusual price behaviour along with a complicated dependence structure between electricity, natural gas, coal and carbon, as well as other variables. We approach this broad modelling challenge by firstly developing a structural framework to modelling spot electricity prices, through an analysis of the underlying supply and demand factors which drive power prices, and the relationship between them. We propose a stochastic model for fuel prices, power demand and generation capacity availability, as well as a parametric form for the bid stack function which maps these price drivers to the spot electricity price. Based on the intuition of cost-related bids from generators, the model describes mathematically how different fuel prices drive different portions of the bid stack (i.e., the merit order) and hence influence power prices at varying levels of demand. Using actual bid data, we find high correlations between the movements of bids and the corresponding fuel prices (coal and gas). We fit the model to the PJM and New England markets in the US, and assess the performance of the model, in terms of capturing key properties of simulated price trajectories, as well as comparing the model’s forward prices with observed data. We then discuss various mathematical techniques (explicit solutions, approximations, simulations and other numerical techniques) for calibrating to observed fuel and electricity forward curves, as well as for pricing of various single and multi-commodity options. The model reveals that natural gas prices are historically the primary driver of power prices over long horizons in both markets, with shorter term dynamics driven also by fluctuations in demand and reserve margin. However, the framework developed in this thesis is very flexible and able to adapt to different markets or changing conditions, as well as capturing automatically the possibility of changes in the merit order of fuels. In particular, it allows us to begin to understand price movements in the recently-formed carbon emissions markets, which add a new level of complexity to energy price modelling. Thus, the bid stack model can be viewed as more than just an original and elegant new approach to spot electricity prices, but also a convenient and intuitive tool for understanding risks and pricing contracts in the global energy markets, an important, rapidly-growing and fascinating area of research.
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Costa, Antônio Geraldo Lacerda da. "Números complexos: um pouco de história, ensino e aplicações". Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7509.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
We present the main properties related to complex numbers. We justify as the history of mathematics can contribute to learning that content. Then we describe briefly the history of complex numbers. We also show where the complex numbers can be applied both within mathematics itself, and beyond.
Neste trabalho apresentamos as principais propriedades referentes aos números complexos. Justificamos como a História da Matemática pode contribuir para a aprendizagem desse conteúdo. Em seguida descreveremos de forma sucinta a história dos números complexos. Mostramos também onde os números complexos podem ser aplicados, tanto dentro da própria Matemática, como fora dela.
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Pinsky, Vanessa Cuzziol. "Experimentalist governance in climate finance: the case of REDD+ in Brazil". Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/12/12139/tde-14122017-163027/.
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Climate change is a daunting problem that results in actions-interactions from a number of actors in complex global systems, which require multi-level governance and a myriad of national policies. Academics and policy makers alike have been grappling with how to devise effective strategies on the international coordination of climate change policies. It is challenging because climate change problems involve actors with different positions, interests and motivation to cooperate due to the risks involved, the uncertainty and the high costs of adaptation and mitigation. Deforestation is the second largest source of GHG emissions. Success in this area can have a large impact on mitigation. This study focuses on the case of REDD+, a large scale governance experiment in climate finance and a promising cost-effective mitigation mechanism to motivate developing countries to implement policy approaches to reducing emissions from deforestation and forest degradation. REDD+ is considered a breakthrough mechanism in international cooperation under the UNFCCC regime as it was designed to be performance-based. Brazil is the world\'s largest recipient and has the most important REDD+ experiment - the Amazon Fund. The lack of developed theory in this domain led to the use of grounded theory methodology to understand the REDD+ governance process in Brazil. The \'REDD+ Governance Theoretical Framework\' emerged from the data. It is a substantive theory formed by seven major categories (Governance, Strategy, Financing, Implementation, Participation of stakeholders, Joint action and Collective learning) that are related to each other and explain the phenomenon. This study suggests that the lack of institutional arrangements to stimulate collective learning and incorporate lessons learned from the ground experience has been a major constraint on improving its governance in Brazil. Improving the effectiveness of the policy cycle may depend upon the establishment of specific arrangements focused on peer review processes involving lower-level entities responsible for implementation and experts from civil society. The establishment of a recursive learning system could solve certain policy coordination problems and create new opportunities to improve the effectiveness of the REDD+ governance process and implementation. This theory adds to the limited body of literature in the field by extending the knowledge on climate finance, stimulating discussion, and creating opportunities for further research and theoretical advances. The theoretical framework and lessons learned in Brazil from success and failure can help other developing countries to implement a national REDD+ strategy, system or regime. The theory can contribute to the international debate on the principles of good governance in official development assistance and aid effectiveness. This study provides an opportunity for policy makers and practitioners to learn about the challenges and constraints faced by Brazil when implementing an unprecedented results-based mechanism focused on mitigation.A mudança climática é um problema desafiador resultante de ações e interações entre diversos atores em sistemas globais complexos, o que demanda governança em vários níveis e uma miríade de políticas nacionais. Acadêmicos e policy makers vêm se desafiando sobre como elaborar estratégias eficazes na coordenação internacional das políticas em mudança climática. É desafiador porque os problemas relacionados à mudança do clima envolvem atores com diferentes posições, interesses e motivação para cooperar, já que existem riscos envolvidos, alto nível de incerteza e custos de adaptação e mitigação. O desmatamento é a segunda maior fonte de emissões de gases causadores do efeito estufa. Sucesso nesta área pode ter um grande impacto em mitigação. Este estudo enfoca no caso de REDD+, um experimento de governança no financiamento do clima e um promissor mecanismo de mitigação com baixo custo para incentivar os países em desenvolvimento a implementar abordagens políticas que reduzam emissões oriundas do desmatamento e da degradação florestal. O REDD + é considerado um mecanismo inovador em acordos de cooperação internacional sob o regime da UNFCCC, pois foi idealizado para ser baseado em desempenho. O Brasil é o maior receptor do mundo e tem o mais importante experimento de REDD+ - o Fundo Amazônia. A ausência de teorias desenvolvidas nessa área levou ao uso da metodologia grounded theory para compreender o processo de governança de REDD+ no Brasil. A partir dos dados primários foi desenvolvido o \'REDD+ Governance Theoretical Framework\'. Trata-se de uma teoria substantiva formada por sete categorias (Governança, Estratégia, Financiamento, Implementação, Participação de stakeholders, Ação coletiva e Aprendizagem coletiva) que se relacionam e explicam o fenômeno. Este estudo sugere que a ausência de arranjos institucionais para estimular a aprendizagem coletiva e incorporar as lições aprendidas durante a implementação tem sido um grande obstáculo para melhorar a governança de REDD+ no Brasil. Melhorar a efetividade do ciclo político pode depender do estabelecimento de arranjos específicos com foco em processos de revisão por pares que envolvam entidades responsáveis pela implementação e especialistas da sociedade civil. O estabelecimento de um sistema de aprendizagem recursiva poderia facilitar a resolução de alguns problemas de coordenação política e criar novas oportunidades para aprimorar o processo de governança de REDD+. Esta teoria contribui para a construção do conhecimento científico focado no financiamento do clima, estimula a discussão, sugere oportunidades para novas pesquisas e avanços teóricos. O framework teórico pode ajudar outros países em desenvolvimento a implementar estratégia, sistema ou regime nacional de REDD+. As lições aprendidas no Brasil, baseadas no sucesso e fracasso, podem ser absorvidas por outros países em desenvolvimento. A teoria contribui para o debate internacional sobre os princípios da boa governança nos acordos de cooperação internacional e na eficácia da ajuda financeira. Este estudo oferece uma oportunidade para que os policy makers e os profissionais aprendam sobre os desafios e obstáculos enfrentados pelo Brasil ao implementar um inovador mecanismo de financiamento do clima baseado em resultados.
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Santos, Walkíria Corrêa dos. "As ideias envolvidas na gênese do teorema fundamental do cálculo, de Arquimedes a Newton e Leibniz". Pontifícia Universidade Católica de São Paulo, 2011. https://tede2.pucsp.br/handle/handle/10872.
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Previous issue date: 2011-05-13Secretaria da Educação do Estado de São Paulo
This paper seeks to contribute to the study of the main ideas that involve the Fundamental Theorem of Calculus (FTC) from the Mathematics in Ancient Greece to contributions of Newton (1642 - 1727) and Leibniz (1646 - 1716), the seventeenth century. Given the scope of this theme, we focus our attention on the question of Incommensurability and in consequence, the definition of Proportion of Eudoxus (390 a.C. - 320 a.C.). Such a definition, results in the 'geometrization' of translating the mathematical ideas that culminated in the concepts of derivative and integral, in quadrature issues and calculation of volumes, through method of exhaustion and method Mechanic Archimedes (287 a.C. - 212 a.C.), and the method of tracing the tangent of Apollonius (262 a.C.) - 190 a.C.). The searches tangent to a curve and the problem of quadrature were a predecessor motive for the work of Newton (1642 - 1727) and Leibniz (1646 - 1716) could establish "Infinitesimal Calculus". The revival of mathematical activity in the fifteenth century, with the need for new routes of commerce and navigation, covering arithmetic, algebra and trigonometry and the sixteenth century, were of great importance, forming the basis of all algebraic development. In the seventeenth century, an important area has been established: the Analytic Geometry, which contributed greatly to the achievements of Newton (1642 - 1727), and Leibniz (1646 - 1716), by establishing, in definitive, that the process of integration and differentiation are inverse operations of one another. The result is now known as the Fundamental Theorem of Calculus. The product of the research conducted is a text, drafted with didactic concern, which aims to facilitate understanding of the interconnection of ideas that have contributed, through centuries, to the result that we now know as the Fundamental Theorem of calculus
Esse trabalho busca contribuir com o estudo das principais ideias que envolvem o Teorema Fundamental do Cálculo (TFC), desde a Matemática na Grécia Antiga até as contribuições de Newton (1642 - 1727) e Leibniz (1646 - 1716), no século XVII. Dada a abrangência de tal tema, focamos nossa atenção na questão da Incomensurabilidade e em decorrência, na definição de Proporção de Eudoxo (390 a.C. - 320 a.C.). Tal definição traz como consequência a ‗geometrização da matemática traduzindo as ideias que culminaram nos conceitos de derivada e integral, nas questões de quadratura e cálculo de volumes, por meio dos métodos de Exaustão e o método Mecânico de Arquimedes (287 a.C. - 212 a.C.), e no método do traçado de tangente de Apolônio (262 a.C. - 190 a.C.) . As buscas da tangente a uma curva e a questão da quadratura foram a mola precursora para que os trabalhos de Newton (1642 - 1727) e Leibniz (1646 - 1716) pudessem estabelecer o Cálculo Infinitesimal. O renascimento da atividade matemática no século XV, pela necessidade de novas rotas de comércios e navegação, abordando a aritmética, a álgebra e a trigonometria e o século XVI, foram de grande importância, constituindo a base de todo desenvolvimento algébrico. No século XVII, uma importante área foi estabelecida: a Geometria Analítica que muito contribuiu para os resultados alcançados por Newton (1642 - 1727) e Leibniz (1646 - 1716), estabelecendo, em definitivo, que o processo de integração e derivação são operações uma inversa da outra. O resultado é hoje conhecido como Teorema Fundamental do Cálculo. O produto da pesquisa realizada é um texto, redigido com preocupação didática, que pretende facilitar o entendimento da interligação das ideias que contribuíram, através de séculos, para o resultado que hoje conhecemos como o Teorema Fundamental do Cálculo
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Lillie, Nicholas J. "Does Fundamental Analysis Lead to a Rudimentary Momentum Strategy for the Inexperienced Investor? Evidence from a Student Investment Fund". Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/cmc_theses/1492.
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Using the Student Investment Fund at Claremont McKenna College as a proxy for inexperienced investors, I demonstrate that inexperienced investors using fundamental analysis produce momentum-like buying patterns. The results show that the Student Investment Fund is on average buying stocks that outperform Carhart’s four-factor asset pricing model in the year before purchase. As a result, the Student Investment Fund has, on average, underperformed the S&P500 by .48% per year since 1996. My thesis explores why the Student Investment Fund may have adopted momentum-like purchasing patterns and what steps can be taken to remedy it.
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Dravenstott, Ronald W. "Restaurant Industry Stock Price Forecasting Model Utilizing Artificial Neural Networks to Combine Fundamental and Technical Analysis". Ohio University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1337780178.
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Möller, Linnéa y Niklas Gambe. "Konsensus - en fundamental osanning? : En studie om aktiemarknadspsykologins påverkan på aktieanalytiker som bidrar till konsensus samt problematiken som medföljer". Thesis, Linköpings universitet, Företagsekonomi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-138976.
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Bakgrund: För att förklara olika händelser på den finansiella marknaden använder sig många forskare av aktiemarknadspsykologi med bakgrund i att aktörerna är människor. Konsensus är aktieanalytikers sammanställda estimat som ska motsvara marknadens aggregerade, fundamentala förväntningar. Det faktum att aktieanalytiker är människor gör att även dessa influeras av psykologi, vilket i sin tur både påverkar konsensus, investerare och till slut även marknaden. Syfte: Syftet med denna uppsats är att analysera och belysa vad som ligger bakom konsensusestimaten för att sedan kunna redogöra för hur aktörer på aktiemarknaden kan förhålla sig till detta. Fokus kommer att ligga på faktorer som, till skillnad från fundamentala och tekniska analyser, har sin utgångspunkt i aktiemarknadspsykologi. Metod: Med en kvalitativ ansats genomfördes intervjuer med tio olika aktieanalytiker. Intervjuerna ligger sedan till grund för analysen där den teoretiska referensramen bestående av aktiemarknadspsykologiska faktorer användes för att dra slutsatser. Slutsats: Resultatet visar på att konsensus inte fullt motsvarar aktieanalytikernas egentliga åsikter och att investerare och analytiker därför snarare bör förhålla sig till konsensus som en referenspunkt än som en riktlinje för investeringar.Background: To explain certain events that transpires on the stock market a lot of scientists use behavioral finance. They use this due to the fact that the market participants are human after all. Consensus estimates is the compiled estimates of sell side analyst which is supposed to be equivalent to the markets fundamental expectations. The fact that sell side analysts are human infers that they also get influenced by psychology, which in turn affect consensus, investors and lastly the market. Purpose: The purpose of this paper is to analyze and shed light on the elements that affect consensus estimates to clarify how stock market participants can relate to them. The focus will be on elements that, unlike fundamental and technical analysis, originates from behavioral finance. Method: Ten different stock analysts have been interviewed with a qualitative research approach. The interviews then acted as a basis for the analysis where the theory, originating from behavioral finance, is used to come to a conclusion. Conclusion: In conclusion, the result exhibits proof that consensus estimates doesn’t, to a full extent, truly reflect the sell side analysts’ true beliefs. Investors and other stock analysts should therefore relate to consensus as a reference point rather than a guideline for investment decisions.
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Olsson, Anton. "Malgrange-Ehrenpreis sats och explicita formler för fundamentallösningar". Thesis, Linköpings universitet, Analys och didaktik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-176376.
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This report presents and discusses proofs of the Malgrange-Ehrenpreis theorem, which states that every non-zero linear partial differential operator with constant coefficients has a fundamental solution. The main topic is explicit formulae, and more specifically, how they can be used to prove the theorem. Two different formulas will be considered in detail and the aim is to provide a fundamental and elementary description of how to prove the Malgrange-Ehrenpreis theorem using those formulas. In addition to the proofs, an example of how to use one of the formulas for the Cauchy-Riemann operator is shown. Finally, the report also contains a chapter discussing a few different notable methods of proof and their historical signifance.