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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
71

Non-standard backward stochastic differential equations and multiple optimal stopping problems with applications to securities pricing

Zhang, Jianing 03 April 2013 (has links)
Zentraler Gegenstand dieser Dissertation ist die Entwicklung von mathematischen Methoden zur Charakterisierung und Implementierung von optimalen Investmentstrategien eines Kleininvestors auf einem Finanzmarkt. Zur Behandlung dieser Probleme ziehen wir als Hauptwerkzeug Stochastische Rückwärts-Differenzialgleichungen (BSDEs) mit nicht-linearen Drifts heran. Diese Nicht-Lineariäten ordnen sie außerhalb der Standardklasse der Lipschitz-stetigen BSDEs ein und treten häufig in finanzmathematischen Kontrollproblemen auf. Wir charakterisieren das optimale Vermögen und die optimale Investmentstrategie eines Kleininvestors mit Hilfe einer sog. Stochastischen Vorwärts-Rückwärts-Differenzialgleichung (FBSDE), einem System bestehend aus einer stochastischen Vorwärtsgleichung, die vollständig gekoppelt ist an eine Rückwärtsgleichung. Die Festlegung bestimmter Nutzenfunktionen führt uns schließlich zu einer weiteren Klasse von nicht-standard BSDEs, die in unmittelbarem Zusammenhang zu dem sog. Ansatz der stochastischen partiellen Rückwärts-Differenzialgleichungen (BSPDEs) steht. Anschließend entwickeln wir eine Methode zur numerischen Behandlung von quadratischen BSDEs, die auf einem stochastischen Analogon der Cole-Hopf-Transformation basiert. Wir studieren weiterhin eine Klasse von BSDEs, deren Drifts explizite Pfadabhängigkiten aufweisen und leiten mehrere analytische Eigenschaften her. Schließlich studieren wir Dualdarstellungen für Optimalen Mehrfachstoppprobleme. Wir leiten Martingal-Dualdarstellungen her, die die Grundlage für die Entwicklung von Regressions-basierten Monte Carlo Simulationsalgorithmen bilden, die schnell und effektiv untere und obere Schranken berechnen. / This thesis elaborates on the wealth maximization problem of a small investor who invests in a financial market. Key tools for our studies come across in the form of several classes of BSDEs with particular non-linearities, casting them outside the standard class of Lipschitz continuous BSDEs. We first give a characterization of a small investor''s optimal wealth and its associated optimal strategy by means of a systems of coupled equations, a forward-backward stochastic differential equation (FBSDE) with non-Lipschitz coefficients, where the backward component is of quadratic growth. We then examine how specifying concrete utility functions give rise to another class of non-standard BSDEs. In this context, we also investigate the relationship to a modeling approach based on random fields techniques, known by now as the backward stochastic partial differential equations (BSPDEs) approach. We continue with the presentation of a numerical method for a special type of quadratic BSDEs. This method is based on a stochastic analogue to the Cole-Hopf transformation from PDE theory. We discuss its applicability to numerically solve indifference pricing problems for contingent claims in an incomplete market. We then proceed to BSDEs whose drifts explicitly incorporate path dependence. Several analytical properties for this type of non-standard BSDEs are derived. Finally, we devote our attention to the problem of a small investor who is equipped with several exercise rights that allow her to collect pre-specified cashflows. We solve this problem by casting it into the language of multiple optimal stopping and develop a martingale dual approach for characterizing the optimal possible outcome. Moreover, we develop regression based Monte Carlo algorithms which simulate efficiently lower and upper price bounds.
72

Cole Porter : the social significance of selected love lyrics of the 1930s

Holloway, Marilyn June 11 1900 (has links)
This dissertation examines selected love lyrics composed during the 1930s by Cole Porter, whose witty and urbane music epitomized the Golden era of American light music. These lyrics present an interesting paradox – a man who longed for his music to be accepted by the American public, yet remained indifferent to the social mores of the time. Porter offered trenchant social commentary aimed at a society restricted by social taboos and cultural conventions. The argument develops systematically through a chronological and contextual study of the influences of people and events on a man and his music. The prosodic intonation and imagistic texture of the lyrics demonstrate an intimate correlation between personality and composition which, in turn, is supported by the biographical content. / English / M.A. (English)
73

Em defesa do planejamento urbano: ressonâncias britânicas e a trajetória de Harry James Cole / In defense of the urban planning: britain ressonances and the trajectory of Harry James Cole

Maria Cecilia Lucchese 15 June 2009 (has links)
Apresentamos nesse trabalho a trajetória profissional do arquiteto carioca Harry James Cole, que se formou na Faculdade de Arquitetura da Universidade do Brasil, no Rio de Janeiro, em 1954 e trabalhou como arquiteto e urbanista até 1980. Cole fez um curso de especialização em planejamento urbano na Inglaterra e nesse período também trabalhou no Departamento de Arquitetura do London County Council. Essa experiência marcou profundamente seus trabalhos profissionais, que apresentam fortes ressonâncias do urbanismo inglês. Atuando profissionalmente no Brasil Cole foi partícipe de importantes acontecimentos no campo do planejamento urbano no Brasil entre 1957 e 1973, como a construção de Brasília, a implementação dos planos de desenvolvimento integrado e a concepção do Programa Cura, além de ter elaborado inúmeros trabalhos urbanísticos em seu escritório, o HJ Cole Arquitetos + Associados S/C Ltda até o final dos anos 70. / In this thesis we show Harry James Cole\'s professional life, a carioca architect who graduated at Faculdade de Arquitetura of Universidade do Brazil, in Rio de Janeiro, in 1954 and who worked as an architect and urban planner until 1980. Cole did a course of specialization in town planning in England and in that period he also worked in the London County Council Architecture Department. This experience deeply affected in his professional life and his works show a strong inspiration in the town planning lessons. Working professionally in Brazil Cole took part in the most important brazilian urban planning events between 1957 and 1973, as the construction of Brasília, the implementation of the comprehensive local urban planning and the conception of the Cura Programme, besides having done several urban planning jobs in his office, the HJ Cole Arquitetos + Associados S/C Ltda until the end of 1970.
74

From the Old to the New World: The Transformation of Kongo Minkisi in African American Art

McCurnin, Mary 18 April 2010 (has links)
Minkisi (sing. nkisi) were sacred objects that housed ancestral spirits and were used for divination, healing and social justice by the Kongo people of Central Africa. When the Kongo were brought as slaves to the New World, they contributed significantly to the development of African American artistic and spiritual culture. In the Caribbean, aspects of minkisi have been retained in the creolized spiritual beliefs of Haitian Vodou, Cuban Palo Monte Mayombe and Brazilian Candomble. In North America, evidence of Kongo influence is apparent in examples of folk art and culture, including quilts, mojo hands, Afro-Carolinian face vessels, memory jugs and burial sites. In the twentieth and twenty-first centuries, artists appear to have recontextualized elements of minkisi within their work, among these James “Son Ford” Thomas, James Van Der Zee, Betye and Alison Saar, Willie Cole and Renee Stout, creating a link between the Kongo past and the American present.
75

Exhibiting Women: Sectional Confrontation and Reconciliation in the Woman's Department at the World's Exposition, New Orleans, 1884-85

Pfeffer, Miki 22 May 2006 (has links)
At the World's Industrial and Cotton Centennial Exposition, the Woman's Department offered women of all regions of the country an opportunity to exhibit what they considered "woman's work." As women came together and attempted sectional reconciliation, controversy persisted, especially over the selection of northern suffragist Julia Ward Howe, author of the "Battle Hymn of the Republic," as the Department's president. However, during the course of the event, which lasted from December 16, 1884 to May 31, 1885, New Orleanians and other southern women learned skills and strategies from participants and famous women visitors, and these southerners insinuated their voices into the national debate on late-nineteenth-century women's issues.
76

Chronic inflammation surrounding intra-cortical electrodes is correlated with a local, neurodegenerative state

McConnell, George Charles 18 November 2008 (has links)
Thanks to pioneering scientists and clinicians, prosthetic devices that are controlled by intra-cortical electrodes recording one's 'thoughts' are a reality today, and no longer merely in the realm of science fiction. However, widespread clinical use of implanted electrodes is hampered by a lack of reliability in chronic recordings, independent of the type of electrodes used. The dominant hypothesis has been that astroglial scar electrically impedes the electrodes. However, recent studies suggest that the impedance changes associated with the astroglial scar are not high enough to interfere significantly impair neural recordings. Furthermore, there is a time delay between when scar electrically stabilizes and when neural recordings fail (typically >1 month lag), suggesting that scar, per se, does not cause chronic recording unreliability. In this study, an alternative hypothesis was tested in a rat model, namely, that chronic inflammation surrounding microelectrodes causes a local neurodegenerative state. Chronic inflammation was varied in three ways: 1) stab wound control, 2) age-matched control, and 3) inter-shank spacing of a multishank electrode. The results of this study suggest that chronic inflammation, as indicated by activated microglia and reactive astrocytes, is correlated with local neurodegeneration, marked by neuron cell death and dendritic loss. Surprisingly, axonal pathology in the form of hyperphosphorylation of the protein Tau (the hallmark of many tauopathies, including Alzheimer's Disease) was also observed in the immediate vicinity of microelectrodes implanted for 16 weeks. Additionally, work is presented on a fast, non-invasive method to monitor the astrocytic response to intra-cortical electrodes using electrical impedance spectroscopy. This work provides a non-invasive monitoring tool for inflammation, albeit an indirect one, and fills a gap which has slowed the development of strategies to control the inflammatory tissue response surrounding microelectrodes and thereby improve the reliability of chronic neural recordings. The results of these experiments have significance for the field of neuroengineering, because a more accurate understanding of why recordings fail is integral to engineering reliable solutions for integrating brain tissue with microelectrode arrays.
77

De Escola Normal de Natal a Instituto de Educa??o de Presidente a Kennedy (1950−1965): configura??es, limites e possibilidades da forma??o docente

Aquino, Luciene Chaves de 30 August 2007 (has links)
Made available in DSpace on 2014-12-17T14:35:52Z (GMT). No. of bitstreams: 1 LucieneCA.pdf: 1713182 bytes, checksum: 6f95f280159eda95c2dc51bed9b90b15 (MD5) Previous issue date: 2007-08-30 / La recherche ci-pr?sent?e consiste dans une narrative historique problematis?e par rapport ? la trajectoire de l ?cole Normale de Natal. Dans ce parcours, nous distingons sa transformation en Institut d ?ducation Pr?sident Kennedy, en envisageant la p?riode de 1950 jusqu ? 1965. L investigation a ?t? proc?d?e ayant pour base les principes de l histoire des institutions ?ducatives, on a pris deux cat?gories d analyse historique : la culture scolaire, utile ? la compr?hension des pratiques ?ducatives developp?es dans l institution d enseignement ; et celle de genre, l ?cole Normale de Natal/Institut d ?ducation pour avoir ?t? fr?quent?s principalement par des femmes qui voulaient travailler dans l enseignement primaire ; alors, une place de genre. Dans cette perspective, nous estimons sa multiplicit? d acteurs et de leurs pratiques dans l institution. Nous mettons en ?vidence sa cr?ation et les cycles de son d?veloppement (mat?rialis?s dans les plusieurs configurations), en les reliant aux faits locaux et nationaux. Nous distingons les conflits tout le long des ann?es en ce qui concerne l inexistence de l espace physique pour le fonctionnement ad?quat de l ?cole, et les changements du savoir apport? moyennant la renovation du programme d enseigement et de la pratique p?dagogique. Ainsi, de la tradictionnelle ?cole Normale de Natal ? l Institut d ?ducation Pr?sident Kennedy, cette institution ?ducative a gard?, dans son identit?, le caracter de mod?le et d innovation, quand elle a pu assimiler les changements didactico- p?dagogique qui avaient eu lieu dans le sc?nario national se transformant en un centre de r?f?rence pour la formation des professeurs, particuli?rement des femmes, en diff?rentes ?poques dans l enseignement potiguar. L ?cole Normale de Natal s est constitu?e surtout en un ?tablissement pour la conqu?te, un chemin pour l ?largissement de l univers du r?le de ces femmes qui se d?placent de la sph?re de l enseignement priv? pour acc?der au domaine de l enseignement publique, acqu?rant ainsi un travail r?mun?r? / A pesquisa ora apresentada consiste numa narrativa hist?rica problematizada acerca da trajet?ria da Escola Normal de Natal. Nesse percurso, real?amos a sua transforma??o no Instituto de Educa??o Presidente Kennedy, focalizando especialmente o per?odo de 1950 a 1965. A investiga??o foi processada com base nos princ?pios da hist?ria das institui??es educativas, tomando duas categorias de an?lise hist?rica: a cultura escolar, ?til para a compreens?o das pr?ticas educativas desenvolvidas nessa institui??o de ensino; e a de g?nero, por ter sido a Escola Normal de Natal/Instituto de Educa??o uma institui??o de ensino freq?entada majoritariamente por mulheres que se destinavam a atuar no magist?rio prim?rio; portanto, um lugar generificado. Nessa perspectiva, consideramos a multiplicidade dos atores e de suas pr?ticas no interior dessa institui??o. Destacamos a sua cria??o e os ciclos de seu desenvolvimento (materializados nas diferentes configura??es), relacionando-os aos acontecimentos locais e nacionais. Ressaltamos os conflitos ao longo das d?cadas em torno da aus?ncia de espa?o f?sico para o funcionamento adequado da Escola, e as mudan?as do saber veiculado por meio da renova??o do curr?culo e de sua pr?tica pedag?gica. Assim, da tradicional Escola Normal de Natal a Instituto de Educa??o de Educa??o Presidente Kennedy, essa institui??o educativa resguardou, na sua identidade, o car?ter modelar e inovador, ao assimilar as mudan?as did?tico-pedag?gicas que vinham ocorrendo no cen?rio nacional, transformando-se, por isso mesmo, em um centro de refer?ncia na forma??o docente, particularmente de mulheres professoras, em diferentes ?pocas, no Estado Potiguar. A Escola Normal de Natal constituiu-se num lugar, acima tudo, de conquista, um caminho para o alargamento do universo de atua??o dessas mulheres, que se deslocam da esfera privado para ingressarem no dom?nio p?blico, assumindo um trabalho remunerado
78

Educar para o lar, educar para a vida :cultura escolar e modernidade educacional na Escola Dom?stica de Natal (1914-1945)

Rodrigues, Andr?a Gabriel Francelino 30 October 2006 (has links)
Made available in DSpace on 2014-12-17T14:36:44Z (GMT). No. of bitstreams: 1 AndreaGRF.pdf: 2277320 bytes, checksum: 728bbef435d686d8daacb790922ad7e9 (MD5) Previous issue date: 2006-10-30 / La recherche propose un nouveau regard sur l Institution Scolaire ?cole Dom?stica de Natal, en essayant de tenir compte de la multiplicit? des auteurs et des pratiques d?velopp?es ? l ?cole qui d?finissaient le mieux et expliquaient les ph?nom?nes de cette r?alit? ?ducative et des rapports avec le temps et le lieu o? elle s ins?rait. Pour ce faire, les concepts de m?moire et culture scolaire ont ?t? fondamentaux pour la compr?hension de ces pratiques, parce qu ils ont contribu? ? notre lecture historique-culturelle de l ensemble d aspects institutionnalis?s ? l ?cole, comme son curriculum, ses finalit?s, ses fa?ons d enseigner et d apprendre, ses r?gles de conduite, ses normes, enfin, ce qui caract?risait son organisation et ses pratiques quotidiennes. C ?tait l ?cole Dom?stica de Natal l institution pionni?re dans le mod?le d ?ducation f?minine au Br?sil, nous le reconnaissons en priorit? et nous visons ? le circonscrire ? son ind?l?bile contribution ? l Histoire de l ?ducation de Rio Grande do Norte. Con?ue par un mod?le d organisation scolaire europ?en pour l ?ducation f?minine, l ?cole Dom?stica de Natal a ?t? inaugur?e en 1914, en ayant comme cr?ateur l intelectuel de Rio Grande do Norte Henrique Castriciano de Souza. Sa singularit?, s opposant aux ?coles f?minines existantes au Rio Grande do Norte et au Br?sil en ce temps-l?, ?tait d? au mod?le scolaire adopt?, qui appuyait sur la formation d une femme pr?par?e ? r?pondre aux aspirations modernes surgissant avec l av?nement de la R?publique. Ce contexte exigeait de l ?cole la formation d un mod?le de femme dans les aspects moral, physique, culturel et intelectuel model?s sur les id?aux de l ordre et du progr?s. Ce serait une nouvelle m?thode d ?ducation scolaire qui pourrait favoriser la modernisation des anciennes m?thodes d enseignement, provoquant le surgissement de mod?les qui impliqueraient une nouvelle organisation p?dagogique aux ?coles de l`?tat et conduiraient la ville ? de nouveaux et hauts paliers de culture et civilit?. Avec cela, l ?cole contribuerait ? ce que la femme joue un r?le dans la soci?t? d une mani?re plus active, sociale et mieux adapt?e. Les mots ordre, nouveau, civilit?, moderne et progr?s se r?pandaient et s entrecroisaient avec des valeurs archa?ques toujours permanentes et enracin?es dans la vision de vie et l id?e de monde d alors. Ainsi, on voyait que l ?cole Dom?stica ?tait une institution mod?le, sp?cifique dans sa fonction, qui apporterait ? la ville et, particuli?rement au Rio Grande do Norte, des id?es de civilit?, ordre et progr?s / A pesquisa apresenta um novo olhar para a institui??o escolar Escola Dom?stica de Natal, tentando dar conta da multiplicidade dos atores e pr?ticas envolvidas na escola que melhor definiam e explicavam os fen?menos daquela realidade educativa e das rela??es com o tempo e lugar em que estava inserida. Neste sentido, os conceitos de mem?ria e cultura escolar foram fundamentais para a compreens?o dessas pr?ticas, porque contribu?ram para fazermos uma leitura hist?rico-cultural do conjunto de aspectos institucionalizados na escola, como o seu curr?culo, finalidades, modos de ensinar e aprender, condutas, normas, enfim, o que caracterizavam a sua organiza??o e pr?ticas cotidianas. Sendo a Escola Dom?stica de Natal uma institui??o pioneira no modelo de ensino voltado para a educa??o feminina no Brasil, priorizamos reconhec?-la e circunscrev?-la na sua indel?vel contribui??o ? Hist?ria da Educa??o norte-rio-grandense. Concebida por um modelo de organiza??o escolar europeu para a educa??o feminina, a Escola Dom?stica de Natal foi inaugurada em 1914, tendo como seu criador, o intelectual norte-rio-grandense Henrique Castriciano de Souza. Sua singularidade, divergindo das escolas femininas existentes no RN e no pa?s naquele momento, advinha do modelo escolar adotado, que enfatizava a forma??o de uma mulher voltada para atender aos anseios modernos despontados com o advento da Rep?blica. Esse ide?rio exigia, por parte da escola, a forma??o de um modelo de mulher em seus aspectos moral, f?sico, cultural e intelectual moldados nos ideais da ordem e do progresso. Essa seria uma nova forma de educa??o escolar que poderia favorecer a moderniza??o dos velhos m?todos de ensino, provocando o surgimento de modelos que implicariam numa nova organiza??o pedag?gica nas escolas existentes no Estado e conduziriam a cidade a novos e elevados patamares de cultura e civilidade. Estava presente, tamb?m a representa??o de que, com essa forma??o, a escola contribuiria para que a mulher atuasse na sociedade de forma mais ativa, social e ajust?vel ao meio. As palavras ordem, novo, civilidade, moderno e progresso circulavam e se entrecruzavam com valores arcaicos ainda arraigados e permanentes na vis?o da vida e na id?ia de mundo de ent?o. Assim, percebia-se a Escola Dom?stica como institui??o modelo, espec?fica em sua fun??o, que iria trazer para a cidade e, particularmente para o Estado do RN, id?ias de civilidade, ordem e progresso
79

Expans?o urbana de Mossor? : per?odo de 1980 a 2004

Rocha, Aristotelina Pereira Barreto 12 April 2005 (has links)
Made available in DSpace on 2015-03-13T17:10:35Z (GMT). No. of bitstreams: 1 AristotelinaPBR.pdf: 3456529 bytes, checksum: 46cbab61e5692bdcef280c6d9260ff57 (MD5) Previous issue date: 2005-04-12 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / The purpose of this Academic Work is to identify the process of urban expansion of Mossoro city, connect them with the economy that moves the society of Mossoro. This analysis is about the period from 1980 to 2004 and the economy activities selected are compose the structure of the Mossoro' s life, fixing shapes, functions and contents of the city territory, especially in its urban space to understand the present process of urban expansion and its relations with the dynamic of the city we recall history of this territory, wich as a urban word, connect the changes with the primary economy actives - commerce and sea salt extraction. ln this relation between the present process of urban expansion and the dynamic of the city economy, the economy activities studies where the sea salt extraction, and irrigated fruit crops organizes the space so they can be viable in all stages - production, trade and circulation - to be viable they change, amplify and build a urban space together with public policy, that also increases with the arrival of new inhabitant, service structure, mount by the public administration as well as by private resources. This work point out the needs of a development a new main plan for Mossoro, that will reorganize it's territory, but also grant the needs of its society, wich desires a more given city, where citizenship will be exercise with dignity / Este Trabalho tem por objetivo identificar os processos de expans?o urbana da cidade de Mossor?, relacionando-os com as Economias que dinamizam esta Sociedade. Esta an?lise corresponde ao per?odo de 1980 a 2004 e as atividades econ?micas selecionadas s?o aquelas que exercem um papel estruturante na vida da Cidade, por determinarem formas, fun??es e conte?dos no territ?rio do Munic?pio, e, principalmente em seu espa?o urbano. Para que se possam entender os processos da expans?o urbana atual e suas rela??es com a din?mica da Cidade, recorremos ? hist?ria desse territ?rio, que, ao definir-se como mundo urbano, sintonizam essas transforma??es com as atividades econ?micas fundadoras - o Emp?rio Comercial e a Extra??o de sal marinho. Nesta rela??o entre a expans?o urbana atual e a din?mica econ?mica da Cidade, as atividades econ?micas trabalhadas foram a Economia Salineira, a Extra??o de Petr?leo e G?s, e a Fruticultura Irrigada. Essas Economias (re)organizam um espa?o para viabilizar-se nas suas mais diversas etapas - produ??o, comercializa??o e circula??o - e, para tanto, modificam, ampliam e criam juntamente com as Pol?ticas P?blicas um espa?o urbano, que se expande tamb?m pela chegada de migrantes, pela estrutura de servi?os, montada pelo Poder P?blico, bem como pelo Capital Privado. O Trabalho aponta para necessidade de elabora??o um novo Plano Diretor para a Cidade, que reorganize esse territ?rio, n?o apenas na perspectiva do Capital e dos seus interesses, mas que tamb?m incorpore as aspira??es da sua Sociedade, que deseja uma Cidade mais generosa, onde a cidadania possa ser exercida com dignidade
80

Uma sequencia did?tica para o ensino da resolu??o da equa??o do 2. grau : adequa??o para o uso com professores

Macedo, Elaine Souza de 18 July 2011 (has links)
Made available in DSpace on 2014-12-17T15:04:57Z (GMT). No. of bitstreams: 1 ElaineSM_DISSERT.pdf: 886598 bytes, checksum: 7ef8596ff5cd48451e6de3947c852c6d (MD5) Previous issue date: 2011-07-18 / The present study aims to check whether the use of activities mediated by the History of Mathematics can contribute to improve the understanding of resolution the 2nd degree equation for teachers and undergraduates that reproduce methods of solving such equations, uncritically, without domain of the justifications for their actions. For this, we adapted a didactic sequence with activities that aims to cause a rediscovery of resolutive formula of 2nd degree equation through the method known as cut and paste. Finally, we presented the activity module containing the didactic sequence used during the study, as suggestion for use in the classroom, by the math teacher / O presente estudo tem como objetivo verificar se o uso de atividades mediadas pela Hist?ria da Matem?tica pode contribuir para a melhoria da compreens?o da resolu??o da equa??o do 2? grau para professores e licenciandos que reproduzem m?todos de resolu??o de tais equa??es, de maneira acr?tica, sem o dom?nio das justificativas de suas a??es. Para isso, adaptamos uma sequ?ncia did?tica com atividades que tem como prop?sito fazer com que haja uma redescoberta da f?rmula resolutiva da equa??o do 2? grau atrav?s do m?todo denominado corte e cole. Por fim, apresentamos o m?dulo de atividades contendo a sequ?ncia did?tica utilizada durante o estudo, como sugest?o para uso em sala de aula, pelo professor de matem?tica

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