Este trabalho tem como objetivo apresentar os conteúdos de matrizes, determinantes e sistemas lineares aos professores de matemática que lecionam no ensino médio, ressaltando as situações-problema bem como suas aplicações, contextualizando através de problemas. / The goal of this work is to present an introduction to matrices, determinants, and linear systems to high school mathematics teachers highlighting some applications.

Este trabalho tem como objetivo apresentar os conteúdos de matrizes, determinantes e sistemas lineares aos professores de matemática que lecionam no ensino médio, ressaltando as situações-problema bem como suas aplicações, contextualizando através de problemas. / The goal of this work is to present an introduction to matrices, determinants, and linear systems to high school mathematics teachers highlighting some applications.

Kwok-po Ng. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 138-139). / Abstracts / Summary / Introduction --- p.1 / Summary of the papers A-F --- p.2 / Paper A --- p.15 / Paper B --- p.36 / Paper C --- p.63 / Paper D --- p.87 / Paper E --- p.109 / Paper F --- p.122

La presente tesis muestra una propuesta sobre el estudio de matrices de orden m×n, sus operaciones, determinantes y la matriz inversa de matrices cuadradas de orden 2, diseñada aplicando los criterios de la Teoría de la Idoneidad Didáctica en el marco del Enfoque Ontosemiótico del Conocimiento y la Instrucción Matemática (EOS), a ser incluida en el sétimo ciclo de la Educación Básica Regular (EBR) del Perú. La pertinencia de este trabajo de investigación radica en las características del currículo: abierto, flexible, integrador y diversificado (ley general de educación–28044, artículo 33º). Estas características permiten, a los docentes, trabajar temas que no se consideran en forma específica en el currículo. Además, creemos que los conocimientos previos que se requieren, para que emerja el objeto matemático matriz, están al alcance de los estudiantes del sétimo ciclo de la EBR. Esta propuesta se presenta a través de cinco tareas. En estas tareas los modelos mediadores entre lo concreto (problemas contextualizados) y lo abstracto (objeto matemático matriz) son grafos dirigidos y tablas (datos numéricos ordenados en forma tabular). El docente a través de los diversos ítemes de las tareas dará la oportunidad guiada a los estudiantes de “construir” el objeto matemático matriz y sus operaciones. Una vez que los estudiantes se encuentren familiarizados con las matrices y sus operaciones, usaremos algunos problemas de codificación y de decodificación de mensajes de textos para hacer emerger el determinante de una matriz cuadrada y la inversa de una matriz cuadrada de orden 2 (si existiese). Las tareas han sido diseñadas (planificadas) de tal manera que, sean cercanas al estudiante; es decir, puedan imaginarlas, conteniendo un lenguaje adecuado y una dificultad manejable (respetando sus conocimientos previos). Estas tareas permitirán problematizar al estudiante –que el desarrollo no sea siempre rutinario o algorítmico–, manejar diferentes modos de expresión matemática como verbal, gráfica y simbólica pudiendo transitar de un modo de expresión a otro para poder interpretar, generalizar y justificar sus soluciones. También las tareas se presentan secuencialmente, de modo tal que, los estudiantes vayan acoplando y enlazando los nuevos conocimientos con sus conocimientos previos logrando así que los estudiantes valoren el conocimiento matemático y puedan aplicarlos en la vida cotidiana. De esta manera pretendemos impulsar algunos de los principios de la educación peruana, como la equidad, la inclusión, la calidad, la creatividad y la innovación para favorecer a la EBR. Otro aspecto importante de esta tesis es dejar en evidencia la brecha que existe entre la educación secundaria y la educación superior. Esto se percibe al tomar el objeto matemático matriz, que solo se estudia en la educación superior, de manera que pueda ser estudiado en el sétimo ciclo de la EBR desde un punto de vista innovador (cambiando su configuración epistémica en diversos contextos). A la vez mostramos que al planificar unas “buenas matemáticas” contribuimos a articular de manera coherente la educación secundaria y la educación superior logrando disminuir la brecha existente entre ellas. / Tesis

by Foon-Yip Ng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 111-115). / Abstract also in Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Main Problems --- p.1 / Chapter 1.2 --- The Basic Concept of Decision Theory --- p.4 / Chapter 1.3 --- The Class of Orthogonally Invariant Estimators --- p.6 / Chapter 1.4 --- Related Works --- p.8 / Chapter 1.5 --- Summary --- p.10 / Chapter Chapter 2 --- Estimation of the Scale Matrix in a Wishart Distribution --- p.12 / Chapter 2.1 --- Review of the Previous Works --- p.13 / Chapter 2.2 --- Some Useful Statistical and Mathematical Results --- p.15 / Chapter 2.3 --- Improved Estimation of Σ under the Loss L1 --- p.18 / Chapter 2.4 --- Simulation Study for Wishart Distribution under the Loss L1 --- p.22 / Chapter 2.5 --- Improved Estimation of Σ under the Loss L2 --- p.25 / Chapter 2.6 --- Simulation Study for Wishart Distribution under the Loss L2 --- p.28 / Chapter Chapter 3 --- Estimation of the Scale Matrix in a Multivariate F Distribution --- p.31 / Chapter 3.1 --- Review of the Previous Works --- p.32 / Chapter 3.2 --- Some Useful Statistical and Mathematical Results --- p.35 / Chapter 3.3 --- Improved Estimation of Δ under the Loss L1____ --- p.38 / Chapter 3.4 --- Simulation Study for Multivariate F Distribution under the Loss L1 --- p.42 / Chapter 3.5 --- Improved Estimation of Δ under the Loss L2 ________ --- p.46 / Chapter 3.6 --- Relationship between Wishart Distribution and Multivariate F Distribution --- p.51 / Chapter 3.7 --- Simulation Study for Multivariate F Distribution under the Loss L2 --- p.52 / Chapter Chapter 4 --- Estimation of the Scale Matrix in an Elliptically Contoured Matrix Distribution --- p.57 / Chapter 4.1 --- Some Properties of Elliptically Contoured Matrix Distributions --- p.58 / Chapter 4.2 --- Review of the Previous Works --- p.60 / Chapter 4.3 --- Some Useful Statistical and Mathematical Results --- p.62 / Chapter 4.4 --- Improved Estimation of Σ under the Loss L3 --- p.63 / Chapter 4.5 --- Simulation Study for Multivariate-Elliptical t Distributions under the Loss L3 --- p.67 / Chapter 4.5.1 --- Properties of Multivariate-Elliptical t Distribution --- p.67 / Chapter 4.5.2 --- Simulation Study for Multivariate- Elliptical t Distributions --- p.70 / Chapter 4.6 --- Simulation Study for ε-Contaminated Normal Distributions under the Loss L3 --- p.74 / Chapter 4.6.1 --- Properties of ε-Contaminated Normal Distributions --- p.74 / Chapter 4.6.2 --- Simulation Study for 2-Contaminated Normal Distributions --- p.76 / Chapter 4.7 --- Discussions --- p.79 / APPENDIX --- p.81 / BIBLIOGRAPHY --- p.111

Traditional visualization techniques for multidimensional data sets, such as parallel coordinates, star glyphs, and scatterplot matrices, do not scale well to high dimensional data sets. A common approach to solve this problem is dimensionality reduction. Existing dimensionality reduction techniques, such as Principal Component Analysis, Multidimensional Scaling, and Self Organizing Maps, have serious drawbacks in that the generated low dimensional subspace has no intuitive meaning to users. In addition, little user interaction is allowed in those highly automatic processes. In this thesis, we propose a new methodology to dimensionality reduction that combines automation and user interaction for the generation of meaningful subspaces, called the visual hierarchical dimension reduction (VHDR) framework. Firstly, VHDR groups all dimensions of a data set into a dimension hierarchy. This hierarchy is then visualized using a radial space-filling hierarchy visualization tool called Sunburst. Thus users are allowed to interactively explore and modify the dimension hierarchy, and select clusters at different levels of detail for the data display. VHDR then assigns a representative dimension to each dimension cluster selected by the users. Finally, VHDR maps the high-dimensional data set into the subspace composed of these representative dimensions and displays the projected subspace. To accomplish the latter, we have designed several extensions to existing popular multidimensional display techniques, such as parallel coordinates, star glyphs, and scatterplot matrices. These displays have been enhanced to express semantics of the selected subspace, such as the context of the dimensions and dissimilarity among the individual dimensions in a cluster. We have implemented all these features and incorporated them into the XmdvTool software package, which will be released as XmdvTool Version 6.0. Lastly, we developed two case studies to show how we apply VHDR to visualize and interactively explore a high dimensional data set.

<p>Prisustvo organskih zagađujućih supstanci (farmaceutski aktivnih komponenata i prirodnih toksina‐mikotoksina) u uzorcima životne sredine i namirnicama je u porastu kao posledica novih industrijskih procesa i ostalih antropogenih aktivnosti, kao i klimatskih promena. Takođe veliku pažnju javnosti privlače i neorganske zagađujuće supstance kao &scaron;to su te&scaron;ki elementi. S obzirom da zagađujuće supstance imaju negativan uticaj na životnu sredinu i zdravlje ljudi, u svetu se preduzimaju mere u cilju smanjenja stepena izloženosti toksičnim jedinjenjma i posledicama izlaganja. Trenutno, jedan od najvećih izazova, jeste procena rizika povezana sa velikim brojem zagađujućih supstanci u tragovima ili u tzv. ultratragovima, uključujući &ldquo;novo&rdquo; otkrivena zagađujuća jedinjenja, a jedan od osnovnih trendova je razvoj i primena brzih i efikasnih metoda za njihovu analizu u ispitivanim uzorcima na bazi naprednih hromatografskih i spektrometrijskih tehnika.<br />Tehnike bazirane na tečnoj hromatografiji sa različitim masenim analizatorima za<br />kvantifikaciju organskih zagađujućih supstanci kao i metode zasnovane na atomskoj<br />apsorpcijonoj spektrometriji za određivanje ultratragova neorganskih zagađujućih supstanci postale su referentne na međunarodnom nivou. Ovakve napredne spregnute tehnike postale su važne za identifikaciju, kvantifikaciju i praćenje različitih zagađujućih supstanci u uzorcima životne sredine i namirnicama i proceni njihovog &scaron;tetenog uticaja na zdravlje čoveka. S obzirom da su u literaturi retka istraživanja koja se bave razvojem i primenom metoda zasnovanih na naprednim hromatografskim i spektrometrijskim tehnikama i određivanju organskih i neorganskih zagađujućih supstanci u matriksima životne sredine i namirnicama sa prostora zapadnog Balkana, a uzimajući u obzir njihovu važnost, specifični ciljevi disertacije su:<br />&bull; unutra&scaron;nja (&bdquo;inhouse&ldquo;)<br />provera kvaliteta i pouzdanosti postojeće &bdquo;multi‐rezidualne&ldquo;<br />metode zasnovane na UHPLC‐QqLIT‐MS/MS za analizu 81‐e farmaceutski aktivne<br />komponente (PhAC) u otpadnoj, povr&scaron;inskoj, podzemnoj i pijaćoj vodi i po prvi put<br />dobijanje sveobuhvatnih rezultata njihovog prisustva u različitim tipovima vode sa<br />područja Srbije;<br />&bull; unutra&scaron;nja (&bdquo;inhouse&ldquo;) provera kvaliteta i pouzdanosti postojeće &bdquo;multi‐toksin&ldquo;<br />metode za analizu 8 Fusarium mikotoksina u uzorcima ozime p&scaron;enice različitih sorti<br />zasnovane na HPLC‐QqQ‐MS/MS radi određivanja regionalnih razlika između žitnih<br />regiona kao i otpornosti ispitivanih sorti p&scaron;enice na kontaminaciju Fusarium<br />toksinima;<br />&bull; modifikacija postojeće &bdquo;multi‐toksin&ldquo; metode zasnovane na UHPLC‐QqQ‐MS/MS za<br />analizu 11 osnovnih mikotoksina u uzorcima bra&scaron;na i njena unutra&scaron;nja (&bdquo;inhouse&ldquo;)<br />provera kvaliteta i pouzdanosti, kao i provera kroz interlaboratorijsko poređenje,<br />radi dobijanja podataka za procenu &scaron;tetnog uticaja ispitivanih mikotoksina na<br />zdravlje populacije;<br />&bull; razvoj &bdquo;multi‐toksin&ldquo; (vi&scaron;ekomponentne) i &bdquo;multi‐matriks&ldquo; (za vi&scaron;e matriksa) metode<br />bazirane na UHPLC‐QqQ‐MS/MS za analizu 10 mikotoksina u različitim vrstama<br />ko&scaron;tuničavog voća čija provera kvaliteta je zasnovana na intralaboratorijskoj proveri<br />tačnosti i preciznosti dobijenih rezultata;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &bull; primena postojeće analitičke procedure zasnovane na naprednoj tehnici pripreme<br />(mikrotalasnoj digestiji) različitih uzoraka biljnog i životinjskog porekla i provera<br />kvaliteta metode identifikacije i kvantifikacije zasnovane na atomskom apsorpcionom spektrometru sa grafitnom kivetom (GFAAS) radi dobijanja sveobuhavatnih rezultata o prisustvu te&scaron;kih elemenata (arsena, olova i kadmijuma) radi procene izloženosti stanovni&scaron;tva Srbije toksičnim neorganskim elementima.<br />Postignuti rezultati predstavljaju jedinstvene rezultate za područje Srbije dobijene<br />primenom naprednih spregnutih tehnika koje imaju značajnu ulogu u praćenju prisustva većeg broja organskih i neorganskih zagađujućih supstanci u izabranim uzorcima životne sredine i namirnica, (regulisanih postojećim zakonodavstvom) radi procene stepena zagađenosti ili u slučaju jedinjenja koja nisu regulisana zakonodavstvom radi sticanja novih saznanja o njihovom prisustvu i proceni mogućeg negativnog uticaja na životnu sredinu i zdravlje populacije.</p> / <p>The presence of organic pollutants in environmental samples and food (pharmaceutically active components and natural toxins‐mycotoxins) is increased as a result of new industrial processes and other anthropogenic activities, as well as climate change. Similarly heavy elements as inorganic pollutants have attracted worldwide attention. Since, these pollutants have negative impact on environment and human health, extremely efforts are undertaken in the world to reduce the level of exposure to these pollutants and consequences of the exposure. Currently, one of the highest challenges is to assess the risk associated with a large number of pollutants in trace or ultra trace levels, including &quot;new&quot; (emerging) discovered pollutants, and one of the main trends is development and implementation of fast and efficient methods for their analysis on the basis of advanced chromatographic and spectrometric techniques. Therefore, coupled techniques have become important for the identification, quantification and monitoring of various pollutants in environmental samples and food and assessment of their hazard impact on human health. Since, there are scarce data about the development and application of advanced methods based on chromatographic and spectrometric techniques for determination of organic and inorganic pollutants in environmental matrices and food from the Western Balkan, and taking into account their importance, specific objectives of<br />the dissertation were: &bull; internal (&quot;in‐house&quot;) quality control of the existing &quot;multi‐residual&quot; method based on UHPLC‐QqLIT‐MS/MS for analysis of 81 pharmaceutically active components (PhAC) in wastewater, surface, underground and drinking water due to obtained for the first time comprehensive results of their presence in different types of water from Serbia; &bull; internal (&quot;in‐house&quot;) quality control of the existing &quot;multi‐toxin&quot; method for the analysis of 8 Fusarium mycotoxins in samples of different winter wheat cultivars based on HPLC‐QqQ‐MS/MS to determine the differences among wheat-growing regions as well as the resistance of the analysed wheat cultivars towards Fusarium toxins; &bull; modification of existing &quot;multi‐toxin&quot; method based on UHPLC‐QqQ‐MS/MS for analysis of 11 principal mycotoxins in samples of flour and its internal (&quot;in‐house&quot;) quality control as well as verification through the interlaboratory comparison, in order to obtain data for assessing the hazard effect of these mycotoxins on the health of the population; &bull; the development of &quot;multi‐toxin&quot; and &quot;multi‐matrix&quot; method based on UHPLC‐QqQMS/ MS for the analysis of 10 mycotoxins in various types of nuts based on intralaboratory verification of the accuracy and precision of the obtained results; &bull; application of analytical procedure based on advanced preparation technique (microwave digestion) and atomic absorption spectrometer with a graphite furnace (GFAAS) and its verification in order to obtain comprehensive results on the presence of heavy elements (arsenic, lead and cadmium) in different samples of plant and animal origin to assess the exposure of the Serbian population to toxic inorganic elements. The obtained results are unique for the Serbia. They are obtained by applying advanced coupled techniques that have a significant role in monitoring the presence of a numerous organic and inorganic pollutants in analyzed samples of the environment and food. The presented results contribute to the assessment of pollution degree and in the case of new (emerging) not regulated polutant they might give new information about the possible negative impact on the environment and health of the population.</p>

Made available in DSpace on 2017-07-21T20:56:31Z (GMT). No. of bitstreams: 1 Marta Lena Jahn.pdf: 1783494 bytes, checksum: c6497fd4a435d106076c444a8c6fc4cc (MD5) Previous issue date: 2013-04-11 / The objective of this study is to propose a different approach to teaching of matrices, seeking value the geometric aspect of them, and determinants. In fact, the matrices are important not only as a way to organize numerical data (tables), but also by the different properties of the operations that define the matrix algebra. However, the traditional way of teaching matrices and determinants in a secondary education, such as tables of numbers and a number associated with a matrix, respectively, the definitions of matrix operations and determinants, as well as their properties become quite unnatural. The Geometry not only turns these concepts more natural, but also develops our intuition about it. Furthermore, the geometrical aspects of the matrices and determinants are present in technological applications such as in Computer Graphics, for example. We begin this work by analyzing some textbooks adopted in secondary education, in order to see how the theory of matrices and determinants have been approached in classrooms, and to relate it to national education curriculum guidelines. Later, we explore the geometric content of matrices and determinants and propose a methodology for teaching, which brings out this aspect. This approach by middle of the Geometry is intended to stimulate the student to deduce properties and reflect on the results in operations with matrices, for example, addition, multiplication and also in the calculation of determinants. In proposing this methodology, we use the free software Geogebra, with the intent of providing a better view of the content for the student. / O objetivo deste estudo é propor uma abordagem diferente para o ensino das matrizes, buscando valorizar o aspecto geométrico delas, e dos determinantes. De fato, as matrizes são importantes não apenas como forma de organizar dados numéricos (tabelas), mas também pelas diversas propriedades das operações que definem a álgebra matricial. Todavia, na forma tradicional de ensinar matrizes e determinantes no ensino médio, como tabelas de números e um número associado a uma matriz, respectivamente, as definições das operações matriciais e determinantes, assim como as suas propriedades, tornam-se bastante artificiais. A Geometria não apenas ajuda a tornar estes conceitos mais naturais, como também desenvolve a nossa intuição sobre o assunto. Além disso, os aspectos geométricos das matrizes e determinantes estão presentes em aplicações tecnológicas tais como em Computação Gráfica, por exemplo. Começaremos este trabalho analisando alguns livros didáticos adotados no ensino médio, para verificar como a teoria de matrizes e determinantes vem sendo abordada em sala de aula; e relacionar essa teoria com os parâmetros curriculares nacionais do ensino médio. Posteriormente, exploraremos o conteúdo geométrico de matrizes e determinantes e proporemos uma metodologia para o seu ensino que valorize este aspecto. Esta abordagem por meio da geometria tem a finalidade de estimular o aluno a deduzir propriedades e refletir sobre os resultados obtidos nas operações realizadas com matrizes, por exemplo, a adição, a multiplicação e também, no cálculo de determinantes. Ao propor esta metodologia, faremos uso do software livre Geogebra, com o intento de propiciar uma melhor visualização do conteúdo pelo aluno.

Submitted by Eunice Novais (enovais@uepg.br) on 2018-04-25T18:43:42Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Elisemare Viapiana Pelenz.pdf: 7586627 bytes, checksum: 03050e24912a47c32e5ba62708cb23b2 (MD5) / Made available in DSpace on 2018-04-25T18:43:42Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Elisemare Viapiana Pelenz.pdf: 7586627 bytes, checksum: 03050e24912a47c32e5ba62708cb23b2 (MD5) Previous issue date: 2018-02-20 / Essa pesquisa tem por objetivo subsidiar os docentes nas atividades de matemática relacionadas aos conteúdos de matrizes e sistemas lineares, tendo em vista as habilidades e competências estabelecidas pela Matriz de Referência do Exame Nacional do Ensino Médio (ENEM). Para isso, foram realizadas pesquisas bibliográficas e análises documentais com o intuito de caracterizar o estudo de matrizes e sistemas lineares no âmbito escolar, considerando tais competências e habilidades. Em seguida foram selecionadas algumas questões que compuseram o ENEM no período de 2009 a 2017 para aplicação da atividade com 1 turma da 2a série e 1 turma da 3a série do ensino médio, de uma escola do campo no município de São Miguel do Iguaçu - Paraná. Este processo foi categorizado em um estudo de caso, abrangendo a competência de área 5 da Matriz de Referência do ENEM, “Modelar e resolver problemas que envolvem variáveis socioeconômicas ou técnico científicas, usando representações algébricas”. A partir da aplicação dessa atividade foram feitas as análises das diferentes estratégias de resolução e os tipos de erros envolvidos, buscando oferecer um suporte didático ao trabalho do docente no sentido de desenvolver nos alunos as competências e habilidades requeridas. / This research aims to subsidize mathematics educators towards matrices and linear systems, given the competences and abilities established by the Reference Matrix of The National Exam of High School (ENEM). For those purposes, bibliographical studies and documentary analyzes were carried out with the goal of characterizing the study of matrices and linear systems within the school environment attending to compentences and abilities. Next, some questions featured in ENEM from 2009 to 2017 were selected to be resolved by one class taking the 2nd grade and one taking the 3rd year of a rural high school in the municipality of São Miguel do Iguaçu – Paraná. This process was categorized as a study of case, reaching the competence of area 5 from the ENEM’s Reference Matrix, “Modeling and solving problems that involve socioeconomic or scientific variables, using algebraic representations”. From the application of this activity analyzes were made on the different strategies to resolving the kinds of mistakes involved, seeking to offer didactic support to the work of the teacher in the sense of developing in students the skills and abilities required.

Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2012Bitstream added on 2014-06-13T20:09:07Z : No. of bitstreams: 1 silva_glf_me_sjrp.pdf: 4891307 bytes, checksum: d50ac695507aa5097767c494c073e3f8 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho estudaremos a relação existente entre polinômios ortogonais e matrizes aleatórias. Exibiremos uma caracterização de polinômios ortogonais via problemas de Riemann-Hilbert, a qual tem se mostrado uma ferramenta única para obtenção de assintóticas de polinômios ortogonais. Posteriormente, estudaremos a teoria básica dos ensembles unitários de matrizes aleatórias. Por fim, mostraremos como a teoria de assintóticas de polinômios ortogonais pode ser usada na análise assintótica de estatísticas de matrizes aleatórias, nos levando a resultados de universalidade para os ensembles unitários / We will exhibit a characterization of orthogonal p olynomials via Riemann-Hilbert problems, which has been shown a powerful to ol for studying asymptotics of orthogonal polynomials. Posteriorly we will review the basic theory of unitary ensembles of random matrices. At the end, we will show how asymptotics of orthogonal polynomials can be used to study asymptotics of several statistics in random matrix theory, obtaining universality results for the unitary ensembles