Thesis (M.Sc.) - Simon Fraser University, 2005. / Thesis (School of Computing Science) / Simon Fraser University.

Thesis (M.Sc.) - Simon Fraser University, 2005. / Thesis (School of Computing Science) / Simon Fraser University.

Liu, Xin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 61-63). / Abstracts in English and Chinese. / Abstract --- p.1 / Acknowledgments --- p.4 / Chapter 0 --- Introduction --- p.5 / Chapter 1 --- Basics of self-affine tiles --- p.8 / Chapter 1.1 --- Self-affine sets --- p.8 / Chapter 1.2 --- Self-affine tiles --- p.11 / Chapter 1.3 --- Structure of tiling sets --- p.15 / Chapter 1.4 --- Integral self-affine tiles --- p.20 / Chapter 1.4.1 --- Lebesgue measure of integral self-affine tile --- p.22 / Chapter 1.4.2 --- Classification of digit set --- p.24 / Chapter 2 --- Connectedness of self-affine tiles --- p.28 / Chapter 2.1 --- Connectedness --- p.28 / Chapter 2.2 --- Disk-likeness --- p.33 / Chapter 3 --- Tiles with rotations and reflections --- p.39 / Chapter 3.1 --- Tiles --- p.39 / Chapter 3.2 --- Integral tiles --- p.54 / Bibliography --- p.60

Thesis (M.Sc.)--Victoria University of Wellington, 2009. / Includes bibliographical references.

The teaching and learning of Euclidean geometry in black South African schools is characterised by teachers' poor knowledge of Euclidean geometry and the use of traditional taaching methods that encourage rote learning. In the light of this, the study investigated the extent to which learners perform in Process-Based Instruction. Process-Based Instruction is charactarised by the gradual transfer of instruction from the teacher to the learner. In Process-Based Instruction learners are expected to communicate thought,form concepts and master theorems by drawing, 'showed with and used hands', talking and writing. Learners' performance is assessed by rubrics and is analysed using graphs. The findings of the empirical investigation revealed that learners of both grades 8 and 9 cannot communicate thought by any media (talking, writing, 'showed with and used hands' and drawing). A few learners formed a few concepts and mastered theorems. On the basis of the findings and the shortcomings of the study recommendations are made. / Educational studies / M. Ed. (Didactics)

Text in English, abstract in English and Afrikaans / The teaching and learning of Euclidean geometry in black South African schools is characterised by teachers' poor knowledge of Euclidean geometry and the use of traditional teaching methods that encourage rote learning. In the light of this, the study investigated the extent to which learners perform in Process-Based Instruction. Process-Based Instruction is characterised by the gradual transfer of instruction from the teacher to the learner. In Process-Based Instruction learners are expected to communicate thought, form concepts and master theorems by drawing, 'showed with and used hands', talking and writing. Learners' performance is assessed by rubrics and is analysed using graphs. The findings of the empirical investigation revealed that learners of both grades 8 and 9 cannot communicate thought by any media (talking, writing 'showed with and used hands' and drawing). A few learners formed a few concepts and mastered theorems. On the basis of the findings and the shortcomings of the study recommendations are made. / Die onderrig van Euclediaanse Meetkunde in swart Suid-Afrikaanse skole word gekenmerk aan onderwysers se swak kennis van die vak, asook die gebruik van onderrigmetodes wat op die leerder se geheue staatmaak. Hierdie studie ondersoek die sukses van leerders se prestasie in proses-gebasseerde ondenig. Proses-gebaseerde onderig word gekenmerk aan die geleidelike oordra van kennis, van die onderwyser na die leerder. Daar word van leerders verwag om gedagtes oor te dra, konsepte (begrippe) te verstaan en stellings onder die knie te kry deur middel van sketse, die gebruik van gebare, verbale verduideliking en skriftelike werk. Leerders se prestasie word geevalueer deur die gebruik van klassifisering in kolomme (rubrics) en word ge-analiseer deur gralieke. Die bevinding van die empieriese ondersoek het getoon dat leerders van sowel graad 8 as graad 9 nie gedagtes kan oordra deur enige van die gemelde metodes nie. 'n Paar leerders het wel enkele begrippe verstaan en kon stellings bemeester. Na aanleiding van die bevindings van die studie en die tekortkominge wat daardeur opgespoor is, word sekere voorstelle gemaak. / Didactics / M. Ed. (Didactics)

Part I discusses the problem of determining the set of intersection points, with corresponding multiplicities, of two algebraic plane curves. We derive an algorithm based on the Euclidean Algorithm for polynomials and show how to use it to find the intersection points of two given curves. We also show that an easy proof of Bézout’s Theorem follows. We then discuss how, for curves with rational coefficients, this algorithm can bemodified to find the intersection points with coordinates expressed in terms of algebraic extensions of the rational numbers. Part II deals with the problem of determining the (monic) integer transfinite diameter of a given real interval. We show how this problem relates to the problem of determining the structure of the spectrum of normalised leading coefficients of polynomials with integer coefficients and all roots in the given interval. We then find dense regions of this spectrum for a number of intervals and discuss algorithms for finding discrete subsets of the spectrum for the interval [0,1]. This leads to an improvement in the known upper bound for the integer transfinite diameter. Finally, we discuss the connection between the infimum of the spectrum and the monic integer transfinite diameter.

The teaching and learning of Euclidean geometry in black South African schools is characterised by teachers' poor knowledge of Euclidean geometry and the use of traditional taaching methods that encourage rote learning. In the light of this, the study investigated the extent to which learners perform in Process-Based Instruction. Process-Based Instruction is charactarised by the gradual transfer of instruction from the teacher to the learner. In Process-Based Instruction learners are expected to communicate thought,form concepts and master theorems by drawing, 'showed with and used hands', talking and writing. Learners' performance is assessed by rubrics and is analysed using graphs. The findings of the empirical investigation revealed that learners of both grades 8 and 9 cannot communicate thought by any media (talking, writing, 'showed with and used hands' and drawing). A few learners formed a few concepts and mastered theorems. On the basis of the findings and the shortcomings of the study recommendations are made. / Educational studies / M. Ed. (Didactics)

Text in English, abstract in English and Afrikaans / The teaching and learning of Euclidean geometry in black South African schools is characterised by teachers' poor knowledge of Euclidean geometry and the use of traditional teaching methods that encourage rote learning. In the light of this, the study investigated the extent to which learners perform in Process-Based Instruction. Process-Based Instruction is characterised by the gradual transfer of instruction from the teacher to the learner. In Process-Based Instruction learners are expected to communicate thought, form concepts and master theorems by drawing, 'showed with and used hands', talking and writing. Learners' performance is assessed by rubrics and is analysed using graphs. The findings of the empirical investigation revealed that learners of both grades 8 and 9 cannot communicate thought by any media (talking, writing 'showed with and used hands' and drawing). A few learners formed a few concepts and mastered theorems. On the basis of the findings and the shortcomings of the study recommendations are made. / Die onderrig van Euclediaanse Meetkunde in swart Suid-Afrikaanse skole word gekenmerk aan onderwysers se swak kennis van die vak, asook die gebruik van onderrigmetodes wat op die leerder se geheue staatmaak. Hierdie studie ondersoek die sukses van leerders se prestasie in proses-gebasseerde ondenig. Proses-gebaseerde onderig word gekenmerk aan die geleidelike oordra van kennis, van die onderwyser na die leerder. Daar word van leerders verwag om gedagtes oor te dra, konsepte (begrippe) te verstaan en stellings onder die knie te kry deur middel van sketse, die gebruik van gebare, verbale verduideliking en skriftelike werk. Leerders se prestasie word geevalueer deur die gebruik van klassifisering in kolomme (rubrics) en word ge-analiseer deur gralieke. Die bevinding van die empieriese ondersoek het getoon dat leerders van sowel graad 8 as graad 9 nie gedagtes kan oordra deur enige van die gemelde metodes nie. 'n Paar leerders het wel enkele begrippe verstaan en kon stellings bemeester. Na aanleiding van die bevindings van die studie en die tekortkominge wat daardeur opgespoor is, word sekere voorstelle gemaak. / Didactics / M. Ed. (Didactics)

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-11-09T17:51:39Z No. of bitstreams: 1 ALECIO SOARES SILVA – DISSERTAÇÃO (PPGMat) 2014.pdf: 873139 bytes, checksum: 9a35db2563d66eb36f4dabfe6e5cd45e (MD5) / Made available in DSpace on 2018-11-09T17:51:39Z (GMT). No. of bitstreams: 1 ALECIO SOARES SILVA – DISSERTAÇÃO (PPGMat) 2014.pdf: 873139 bytes, checksum: 9a35db2563d66eb36f4dabfe6e5cd45e (MD5) Previous issue date: 2014-08 / Capes / Neste trabalho consideramos o uso de algoritmo de Euclides com o intuito de aplicá-lo de uma forma interdisciplinar. Para atingir este objetivo construimos o conjunto dos números naturais, com base nos quatro axiomas de Peano e o conjunto dos inteiros por uma relação de equivalência específica. Além disto, fizemos um estudo de algumas propriedades aritméticas dos números inteiros, bem como do magnífico algoritmo de Euclides. Em seguida utilizamos este algoritmo como uma ferramenta para calcular o maximo divisor comum (MDC) de números inteiros e a partir do MDC estudamos a resolução de equações lineares diofantinas, as quais foram empregadas para fazer o balanceamento de Reações Quimicas. / In this work we consider the use of the Euclid’s algorithm in order to apply it in an interdisciplinary way. To achieve this we constructed the set of the natural numbers based on the four Peano axioms and the set of integers by a specific equivalence relation. Moreover, we have studied some arithmetic properties of integers, as well as the magnificent Euclidean algorithm. We then use this algorithm as a tool to calculate the Greatest Common Divisor (GCD) of integers and from this study the resolution of Diophantine linear equations, which were employed to do the balance of Chemical Reactions.