Proefschrift--Utrecht.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Oregon, 2006. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 146-147). Also available for download via the World Wide Web; free to University of Oregon users.

No description available.

Thesis (Ed.M.)--Boston University / The primary purpose of constructing a test on informal geometry is to provide the eighth-grade mathematics teacher with an objective means of measuring the achievement of his students in geometry. A secondary purpose is to explore the possibility that this test alone, or in conjunction with other criteria, might have value in predicting the degree of success of a student in demonstrative geometry.

Thesis (M.A.)--Boston University / This study proposed to determine by experiment the effect of the study of symbolic logic on the student's achievement in geometry. Its secondary purpose was to test the influence of the study of logic on the student's ability to solve non-mathematical problems. As a means of teaching the nature and value of proof, the study presented a unit on symbolic logic taught in conjunction with geometry. Current stress on concept as well as content, sustained interest in "the nature of proof," emphasis on the "foundations" in mathematics, and experiments with symbolic and Aristotelian logic all served to suggest the vitality of the problem and to set the direction for the experiment [TRUNCATED]

The Constitution (1996) of the Republic of South Africa forms the basis for social transformation in our new society. The Constitution (Act 108 of 1996) and the amendments that followed provided a basis for curriculum transformation and development in South Africa. The Department of Education introduced the present curriculum known as the National Curriculum Statement, which is modern and internationally benchmarked, in grade 10 in 2006. It required the learners to do seven subjects in grades 10 to 12 of which mathematics or mathematical literacy was prescribed as compulsory subjects. To attain social transformation, the South African Government attached a great deal of importance to the learning and teaching of mathematics and sciences in the South African schools. This study was undertaken in an effort to improve the understanding of geometry and, consequently, the performance and achievement of senior secondary school learners in geometry. The study was inspired by the van Hiele theory. The study made use of the different levels of the van Hiele theory for the development of an instructional framework for geometry in senior secondary schools. The research was conducted in a previously disadvantaged area in South Africa. Given the setting of this study and the wider application of it, the use of ‘hands-on’ and practical approach to use manipulatives and worksheets to improve the geometric understanding was tried and tested in this study. The assumption was that such experiences would make the learning of geometry more relevant and enjoyable for learners from limited financial and underprivileged circumstances. A quasi-experimental design was chosen. A total of 359 learners from five purposively selected schools in Mthatha district in the Eastern Cape Province participated in this study. Qualitative data through interviews were gathered. The data were analysed using IBM SPSS Version 19 and Microsoft Excel. Findings indicated that there was a notable improvement in the performance of learners who were taught by the application of the van Hiele theory. The results revealed that most of the learners were not ready for the application of deductive principles of geometry in terms of formal proof in senior secondary school geometry. Based on the results, some recommendations are made to enhance the teaching and learning of geometry in senior secondary schools.

Made available in DSpace on 2014-06-11T19:32:21Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-11-27Bitstream added on 2014-06-13T19:02:55Z : No. of bitstreams: 1 sousa_mol_dr_rcla.pdf: 7582087 bytes, checksum: 3ca5ed6f75e18abf79505617dc600da8 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Os altos estruturais de Pitanga, Artemis, Pau d Alho e Jibóia, localizados na borda leste da Bacia do Paraná, centro do Estado de São Paulo, foram estudados com ênfase ao papel das falhas na configuração geométrica e cinemática, com o propósito de avançar no entendimento da evolução tectônica da região. O padrão estrutural principal da área é caracterizado por zonas de falhas de orientação preferencial NW-SE, que promovem soerguimentos e abatimentos de blocos e formam altos e baixos estruturais. As unidades litoestratigráficas mais antigas afloram ao lado das mais jovens e formam o arranjo geométrico principal. Falhas direcionais NE-SW e E-W também aparecem na estruturação regional, com menor importância. Feições de reativação e ressurgência ocorrem em vários destes conjuntos. O quadro morfoestrutural da área apresenta relação com os principais feixes de lineamentos tectônicos NW-SE, E-W e NE-SW. O quadro evolutivo é resultado de pelo menos quatro eventos tectônicos: o primeiro reconhecido para falhas associadas aos depósitos sedimentares da Formação Tatuí, com indicação de falhas normais NWSE; o segundo é marcado por falhas e fraturas preenchidas por rochas básicas de orientação NW-SE, apontando para uma deformação pré- a sinmagmatismo basáltico juro-cretáceo com distensão próximo a NE-SW; o terceiro é marcado por falhas normais NE-SW, que controlam a sedimentação de coberturas cenozóicas (Formação Rio Claro). O último evento é reconhecido através de levantamento de falhas que deformam as coberturas sedimentares superficiais e pela distribuição espacial de feições morfotectônicas e feições anômalas da rede de drenagem, como capturas, inflexões, assimetria, meandros abandonados, relacionadas aos soerguimentos e basculamentos de blocos que ocorrem ao longo das principais falhas que formam os altos estruturais estudados. / The Pitanga, Artemis, Pau d Alho and Jibóia structural highs, located on the eastern border of the Paraná Basin in the central part of São Paulo State, were studied emphasizing the role of faults in the geometrical configuration and their kinematic behavior. The major structural pattern is characterized by faults with NW-SE preferred orientation, promoting tilting, uplifting and down dropping of blocks, leading to older stratigraphic units cropping out beside younger ones. Subordinate NE-SW and E-W strike-slip faults are recognized as part of the structural pattern as well. Reactivation features occur along all the fault sets and a total of four tectonic events are recognized. The first one occurs along synsedimentary normal NW-SE faults that resulted in the deposition of the Tatuí Formation. The second event is characterized by faults and fractures filled by basic rocks, interpreted to be pre- to syn-deformation (NE-SW trending distension) associated with Juro-Cretaceous basaltic rift volcanism. In the third tectonic event NE-SW normal faults were activated resulting in the deposition of the Cenozoic Rio Claro Formation. Finally, the fourth and last event was associated with neotectonics that deformed surface sedimentary cover and influenced the current distribution of morphotectonic features, drainage patterns and the general landscape.

In this thesis I will study noncommutative differential geometry, after the style of Connes and Woronowicz. In particular two examples of differential calculi on Hopf algebras are considered, and their associated covariant derivatives and Riemannian geometry. These are on the Heisenberg group, and on the finite group A4. I consider bimodule connections after the work of Madore. In the last chapter noncommutative fibrations are considerd, with an application to the Leray spectral sequence. NOTATION. In this thesis equations are numbered as round brackets (), where (a.b) denotes equation b in chapter a, and references are indicated by square brackets []. This thesis has been typeset using Latex, and some figures using the Visio program.

abstract: When manufacturing large or complex parts, often a rough operation such as casting is used to create the majority of the part geometry. Due to the highly variable nature of the casting process, for mechanical components that require precision surfaces for functionality or assembly with others, some of the important features are machined to specification. Depending on the relative locations of as-cast to-be-machined features and the amount of material at each, the part may be positioned or ‘set up’ on a fixture in a configuration that will ensure that the pre-specified machining operations will successfully clean up the rough surfaces and produce a part that conforms to any assigned tolerances. For a particular part whose features incur excessive deviation in the casting process, it may be that no setup would yield an acceptable final part. The proposed Setup-Map (S-Map) describes the positions and orientations of a part that will allow for it to be successfully machined, and will be able to determine if a particular part cannot be made to specification. The Setup Map is a point space in six dimensions where each of the six orthogonal coordinates corresponds to one of the rigid-body displacements in three dimensional space: three rotations and three translations. Any point within the boundaries of the Setup-Map (S-Map) corresponds to a small displacement of the part that satisfies the condition that each feature will lie within its associated tolerance zone after machining. The process for creating the S-Map involves the representation of constraints imposed by the tolerances in simple coordinate systems for each to-be-machined feature. Constraints are then transformed to a single coordinate system where the intersection reveals the common allowable ‘setup’ points. Should an intersection of the six-dimensional constraints exist, an optimization scheme is used to choose a single setup that gives the best chance for machining to be completed successfully. Should no intersection exist, the particular part cannot be machined to specification or must be re-worked with weld metal added to specific locations. / Dissertation/Thesis / Masters Thesis Engineering 2016