The effective integration of technology into the teaching and learning of mathematics remains one of the critical challenges facing tertiary mathematics, which has traditionally been slow to respond to technological innovation. This thesis reveals that the term integration is widely used in the literature with respect to technology and the curriculum, although its meaning can vary substantially, and furthermore, the term is seldom well defined. A review of the literature provides the basis for a survey of undergraduate mathematics educators, to determine their use of technology, their views of what an Integrated Technology Mathematics Curriculum (ITMC) may resemble, and how it may be achieved. Responses to this survey, and factors identified in the literature, are used to construct a taxonomy of integrated technology. The taxonomy identifies six defining characteristics of an ITMC, each with a number of associated elements. A visual model using radar diagrams is developed to compare courses against the taxonomy, and to identify aspects needing attention in individual courses. T Evidence from an observational study of initiatives to introduce Computer Algebra Systems into undergraduate mathematics courses at The University of Auckland, firstly using CAS-calculators and latterly computer software, is examined against the taxonomy. A number of critical issues influencing the integration of these technologies are identified. These include mandating technology use in official departmental policy, attention to congruency and fairness in assessment, re-evaluating the value of topics in the curriculum, re-establishing the goals of undergraduate courses, and developing the pedagogical technical knowledge of teaching staff. The thesis concludes that effective integration of technology in undergraduate mathematics requires a recognition of, and comprehensive attention to, the interdependence of the taxonomy components. An integrated, holistic approach, which aims for curricular congruency across all elements of the taxonomy, provides the basis for a more consistent, effective and sustainable ITMC.

Quandles were introduced to Knot Theory in the 1980s as an almost complete algebraic invariant for knots and links. Like their more basic siblings, groups, they are difficult to distinguish so a major challenge is to devise means for determining when two quandles having different presentations are really different. This thesis addresses this point by studying algebraic aspects of quandles. Following what is mainly a recapitulation of existing work on quandles, we firstly investigate how a link quandle is related to the quandles of the individual components of the link. Next we investigate coset quandles. These are motivated by the transitive action of the operator, associated and automorphism group actions on a given quandle, allowing techniques of permutation group theory to be used. We will show that the class of all coset quandles includes the class of all Alexander quandles; indeed all group quandles. Coset quandles are used in two ways: to give representations of connected quandles, which include knot quandles; and to provide target quandles for homomorphism invariants which may be useful in enabling one to distinguish quandles by counting homomorphisms onto target quandles. Following an investigation of the information loss in going from the fundamental quandle of a link to the fundamental group, we apply our techniques to calculations for the figure eight knot and braid index two knots and involving lower triangular matrix groups. The thesis is rounded out by two appendices, one giving a short table of knot quandles for knots up to six crossings and the other a computer program for computing the homomorphism invariants.

This work addresses the development and application of gene set analysis methods to problems in microarray-based data sets. The work consists of three parts. In the first part a gene set analysis method (PCOT2) is developed. It utilizes inter-gene correlation to detect significant alteration in gene sets across experimental conditions. The second part is focused on the exploration of correlation-based gene sets in conjunction with the application of the PCOT2 testing method in the investigation of biological mechanisms underlying breast cancer recurrence. In the third part, statistical models for analyzing combined microarray-based expression and genomic copy number data are developed. In addition, an analysis which incorporates tumour subgroups is shown to provide more accurate prognosis assessment for breast cancer patients.

The effective integration of technology into the teaching and learning of mathematics remains one of the critical challenges facing tertiary mathematics, which has traditionally been slow to respond to technological innovation. This thesis reveals that the term integration is widely used in the literature with respect to technology and the curriculum, although its meaning can vary substantially, and furthermore, the term is seldom well defined. A review of the literature provides the basis for a survey of undergraduate mathematics educators, to determine their use of technology, their views of what an Integrated Technology Mathematics Curriculum (ITMC) may resemble, and how it may be achieved. Responses to this survey, and factors identified in the literature, are used to construct a taxonomy of integrated technology. The taxonomy identifies six defining characteristics of an ITMC, each with a number of associated elements. A visual model using radar diagrams is developed to compare courses against the taxonomy, and to identify aspects needing attention in individual courses. T Evidence from an observational study of initiatives to introduce Computer Algebra Systems into undergraduate mathematics courses at The University of Auckland, firstly using CAS-calculators and latterly computer software, is examined against the taxonomy. A number of critical issues influencing the integration of these technologies are identified. These include mandating technology use in official departmental policy, attention to congruency and fairness in assessment, re-evaluating the value of topics in the curriculum, re-establishing the goals of undergraduate courses, and developing the pedagogical technical knowledge of teaching staff. The thesis concludes that effective integration of technology in undergraduate mathematics requires a recognition of, and comprehensive attention to, the interdependence of the taxonomy components. An integrated, holistic approach, which aims for curricular congruency across all elements of the taxonomy, provides the basis for a more consistent, effective and sustainable ITMC.

Quandles were introduced to Knot Theory in the 1980s as an almost complete algebraic invariant for knots and links. Like their more basic siblings, groups, they are difficult to distinguish so a major challenge is to devise means for determining when two quandles having different presentations are really different. This thesis addresses this point by studying algebraic aspects of quandles. Following what is mainly a recapitulation of existing work on quandles, we firstly investigate how a link quandle is related to the quandles of the individual components of the link. Next we investigate coset quandles. These are motivated by the transitive action of the operator, associated and automorphism group actions on a given quandle, allowing techniques of permutation group theory to be used. We will show that the class of all coset quandles includes the class of all Alexander quandles; indeed all group quandles. Coset quandles are used in two ways: to give representations of connected quandles, which include knot quandles; and to provide target quandles for homomorphism invariants which may be useful in enabling one to distinguish quandles by counting homomorphisms onto target quandles. Following an investigation of the information loss in going from the fundamental quandle of a link to the fundamental group, we apply our techniques to calculations for the figure eight knot and braid index two knots and involving lower triangular matrix groups. The thesis is rounded out by two appendices, one giving a short table of knot quandles for knots up to six crossings and the other a computer program for computing the homomorphism invariants.

Thesis (MSc (Mathematical Sciences))--University of Stellenbosch, 2007. / In this thesis, we surveyed the most important methods for factorization of polynomials over a global field, focusing on their strengths and showing their most striking disadvantages. The algorithms we have selected are all modular algorithms. They rely on the Hensel factorization technique, which can be applied to all global fields giving an output in a local field that can be computed to a large enough precision. The crucial phase of the reconstruction of the irreducible global factors from the local ones, determines the difference between these algorithms. For different fields and cases, different techniques have been used such as residue class computations, ideal calculus, lattice techniques. The tendency to combine ideas from different methods has been of interest as it improves the running time. This appears for instance in the latest method due to van Hoeij, concerning the factorization over a number field. The ideas here can be used over a global function field in the form given by Belabas et al. using the logarithmic derivative instead of Newton sums. Complexity analysis was not our objective, nevertheless it was important to mention certain results as part of the properties of these algorithms.

This thesis provides an assessment of the readiness levels within both urban and rural hospitals and clinics in Libya for the implementation of E-health systems. This then enabled the construction of a framework for E-health implementation in the Libyan National Health Service (LNHS). The E-health readiness study assessed how medications were prescribed, how patients were referred, how information communication technology (ICT) was utilised in recording patient records, how healthcare staff were trained to use ICT, and how the ways in which consultations were carried out by healthcare staff. The research was done in five rural clinics and five urban medical centres and focused on the E-health readiness levels of the technology, social attitudes, engagement levels and any other needs that were apparent. Collection of the data was carried out using a mixed methods approach with qualitative interviews and quantitative questionnaires. The study indicated that any IT equipment present was not being utilised for clinical purposes and there was no evidence of any E-health technologies being employed. This implies that the maturity level of the healthcare institutions studied was at level zero in the E-health maturity model used in this thesis. In order for the LNHS to raise its maturity levels for the implementation of E-health systems, it needs to persuade LNHS staff and patients to adopt E-health systems. This can be carried out at a local level throughout the LNHS, though this will need to be coordinated at a national level through training, education and programmes to encourage compliance and providing incentives. In order to move E-health technology usage in the participating Libyan healthcare institutions from Level 0 to Level 2 in the E-health Maturity Model levels, an E-health framework was created that is based on the findings of this research study. The primary aim of the LNHS E-Health Framework is the integration of E-health services for improving the delivery of healthcare within the LNHS. To construct the framework and ensure that it was creditable and applicable, work on it was informed directly by the findings from document analysis, literature review, and expert feedback, in conjunction with the primary research findings presented in Chapter Five. When the LNHS E-Health Framework was compiled there were several things taken into consideration, such as: the abilities of healthcare staff, the needs of healthcare institutions and the existing ICT infrastructure that had been recorded in the E-readiness assessment which was carried out in the healthcare institutions (Chapter 5). The framework also provides proposals for E-health systems based on the infrastructure network that will be developed. The processes addressed are electronic health records, E-consultations, E-prescriptions, E-referrals and E-training. The researcher has received very positive, even enthusiastic, feedback from the LNHS and other officals, and that expect the framework to be further developed and implemented by the LNHS in the near future.

Nowadays, the European automotive market is dominated by Diesel engines. Despite their high efficiency, these produce significant levels of pollutants. Among the various pollutants released, nitrogen oxides and soot are the main issues. Their formation is linked to the combustion process and attempts to reduce one often lead to an increase of the other. Laser diagnostics are among the best tools for experimental, non-intrusive studies inside combustion chambers for a better understanding of the complex combustion processes. Depending on the optical diagnostic, numerous combustion characteristics and processes can be investigated. The work presented here intends initially to develop a quantitative laser technique for characterising soot and, secondly, to further the knowledge on soot formation in Diesel engines by the application of this technique in an optical combustion chamber. Some of the main characteristics describing soot formation are the soot volume fraction, number density and particle sizes. Soot volume fraction is the major one as it is representative of the volume of soot produced. Planar characterisation of soot volume fraction, number density and particle size were achieved for the first time by simultaneous recording laser-induced incandescence (LII), laser scattering and two-colour time-resolved (2C-TiRe) LII signals. Qualitative planar distributions of particle diameter and soot volume fraction were derived from the image ratio of scattering and incandescence signals. 2C- TiRe LII technique allowed the simultaneous recording of the temporal LII signal for two different wavelengths in order to obtain quantitative values of the laser-heated particles temperature, soot volume fraction and particle size for a local or global part of the flame. These were used to recalibrate relative size and soot volume distributions. An initial development of the technique was performed on a laminar diffusion flame (Santoro burner) to validate its viability and performance. Equivalent temperature, soot volume fraction and particle diameter were determined throughout the flame. The results were found to be in good agreement with the ones published in the literature. The diagnostic was subsequently applied to an optical Diesel rapid compression machine, and further refinements were undertaken to cope with the higher soot concentration and lower LII signal. Tests were conducted for in-cylinder pressures ranging from 4 to 10 MPa, and injection pressures up to 160 MPa. A fixed injection timing and injected fuel quantity were used. Effects of in-cylinder pressure, fuel injection pressure and cetane number on soot formation and characteristics were observed. High injection pressure, cetane number and in-cylinder pressure caused a reduction of soot particle size and volume fraction but an increase of the soot particle density.

Corpus-based methods are now dominant in Natural Language Processing (NLP). Creating big corpora is no longer difficult and the technology to analyze them is growing faster, more robust and more accurate. However, when an NLP application performs well on one corpus, it is unclear whether this level of performance would be maintained on others. To make progress on these questions, we need methods for comparing corpora. This thesis investigates comparison methods based on the notions of corpus homogeneity and similarity.

This doctoral research is propelled by a single question: when partners from public and private sectors unify with the aim of increasing access to quality community ‘health’ information, what factors shape the selection of technological platforms? In monitoring the processes of planning and decision making, the choice of platform reveals the interests, ideologies and values of groups given labels such as ‘stakeholders.’