Gotowa bibliografia na temat „Descrete Mathematics”

This study establishes a framework for the practice and the acquisition of mathematical knowledge. The natures of mathematics and rituals/ritual-like activities are examined compared and contrasted. Using a four-fold typology of core features, surface features, content features and functions of mathematics it is established that the nature of mathematics, its practice and the acquisition is typologically similar to that of rituals/ ritual-like activities. The practice of mathematics and its acquisition can hence be metaphorically compared to that of rituals/ritual-like activities and be enriched by the latter. A case study was conducted using the ritual metaphor at two levels to introduce and teach a topic within the current year eleven West Australian Geometry and Trigonometry course. In the first level, instructional materials were written using a ritual-like mentor-exemplar, exposition, replicate and extrapolate model (through the use of specially organised examples and exercises) based on the approaches of several mathematics text book authors as they attempted to introduce a topic new to the West Australian mathematics curriculum.In the second level, the classroom instruction was organised using a ritual-like pattern with direct exemplar mentoring and exposition by the teacher followed by replication and extrapolation from the students. Embedded within this ritual-like process was the personal (and communal) engagement with each student vis-a-vis the establishment of the relationships between the referent concepts, procedures and skills. This resulted in the emergence of solution behaviours appropriate to specific tasks imitating and extrapolating the mentored solution behaviours of the teacher. In determining the extent to which the instruction, mentoring and acquisition was successful, each student's solution 'behaviour was compared "topographically" with the expected solution behaviour for the task at various critical points to determine the degree of congruence. Marks were allocated for congruence (or removed for incongruence), hence a percentage of congruence was established. The ritual-like model for the teaching and acquisition of mathematical knowledge required agreement with all stake-holders as to the purpose of the activity, expert knowledge on the part of the teacher, and within a classroom context requires students to possess similar levels of prerequisite mathematical knowledge.This agreement and the presence of an expert practitioner, provides the affirmation and security that is inherent in the practice of rituals. The study concluded that there is evidence to suggest that some aspects of mathematical ability are wired into the cognitive structures of human beings providing support to the hypothesis that some aspects of mathematics are discovered rather than created. The physical origin of mathematical abilities and activities was one of the factors used in this study to establish an isomorphism between the nature and practice of mathematics with that of rituals. This isomorphism provides the teaching and learning of mathematics with a more robust framework that is more attuned to the social nature of human beings. The ritual metaphor for the teaching and learning of mathematics can then be used as a framework to determine the relative adequacies of mathematics curricula, mathematics textbooks and teaching approaches.

This study establishes a framework for the practice and the acquisition of mathematical knowledge. The natures of mathematics and rituals/ritual-like activities are examined compared and contrasted. Using a four-fold typology of core features, surface features, content features and functions of mathematics it is established that the nature of mathematics, its practice and the acquisition is typologically similar to that of rituals/ ritual-like activities. The practice of mathematics and its acquisition can hence be metaphorically compared to that of rituals/ritual-like activities and be enriched by the latter. A case study was conducted using the ritual metaphor at two levels to introduce and teach a topic within the current year eleven West Australian Geometry and Trigonometry course. In the first level, instructional materials were written using a ritual-like mentor-exemplar, exposition, replicate and extrapolate model (through the use of specially organised examples and exercises) based on the approaches of several mathematics text book authors as they attempted to introduce a topic new to the West Australian mathematics curriculum.<br>In the second level, the classroom instruction was organised using a ritual-like pattern with direct exemplar mentoring and exposition by the teacher followed by replication and extrapolation from the students. Embedded within this ritual-like process was the personal (and communal) engagement with each student vis-a-vis the establishment of the relationships between the referent concepts, procedures and skills. This resulted in the emergence of solution behaviours appropriate to specific tasks imitating and extrapolating the mentored solution behaviours of the teacher. In determining the extent to which the instruction, mentoring and acquisition was successful, each student's solution 'behaviour was compared "topographically" with the expected solution behaviour for the task at various critical points to determine the degree of congruence. Marks were allocated for congruence (or removed for incongruence), hence a percentage of congruence was established. The ritual-like model for the teaching and acquisition of mathematical knowledge required agreement with all stake-holders as to the purpose of the activity, expert knowledge on the part of the teacher, and within a classroom context requires students to possess similar levels of prerequisite mathematical knowledge.<br>This agreement and the presence of an expert practitioner, provides the affirmation and security that is inherent in the practice of rituals. The study concluded that there is evidence to suggest that some aspects of mathematical ability are wired into the cognitive structures of human beings providing support to the hypothesis that some aspects of mathematics are discovered rather than created. The physical origin of mathematical abilities and activities was one of the factors used in this study to establish an isomorphism between the nature and practice of mathematics with that of rituals. This isomorphism provides the teaching and learning of mathematics with a more robust framework that is more attuned to the social nature of human beings. The ritual metaphor for the teaching and learning of mathematics can then be used as a framework to determine the relative adequacies of mathematics curricula, mathematics textbooks and teaching approaches.

This work is primarily aimed at determining the effect that an immunisation policy Is likely to have on the incidence of Haemophllus influenzae Type B (HIB) and systematic HIB in Western Australia. There was a significant effort made to collect data pertinent to the estimation of parameter values but since HIB has only been a notifiable disease since 1992, there was a distinct lack of relevant data available. Private communication with individual’s such as Dr Jeffrey Hanna and Dr Beryl Wild resulted in practical information being obtained that was used to estimate certain parameters. The deterministic mathematical models within the thesis are extensions of existing ideas tailored to suit the needs of this thesis. Chapter one is a basic introduction to the pursuit of modelling infectious diseases with a brief description of basic epidemiology concepts. It also shows that even simple models may not deliver analytical results. Chapter two extends a model used by Angela Mclean and allows some analytical results to be obtained by first simplifying the model and then solving using standard methods to give the equilibrium distributions for the proportions of people in each state within the model