For a given abelian category o/, a category E is formed by considering exact sequences of o/. If one imposes the condition that a split sequence be regarded as the zero object, then the resulting sequence category E/S is shown to be abelian. The intrinsic algebraic structure of E/S is examined and related to the theory of coherent functors and functor rings. E/S is shown to be the natural setting for the study of pure and copure sequences and the theory is further developed by introducing repure sequences. The concept of pure semi-simple categories is examined in terms of E/S. Localization with respect to pure sequences is developed, leading to results concerning the existence of algebraically compact objects. The final topic is a study of the simple sequences and their relationship to almost split exact sequences. / Science, Faculty of / Mathematics, Department of / Graduate

This paper establishes a basis for abelian categories, then gives the statement and proof of two equivalent definitions of an abelian category, the development of the basic theory of such categories, and the proof of some theorems involving this basic theory.

Computer vulnerabilities are design flaws, implementation or configuration errors that provide a means of exploiting a system or network that would not be available otherwise. The recent growth in the number of vulnerability scanning (VS) tools and independent vulnerability databases points to an apparent need for further means to protect computer systems from compromise. It is important for these tools and databases to interpret, correlate and exchange a large amount of information about computer vulnerabilities in order to use them effectively. However, this goal is hard to achieve because the current VS products differ extensively both in the way that they can detect vulnerabilities and in the number of vulnerabilities that they can detect. Each tool or database represents, identifies and classifies vulnerabilities in its own way, thus making them difficult to study and compare. Although the list of Common Vulnerabilities and Exposures (CVE) provides a means of solving the disparity in vulnerability names used in the different VS products, it does not standardise vulnerability categories. This dissertation highlights the importance of having a standard vulnerability category set and outlines an approach towards achieving this goal by categorising the CVE repository using a data-clustering algorithm. Prototypes are presented to verify the concept of standardizing vulnerability categories and how this can be used as the basis for comparison of VS products and improving scan reports. / Dissertation (MSc (Computer Science))--University of Pretoria, 2008. / Computer Science / unrestricted

Magister Educationis - MEd / This research investigated how grade 7 learners dealt with introductory aspects of integers when they are introduced through a temperature model. In particular, the study analysed the effect of an intentional teaching strategy on learners’ engagement with integers. The idea of combining an intentional teaching strategy with the introduction of integers in grade 7 learners using a temperature model is what makes this study unique. A qualitative study was adopted. Data was collected by means of audio and video and also by means of learners’ completed worksheets. The results of the study indicate that the majority of learners could recognise, compare and order integers. It is recommended that the application of intentional teaching with a temperature model is a viable strategy to introduce grade 7 learners to integers.

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