<p>The purpose of this study was to investigate the epistemological obstacles that mathematics students at undergraduate level encounter in coming to understand the limit concept. The role played by language and symbolism in understanding the limit concept was also investigated. A group of mathematics students at undergraduate level at the National University of Lesotho (NUL) was used as the sample for the study. Empirical data were collected by using interviews and questionnaires. These data were analysed using both the APOS framework and a semiotic perspective.</p> <p><br /> Within the APOS framework, the pieces of knowledge that have to be constructed in coming to understand the limit concept are actions, processes and objects. Actions are interiorised into processes and processes are encapsulated into objects. The conceptual structure is called a schema. In investigating the idea of limit within the context of a function some main epistemological obstacles that were encountered when actions were interiorised into processes are over-generalising and taking the limit value as the function value. For example, in finding the limit value L for f(x) as x tends to 0, 46 subjects out of 251 subjects said that they would calculate f(0) as the limit value. This method is appropriate for calculating the limit values for continuous functions. However, in this case, the method is generalised to all the functions. When these subjects encounter situations in which the functional value is equal to the limit value, they take the two to be the same. However, the two are different entities conceptually.</p>

<p>Problems of understanding fundamental calculus concepts by students in tertiary education colleges and universities are evidenced by a body of research studies conducted in different parts of the world. The researchers have identified, classified and analysed these problems from historical, epistemological, and learning theory perspectives. History is important because mathematical concepts are a result of the developments of the past. The way knowledge is acquired is an epistemological issue and the major purpose of learning is to acquire knowledge. Hence, these three perspectives qualify to be used as lenses in understanding problems that students encounter in a learning situation. The purpose of this study was to investigate the epistemological obstacles that mathematics students at undergraduate level encounter in coming to understand the limit concept. The role played by language and symbolism in understanding the limit concept was also investigated, because communication in the mathematics classroom takes place by using language and symbols.</p>

"This thesis investigates several non-linear analogues of Lagrange functions in the hope of answering the question 'Is it possible to generalise Lagrange functions such that they may be applied to a range of nonconvex objective problems?' The answer to this question is found to be yes for a particular class of optimization problems. Furthermore the thesis asserts that in derivative free optimization the general schema which is most theoretically and practically appealing involves the reformulation of both objective and constraint functions, whilst the least practically successful approach for everything but the most simple convex case is the augmented Lagrangian approach." / Doctor of Philosophy

"This thesis investigates several non-linear analogues of Lagrange functions in the hope of answering the question 'Is it possible to generalise Lagrange functions such that they may be applied to a range of nonconvex objective problems?' The answer to this question is found to be yes for a particular class of optimization problems. Furthermore the thesis asserts that in derivative free optimization the general schema which is most theoretically and practically appealing involves the reformulation of both objective and constraint functions, whilst the least practically successful approach for everything but the most simple convex case is the augmented Lagrangian approach." / Doctor of Philosophy

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