This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include description of the problem of optimisation and the geometry of Rn, n > 1, convex sets and convex functions, unconstrained optimization: necessary and sufficient conditions for local minima/maxima, constrained optimization: equality and inequality constraints, Lagrange multipliers and the Kuhn-Tucker conditions, computational methods for unconstrained and constrained optimization, steepest descent and Newton's methods, quadratic programming, penalty and barrier methods, sequential quadratic programming (SQP) implementation in MATLAB/OCTAVE.
This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and further topics such as open and closed sets, neighbourhood, basis, convergence, limit point, completeness, subspaces, product spaces, quotient spaces.
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This course provides a critical analysis of competing models of Strategic Human Resource Management (SHRM) and factors that impact on them as well as business viability and relative performance. The course examines whether the strategic management of employees can contribute significantly to the acquisition of competitive advantage by organisations and to their capacity to sustain advantage over time. Human resource strategy is an essential part of any credible understanding of business strategy in ever-changing environment. The course considers the potential of SHRM to enhance organisational flexibility and help create competitive advantage. It is also concerned with how human resource functions and activities align with the overall corporate strategic.
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This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. The topics covered include: Ideals and quotient rings, axioms for the integral domains, with examples, subdomains and subfields, ordered integral domains and fields, polynomial rings and field of quotients of an integral domain.
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