The aim of the course is to allow student to read articles and critic same. It is designed to help student to appreciate the practicality of what they have learnt in research methods in business.
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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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