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Maths (specialist)Open Courseware and Resources (specialist) Mathematics: body of knowledge centered on such concepts as quantity, structure, space and change and also the academic discipline that studies them (Wikipedia).CombinatoricsWhat is, Subsets and binomial coefficients, Lucas' Theorem, Selections and arrangements, Power series, Recurrence relations, Partitions and permutations, The Principle of Inclusion and Exclusion, Families of sets, ErdösKoRado theorem, Systems of distinct representatives, Latin squares, Steiner triple systems, Kirkman's Theorem
Differential Analysisfoundation in theory of elliptic & parabolic linear partial differential equations, theory of harmonic functions, maximum principles for more general elliptic & parabolic equations, Schauder theory
Association Schemes and Partially Balanced Designslinks graphs with nice regularity properties, sets of real symmetric matrices which commute with each other, incompleteblock designs in designed experiments, finite groups: definitions, adjacency matrices, special association schemes, BoseMesner algebra, character tables, techniques, strongly regular graphs, block designs, statistics, efficiency, cyclic designs, families of partitions, orthogonal block structures: reading list
Algebra Igroups, vector spaces, linear transformations, symmetry groups, bilinear forms and linear groups: readings, practice quizzes
Finite Geometry and its Applicationintensive course: embeddings of pointline geometries in projective spaces, matrix techniques for strongly regular graphs & related geometries, history of polar spaces & generalized polygons, nuclei in finite projective planes, partial spreads in finite projective space, collineation groups of finite planes, ovals and ovoids in projective spaces
Uncertainty in Engineeringprobability & statistics with emphasis on applications, events & probability, Bayes' theorem, random variables & vectors, distributions, Bernoulli trials & Poisson point processes, fulldistribution uncertainty propagation, secondmoment representation, propagation, conditional analysis, random sampling, estimation, hypothesis testing, linear regression
Numerical Methods in Engineeringrootfinding, elementary numerical linear algebra, solving systems of linear equations, curve fitting, numerical quadrature and numerical solution to ordinary differential equations
Introduction to Linear Dynamical Systemsapplied linear algebra & dynamical systems, applications to circuits, signal processing, communications, control systems: Leastsquares aproximations of overdetermined equations, leastnorm solutions of underdetermined equations, Symmetric matrices, matrix norm & SVD, Eigenvalues & eigenvectors, Matrix exponential, stability, asymptotic behavior, Multiinput & output, impulse & step matrices, convolution & transfer matrix, Control, reachability, state transfer, leastnorm inputs, Observability & leastsquares state estimation: support notes, MATLAB files
Algebraic Techniques and Semidefinite Optimizationalgebraic and computational techniques for optimization problems involving polynomial equations and inequalities with particular emphasis on the connections with semidefinite optimization, algebraic and numerical approaches to polynomial systems, complex and real cases, techniques of general applicability, convexitybased ideas, complexity results, efficient implementations, examples from several engineering areas, systems and control applications: Readings, Related Resources

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