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Mathematics


Mathematics - Open Courseware (OCW)

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Differential Analysis

MIT (US), OpenCourseWare

foundation 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 Designs

Queen Mary (UK)

links graphs with nice regularity properties, sets of real symmetric matrices which commute with each other, incomplete-block designs in designed experiments, finite groups: definitions, adjacency matrices, special association schemes, Bose-Mesner algebra, character tables, techniques, strongly regular graphs, block designs, statistics, efficiency, cyclic designs, families of partitions, orthogonal block structures: reading list


Algebra I

MIT (US), OpenCourseWare

groups, vector spaces, linear transformations, symmetry groups, bilinear forms and linear groups: readings, practice quizzes


Finite Geometry and its Application

Ghent University (BE)

intensive course: embeddings of point-line 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


Economic Applications of Game Theory

MIT OpenCourseWare (US)

basic tools of game theoretic analysis, applications of game theory, primarily in economics and political science: readings


Uncertainty in Engineering

MIT (US), OpenCourseWare

probability & statistics with emphasis on applications, events & probability, Bayes' theorem, random variables & vectors, distributions, Bernoulli trials & Poisson point processes, full-distribution uncertainty propagation, second-moment representation, propagation, conditional analysis, random sampling, estimation, hypothesis testing, linear regression


Numerical Methods in Engineering

Portland State University (US)

root-finding, elementary numerical linear algebra, solving systems of linear equations, curve fitting, numerical quadrature and numerical solution to ordinary differential equations


Introduction to Linear Dynamical Systems

Stanford University (US)

applied linear algebra & dynamical systems, applications to circuits, signal processing, communications, control systems: Least-squares aproximations of over-determined equations, least-norm solutions of underdetermined equations, Symmetric matrices, matrix norm & SVD, Eigenvalues & eigenvectors, Matrix exponential, stability, asymptotic behavior, Multi-input & output, impulse & step matrices, convolution & transfer matrix, Control, reachability, state transfer, least-norm inputs, Observability & least-squares state estimation: support notes, MATLAB files
 



 

Algebraic Techniques and Semidefinite Optimization

MIT (US), OpenCourseware

algebraic 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, convexity-based ideas, complexity results, efficient implementations, examples from several engineering areas, systems and control applications: Readings, Related Resources


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