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).


What 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, Erdös-Ko-Rado theorem, Systems of distinct representatives, Latin squares, Steiner triple systems, Kirkman's Theorem

Differential Analysis

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

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

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

Finite Geometry and its Application

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

Uncertainty in Engineering

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

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

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

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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