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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).Numerical Methods in Engineeringrootfinding, elementary numerical linear algebra, solving systems of linear equations, curve fitting, numerical quadrature and numerical solution to ordinary differential equations
Convex Optimizationrecognizing & solving convex optimization problems in engineering: Convex sets, functions, optimization problems, Basics of convex analysis, Leastsquares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, Optimality conditions, duality theory, theorems of alternative, applications, Interiorpoint methods, signal processing, control, digital & analog circuit design, computational geometry, statistics, mech engineering
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
Multivariable CalculusJava applets (Graphing along the x or yaxis, Intoduction to Integration, Riemann Sums, Simpson's Rule, Integration, The Chain Rule, Visualizing Vector Fields for First Order Differential Equations, Graphing Parametric Curves, Graphing Polar Curves, Matrix Utility, Polynomial Interpolation, Divided Differences), calculus problems & solutions
The Mathematics of Computationmathematics for modeling and reasoning about problems in computer science, useful applications, proof methods to reason about recursive and iterative programs, data structures (graphs, trees, sets, functions and their asymptotic growth, combinatorics and probability, regular languages and finite automata)
Probabilistic Systems Analysis and Applied Probabilityformulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference: Readings, Recitations, Tools, Related Resources
Mathematical Foundations of Computer Scienceformal mathematical concepts of computer science, elementary logic, set theory, relations, deduction, induction, algorithmic processes, graph theory, models of computation
Game Theorygame theory and strategic thinking, dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, signaling, examples drawn from economics, politics & movies
Geometry and Quantum Field Theorydesigned for mathematicians is rigorous introduction to perturbative quantum field theory using language of functional integrals, basics of classical field theory, free quantum theories & Feynman diagrams, goal to discuss using mathematical language basic notions and results of QFT necessary to for QFT and String Theory

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