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).

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

Convex Optimization

recognizing & solving convex optimization problems in engineering: Convex sets, functions, optimization problems, Basics of convex analysis, Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, Optimality conditions, duality theory, theorems of alternative, applications, Interior-point methods, signal processing, control, digital & analog circuit design, computational geometry, statistics, mech engineering
 

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

Multivariable Calculus

Java applets (Graphing along the x or y-axis, 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 Computation

mathematics 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 Probability

formulation 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 Science

formal mathematical concepts of computer science, elementary logic, set theory, relations, deduction, induction, algorithmic processes, graph theory, models of computation

Game Theory

game theory and strategic thinking, dominance, backward induction, Nash equilibrium, evolutionary stability, commitment, credibility, asymmetric information, adverse selection, signaling, examples drawn from economics, politics & movies
 

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