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This course will teach fundamentals of control design and analysis using state-space methods. This includes both the practical and theoretical aspects of the topic. By the end of the course, you should be able to design controllers using state-space methods and evaluate whether these controllers are robust to some types of modeling errors a

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This course gives a mathematical introduction to neural coding and dynamics. Topics include convolution, correlation, linear systems, game theory, signal detection theory, probability theory, information theory, and reinforcement learning. Applications to neural coding, focusing on the visual system are covered, as well as Hodgkin-Huxley an

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This course focuses on the use of modern computational and mathematical techniques in chemical engineering. Starting from a discussion of linear systems as the basic computational unit in scientific computing, methods for solving sets of nonlinear algebraic equations, ordinary differential equations, and differential-algebraic (DAE) systems

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Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical method

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This course is taken mainly by undergraduates, and explores ideas involving signals, systems and probabilistic models in the context of communication, control and signal processing applications. The material expands out from the basics in 6.003 and 6.041. The treatment involves aspects of analysis, synthesis, and optimization. Topics covere

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This course covers the same material as 18.03 with more emphasis on theory. Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems.

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This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra softwa

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The main aims of this seminar will be to go over the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.