Teaching Assistant
Stanford
Instructor: Lexing Ying
Course Description: Numerical computation for engineering and machine learning applications: error analysis, floating-point arithmetic, numerical solution of linear and nonlinear equations, optimization, gradient descent, polynomial interpolation, numerical differentiation and integration, supervised learning, numerical solution of ordinary differential equations, numerical stability, unsupervised learning, sampling (Monte Carlo algorithms). Implementation of numerical methods in programming assignments (Python or Matlab).
Caltech
Instructor: Yisong Yue
Course Description: This course will cover popular methods in machine learning and data mining, with an emphasis on developing a working understanding of how to apply these methods in practice. This course will also cover core foundational concepts underpinning and motivating modern machine learning and data mining approaches. This course will also cover some recent research developments.
Instructor: Thomas Vidick
Course Description: This course develops core principles for the analysis and design of algorithms. Basic material includes mathematical techniques for analyzing performance in terms of resources, such as time, space, and randomness. The course introduces the major paradigms for algorithm design, including randomized algorithms, linear and semidefinite programming, approximation algorithms, spectral methods, and online learning.
Instructor: Joel A. Tropp
Course Description: This course offers a rigorous introduction to probability and stochastic processes. Emphasis is placed on the interaction between inequalities and limit theorems, as well as contemporary applications in computing and mathematical sciences. Topics include probability measures, random variables and expectation, independence, concentration inequalities, distances between probability measures, modes of convergence, laws of large numbers and central limit theorem, Gaussian and Poisson approximation, conditional expectation and conditional distributions, filtrations, and discrete-time martingales.
Instructor: Elizabeth Y. Qian
Course Description: Matlab: basic syntax and development environment; debugging; help interface; basic linear algebra; visualization and graphical output; control flow; vectorization; scripts, and functions; file i/o; arrays, structures, and strings; numerical analysis (topics may include curve fitting, interpolation, differentiation, integration, optimization, solving nonlinear equations, fast Fourier transform, and ODE solvers); and advanced topics (may include writing fast code, parallelization, object-oriented features). Mathematica: basic syntax and the notebook interface, calculus and linear algebra operations, numerical and symbolic solution of algebraic and differential equations, manipulation of lists and expressions, Mathematica programming (rule-based, functional, and procedural) and debugging, plotting, and visualization. The course will also emphasize good programming habits and choosing the appropriate language/software for a given scientific task.
Instructor: Konstantin M. Zuev
Course Description: This is an intermediate linear algebra course aimed at a diverse group of students, including junior and senior majors in applied mathematics, sciences and engineering. The focus is on applications. Matrix factorizations play a central role. Topics covered include linear systems, vector spaces and bases, inner products, norms, minimization, the Cholesky factorization, least squares approximation, data fitting, interpolation, orthogonality, the QR factorization, ill-conditioned systems, discrete Fourier series and the fast Fourier transform, eigenvalues and eigenvectors, the spectral theorem, optimization principles for eigenvalues, singular value decomposition, condition number, principal component analysis, the Schur decomposition, methods for computing eigenvalues, non-negative matrices, graphs, networks, random walks, the Perron-Frobenius theorem, PageRank algorithm.
Instructor: Shumao Zhang
Course Description: Matlab: basic syntax and development environment; debugging; help interface; basic linear algebra; visualization and graphical output; control flow; vectorization; scripts, and functions; file i/o; arrays, structures, and strings; numerical analysis (topics may include curve fitting, interpolation, differentiation, integration, optimization, solving nonlinear equations, fast Fourier transform, and ODE solvers); and advanced topics (may include writing fast code, parallelization, object-oriented features). Mathematica: basic syntax and the notebook interface, calculus and linear algebra operations, numerical and symbolic solution of algebraic and differential equations, manipulation of lists and expressions, Mathematica programming (rule-based, functional, and procedural) and debugging, plotting, and visualization. The course will also emphasize good programming habits and choosing the appropriate language/software for a given scientific task.
Instructor: Lu Wang
Course Description: The course is aimed at providing an introduction to the theory of ordinary differential equations, with a particular emphasis on equations with well known applications ranging from physics to population dynamics. The material covered includes some existence and uniqueness results, first order linear equations and systems, exact equations, linear equations with constant coefficients, series solutions, regular singular equations, Laplace transform, and methods for the study of nonlinear equations (equilibria, stability, predator-prey equations, periodic solutions and limiting cycles).