CME 303: Partial Differential Equations of Applied Mathematics (MATH 220)
Firstorder partial differential equations; method of characteristics; weak solutions; elliptic, parabolic, and hyperbolic equations; Fourier transform; Fourier series; and eigenvalue problems. Prerequisite: Basic coursework in multivariable calculus and ordinary differential equations, and some prior experience with a proofbased treatment of the material as in
Math 171 or
Math 61CM (formerly
Math 51H).
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Vasy, A. (PI)
;
Sarkar, R. (TA)
CME 305: Discrete Mathematics and Algorithms (MS&E 316)
Topics: Basic Algebraic Graph Theory, Matroids and Minimum Spanning Trees, Submodularity and Maximum Flow, NPHardness, Approximation Algorithms, Randomized Algorithms, The Probabilistic Method, and Spectral Sparsification using Effective Resistances. Topics will be illustrated with applications from Distributed Computing, Machine Learning, and largescale Optimization. Prerequisites:
CS 261 is highly recommended, although not required.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Sidford, A. (PI)
CME 306: Numerical Solution of Partial Differential Equations (MATH 226)
Hyperbolic partial differential equations: stability, convergence and qualitative properties; nonlinear hyperbolic equations and systems; combined solution methods from elliptic, parabolic, and hyperbolic problems. Examples include: Burger's equation, Euler equations for compressible flow, NavierStokes equations for incompressible flow. Prerequisites:
MATH 220A or
CME 302.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ying, L. (PI)
CME 307: Optimization (MS&E 311)
Applications, theories, and algorithms for finitedimensional linear and nonlinear optimization problems with continuous variables. Elements of convex analysis, first and secondorder optimality conditions, sensitivity and duality. Algorithms for unconstrained optimization, and linearly and nonlinearly constrained problems. Modern applications in communication, game theory, auction, and economics. Prerequisites:
MATH 113, 115, or equivalent.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Ye, Y. (PI)
CME 308: Stochastic Methods in Engineering (MATH 228, MS&E 324)
The basic limit theorems of probability theory and their application to maximum likelihood estimation. Basic Monte Carlo methods and importance sampling. Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation. Discrete time stochastic control and Bayesian filtering. Diffusion approximations, Brownian motion and an introduction to stochastic differential equations. Examples and problems from various applied areas. Prerequisites: exposure to probability and background in analysis.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Glynn, P. (PI)
CME 309: Randomized Algorithms and Probabilistic Analysis (CS 265)
Randomness pervades the natural processes around us, from the formation of networks, to genetic recombination, to quantum physics. Randomness is also a powerful tool that can be leveraged to create algorithms and data structures which, in many cases, are more efficient and simpler than their deterministic counterparts. This course covers the key tools of probabilistic analysis, and application of these tools to understand the behaviors of random processes and algorithms. Emphasis is on theoretical foundations, though we will apply this theory broadly, discussing applications in machine learning and data analysis, networking, and systems. Topics include tail bounds, the probabilistic method, Markov chains, and martingales, with applications to analyzing random graphs, metric embeddings, random walks, and a host of powerful and elegant randomized algorithms. Prerequisites:
CS 161 and STAT 116, or equivalents and instructor consent.
Terms: Aut

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Valiant, G. (PI)
CME 321A: Mathematical Methods of Imaging (MATH 221A)
Image denoising and deblurring with optimization and partial differential equations methods. Imaging functionals based on total variation and l1 minimization. Fast algorithms and their implementation.
Terms: alternate years, given next year, last offered Winter 2014

Units: 3

Grading: Letter or Credit/No Credit
CME 321B: Mathematical Methods of Imaging (MATH 221B)
Array imaging using Kirchhoff migration and beamforming, resolution theory for broad and narrow band array imaging in homogeneous media, topics in highfrequency, variable background imaging with velocity estimation, interferometric imaging methods, the role of noise and inhomogeneities, and variational problems that arise in optimizing the performance of array imaging algorithms.
Terms: not given this year, last offered Spring 2016

Units: 3

Grading: Letter or Credit/No Credit
CME 322: Spectral Methods in Computational Physics (ME 408)
Data analysis, spectra and correlations, sampling theorem, nonperiodic data, and windowing; spectral methods for numerical solution of partial differential equations; accuracy and computational cost; fast Fourier transform, Galerkin, collocation, and Tau methods; spectral and pseudospectral methods based on Fourier series and eigenfunctions of singular SturmLiouville problems; Chebyshev, Legendre, and Laguerre representations; convergence of eigenfunction expansions; discontinuities and Gibbs phenomenon; aliasing errors and control; efficient implementation of spectral methods; spectral methods for complicated domains; time differencing and numerical stability.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Moin, P. (PI)
CME 323: Distributed Algorithms and Optimization
The emergence of clusters of commodity machines with parallel processing units has brought with it a slew of new algorithms and tools. Many fields such as Machine Learning and Optimization have adapted their algorithms to handle such clusters. Topics include distributed and parallel algorithms for: Optimization, Numerical Linear Algebra, Machine Learning, Graph analysis, Streaming algorithms, and other problems that are challenging to scale on a commodity cluster. The class will focus on analyzing parallel and distributed programs, with some implementation using Apache Spark and TensorFlow.
Terms: alternate years, given next year, last offered Spring 2018

Units: 3

Grading: Letter or Credit/No Credit
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