## CME 251: Geometric and Topological Data Analysis (CS 233)

Mathematical computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces. Global and local geometry descriptors allowing for various kinds of invariances. The rudiments of computational topology and persistent homology on sampled spaces. Clustering and other unsupervised techniques. Spectral methods for geometric data analysis. Non-linear dimensionality reduction. Alignment, matching, and map computation between geometric data sets. Function spaces and functional maps.Networks of data sets and joint analysis for segmentation and labeling. The emergence of abstractions or concepts from data. Prerequisites: discrete algorithms at the level of 161; linear algebra at the level of
CME103.

Terms: Spr
| Units: 3

Instructors:
Guibas, L. (PI)

## CME 291: Master's Research

Students require faculty sponsor. (Staff)

Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable for credit

Instructors:
Begenau, J. (PI)
;
Biondi, B. (PI)
;
Darve, E. (PI)
;
Gerritsen, M. (PI)
;
Gevaert, O. (PI)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Goel, A. (PI)
;
Gous, A. (PI)
;
Grundfest, J. (PI)
;
Iaccarino, G. (PI)
;
Lai, T. (PI)
;
Leskovec, J. (PI)
;
Marsden, A. (PI)
;
Osgood, B. (PI)
;
Papanicolaou, G. (PI)
;
Pelger, M. (PI)
;
Rao, A. (PI)
;
Re, C. (PI)
;
Suckale, J. (PI)
;
Tchelepi, H. (PI)
;
Wootters, M. (PI)
;
Ying, L. (PI)

## CME 292: Advanced MATLAB for Scientific Computing

Short course running first four weeks of the quarter (8 lectures) with interactive online lectures and application based assignment. Students will access the lectures and assignments on
https://suclass.stanford.edu. Students will be introduced to advanced MATLAB features, syntaxes, and toolboxes not traditionally found in introductory courses. Material will be reinforced with in-class examples, demos, and homework assignment involving topics from scientific computing. MATLAB topics will be drawn from: advanced graphics (2D/3D plotting, graphics handles, publication quality graphics, animation), MATLAB tools (debugger, profiler), code optimization (vectorization, memory management), object-oriented programming, compiled MATLAB (MEX files and MATLAB coder), interfacing with external programs, toolboxes (optimization, parallel computing, symbolic math, PDEs). Scientific computing topics will include: numerical linear algebra, numerical optimization, ODEs, and PDEs.

Terms: Aut, Spr
| Units: 1

Instructors:
Leibovich, M. (PI)

## CME 298: Basic Probability and Stochastic Processes with Engineering Applications (MATH 158)

Calculus of random variables and their distributions with applications. Review of limit theorems of probability and their application to statistical estimation and basic Monte Carlo methods. Introduction to Markov chains, random walks, Brownian motion and basic stochastic differential equations with emphasis on applications from economics, physics and engineering, such as filtering and control. Prerequisites: exposure to basic probability.

Terms: Spr
| Units: 3

Instructors:
Papanicolaou, G. (PI)

## CME 300: First Year Seminar Series

Required for first-year ICME Ph.D. students; recommended for first-year ICME M.S. students. Presentations about research at Stanford by faculty and researchers from Engineering, H&S, and organizations external to Stanford. May be repeated for credit.

Terms: Aut, Win, Spr
| Units: 1
| Repeatable for credit

Instructors:
Iaccarino, G. (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, Navier-Stokes equations for incompressible flow. Prerequisites:
MATH 220 or
CME 302.nnNOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.

Terms: Spr
| Units: 3

Instructors:
Ying, L. (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

Instructors:
Glynn, 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: Spr
| Units: 3

Instructors:
Bosagh Zadeh, R. (PI)

## CME 364B: Convex Optimization II (EE 364B)

Continuation of 364A. Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Monotone operators and proximal methods; alternating direction method of multipliers. Exploiting problem structure in implementation. Convex relaxations of hard problems. Global optimization via branch and bound. Robust and stochastic optimization. Applications in areas such as control, circuit design, signal processing, and communications. Course requirements include project. Prerequisite: 364A.

Terms: Spr
| Units: 3

Instructors:
Pilanci, M. (PI)

## CME 390: Curricular Practical Training

Educational opportunities in high technology research and development labs in applied mathematics. Qualified ICME students engage in internship work and integrate that work into their academic program. Students register during the quarter they are employed and complete a research report outlining their work activity, problems investigated, results, and follow-on projects they expect to perform. May be repeated three times for credit.

Terms: Aut, Win, Spr, Sum
| Units: 1
| Repeatable for credit

Instructors:
Giesecke, K. (PI)
;
Iaccarino, G. (PI)

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