## CME 257: Advanced Topics in Scientific Computing with Julia

This course will rapidly introduce students to the Julia programming language, with the goal of giving students the knowledge and experience necessary to navigate the language and package ecosystem while using Julia for their own scientific computing needs. The course will begin with learning the basics of Julia, and then introduce students to git version control and package development. Additional topics include: common packages, parallelism, interfacing with shared object libraries, and aspects of Julia's implementation (e.g. core numerical linear algebra). Lectures will be interactive, with an emphasis on collaboration and learning by example. Prerequisites: Data structures at the level of
CS106B, experience with one or more scientific computing languages (e.g. Python, Matlab, or R), and some familiarity with the Unix shell. No prior experience with Julia or git is required.

Terms: Aut
| Units: 1

Instructors:
Jambulapati, A. (PI)

## CME 262: Imaging with Incomplete Information (CEE 362G)

Statistical and computational methods for inferring images from incomplete data. Bayesian inference methods are used to combine data and quantify uncertainty in the estimate. Fast linear algebra tools are used to solve problems with many pixels and many observations. Applications from several fields but mainly in earth sciences. Prerequisites: Linear algebra and probability theory.

Terms: Aut
| Units: 3-4

Instructors:
Kitanidis, P. (PI)

## CME 263: Introduction to Linear Dynamical Systems (EE 263)

Applied linear algebra and linear dynamical systems with applications to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular-value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer-matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: Linear algebra and matrices as in
EE 103 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.

Terms: Aut, Sum
| Units: 3

Instructors:
Aggarwal, G. (PI)
;
Lall, S. (PI)
;
Kim, J. (TA)
;
Luxenberg, E. (TA)
;
Tuck, J. (TA)
;
Zhang, J. (TA)

## CME 279: Computational Biology: Structure and Organization of Biomolecules and Cells (BIOE 279, BIOMEDIN 279, BIOPHYS 279, CS 279)

Computational techniques for investigating and designing the three-dimensional structure and dynamics of biomolecules and cells. These computational methods play an increasingly important role in drug discovery, medicine, bioengineering, and molecular biology. Course topics include protein structure prediction, protein design, drug screening, molecular simulation, cellular-level simulation, image analysis for microscopy, and methods for solving structures from crystallography and electron microscopy data. Prerequisites: elementary programming background (
CS 106A or equivalent) and an introductory course in biology or biochemistry.

Terms: Aut
| Units: 3

## 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 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 302: Numerical Linear Algebra

Solution of linear systems, accuracy, stability, LU, Cholesky, QR, least squares problems, singular value decomposition, eigenvalue computation, iterative methods, Krylov subspace, Lanczos and Arnoldi processes, conjugate gradient, GMRES, direct methods for sparse matrices. Prerequisites:
CME 108,
MATH 114,
MATH 104.

Terms: Aut
| Units: 3

## CME 303: Partial Differential Equations of Applied Mathematics (MATH 220)

First-order 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 proof-based treatment of the material as in
Math 171 or
Math 61CM (formerly
Math 51H).

Terms: Aut
| Units: 3

Instructors:
Luk, J. (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

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