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
ENGR 108 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.
Terms: Aut
| Units: 3
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
Instructors:
Dror, R. (PI)
;
Bresette, L. (TA)
;
Li, D. (TA)
;
McAvity, J. (TA)
;
Sayana, R. (TA)
;
Suriana, P. (TA)
;
Xu, J. (TA)
CME 291: Master's Research
Students require faculty sponsor. (Staff)
Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable
for credit
Instructors:
Adeli, E. (PI)
;
Ashlagi, I. (PI)
;
Begenau, J. (PI)
...
more instructors for CME 291 »
Instructors:
Adeli, E. (PI)
;
Ashlagi, I. (PI)
;
Begenau, J. (PI)
;
Biondi, B. (PI)
;
Bohg, J. (PI)
;
Bustamante, C. (PI)
;
Darve, E. (PI)
;
Dunham, E. (PI)
;
Ermon, S. (PI)
;
Fatahalian, K. (PI)
;
Fedkiw, R. (PI)
;
Gerritsen, M. (PI)
;
Gevaert, O. (PI)
;
Giesecke, K. (PI)
;
Glynn, P. (PI)
;
Goel, A. (PI)
;
Gous, A. (PI)
;
Grundfest, J. (PI)
;
Hanson, K. (PI)
;
Hernandez-Boussard, T. (PI)
;
Iaccarino, G. (PI)
;
Leskovec, J. (PI)
;
Li, F. (PI)
;
Marsden, A. (PI)
;
Mignot, E. (PI)
;
Narayan, S. (PI)
;
Onori, S. (PI)
;
Osgood, B. (PI)
;
Palacios, J. (PI)
;
Papanicolaou, G. (PI)
;
Pavone, M. (PI)
;
Pelger, M. (PI)
;
Rao, A. (PI)
;
Re, C. (PI)
;
Rivas, M. (PI)
;
Ross, E. (PI)
;
Rusu, M. (PI)
;
Salzman, J. (PI)
;
Shetty, A. (PI)
;
Suckale, J. (PI)
;
Tchelepi, H. (PI)
;
Tran, K. (PI)
;
Udell, M. (PI)
;
Ugander, J. (PI)
;
Wootters, M. (PI)
;
Xing, L. (PI)
;
Ying, L. (PI)
;
Wang, J. (TA)
CME 300: First Year Seminar Series
Required for first-year ICME Ph.D. students; recommended for first-year ICME M.S. students interested in research. Presentations about research by Stanford faculty and researchers. May be repeated for credit.
Terms: Aut
| Units: 1
| Repeatable
3 times
(up to 3 units total)
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 and one of
Math 104 or
Math 113.
Terms: Aut
| Units: 3
CME 303: Partial Differential Equations of Applied Mathematics (MATH 220A)
Introduction to partial differential equations: basic properties of elliptic, parabolic, and hyperbolic equations; Hamilton-Jacobi equations and applications to optimal control; stochastic modeling, forward and backward Kolmogorov equations; Fourier transform and Fourier series. Prerequisite: multivariable calculus, rigorous courses on basic real analysis and ordinary differential equations. Note: 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: Aut
| Units: 3
Instructors:
Ryzhik, L. (PI)
;
Alieva, A. (TA)
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
Instructors:
Valiant, G. (PI)
;
Gurunathan, V. (TA)
;
Hanley, H. (TA)
...
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Instructors:
Valiant, G. (PI)
;
Gurunathan, V. (TA)
;
Hanley, H. (TA)
;
Pabbaraju, C. (TA)
;
Villa-Renteria, I. (TA)
CME 330: Applied Mathematics in the Chemical and Biological Sciences (CHEMENG 300)
Mathematical solution methods via applied problems including chemical reaction sequences, mass and heat transfer in chemical reactors, quantum mechanics, fluid mechanics of reacting systems, and chromatography. Topics include generalized vector space theory, linear operator theory with eigenvalue methods, phase plane methods, perturbation theory (regular and singular), solution of parabolic and elliptic partial differential equations, and transform methods (Laplace and Fourier). Prerequisites:
CME 102/
ENGR 155A and
CME 104/
ENGR 155B, or equivalents.
Terms: Aut
| Units: 3
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
3 times
(up to 3 units total)
CME 391: Ph.D. Research Rotation
First and second year ICME PhD students enroll under faculty sponsor for research rotation units.
Terms: Aut, Win, Spr, Sum
| Units: 1-6
| Repeatable
3 times
(up to 9 units total)
Instructors:
Athey, S. (PI)
;
Blanchet, J. (PI)
;
Charikar, M. (PI)
...
more instructors for CME 391 »
Instructors:
Athey, S. (PI)
;
Blanchet, J. (PI)
;
Charikar, M. (PI)
;
Darve, E. (PI)
;
Giesecke, K. (PI)
;
Iaccarino, G. (PI)
;
James, D. (PI)
;
Johari, R. (PI)
;
Lei, L. (PI)
;
Marsden, A. (PI)
;
McFarland, D. (PI)
;
Palacios, J. (PI)
;
Papanicolaou, G. (PI)
;
Pelger, M. (PI)
;
Rosenberg, N. (PI)
;
Salzman, J. (PI)
;
Syrgkanis, V. (PI)
;
Udell, M. (PI)
;
Ugander, J. (PI)
;
Wager, S. (PI)
;
Ying, L. (PI)
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