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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: foundation in multivariable calculus and ordinary differential equations.
Terms: Aut | Units: 3
Instructors: Ryzhik, L. (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
Instructors: Valiant, G. (PI)

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
Instructors: Shaqfeh, E. (PI)

CME 334: Advanced Methods in Numerical Optimization (MS&E 312)

Topics include interior-point methods, relaxation methods for nonlinear discrete optimization, sequential quadratic programming methods, optimal control and decomposition methods. Topic chosen in first class; different topics for individuals or groups possible. Individual or team projects. May be repeated for credit.
Terms: Aut | Units: 3 | Repeatable for credit

CME 362: An Introduction to Compressed Sensing (STATS 330)

Compressed sensing is a new data acquisition theory asserting that one can design nonadaptive sampling techniques that condense the information in a compressible signal into a small amount of data. This revelation may change the way engineers think about signal acquisition. Course covers fundamental theoretical ideas, numerical methods in large-scale convex optimization, hardware implementations, connections with statistical estimation in high dimensions, and extensions such as recovery of data matrices from few entries (famous Netflix Prize).
Terms: Aut | Units: 3
Instructors: Donoho, D. (PI)

CME 390: Curricular Practical Training

May be repeated three times for credit.
Terms: Aut, Win, Spr, Sum | Units: 1 | Repeatable 3 times (up to 3 units total)
Instructors: Jain, K. (PI) ; Murray, W. (PI)

CME 399: Special Research Topics in Computational and Mathematical Engineering

Graduate-level research work not related to report, thesis, or dissertation. May be repeated for credit.
Terms: Aut, Win, Spr, Sum | Units: 1-15 | Repeatable 6 times (up to 30 units total)

CME 400: Ph.D. Research

Terms: Aut, Win, Spr, Sum | Units: 1-15 | Repeatable for credit
Instructors: Alonso, J. (PI) ; Athey, S. (PI) ; Bambos, N. (PI) ; Beroza, G. (PI) ; Boahen, K. (PI) ; Boneh, D. (PI) ; Bosagh Zadeh, R. (PI) ; Boyd, S. (PI) ; Candes, E. (PI) ; Carlsson, G. (PI) ; Darve, E. (PI) ; Delp, S. (PI) ; Diaconis, P. (PI) ; Donoho, D. (PI) ; Dror, R. (PI) ; Farhat, C. (PI) ; Fedkiw, R. (PI) ; Fringer, O. (PI) ; Genesereth, M. (PI) ; Gerritsen, M. (PI) ; Giesecke, K. (PI) ; Glynn, P. (PI) ; Goel, A. (PI) ; Golub, G. (PI) ; Guibas, L. (PI) ; Hanrahan, P. (PI) ; Hastie, T. (PI) ; Holmes, S. (PI) ; Hong, H. (PI) ; Iaccarino, G. (PI) ; Jameson, A. (PI) ; Johari, R. (PI) ; Kamvar, S. (PI) ; Khatib, O. (PI) ; Khayms, V. (PI) ; Kitanidis, P. (PI) ; Kosovichev, A. (PI) ; Kumar, S. (PI) ; Lai, T. (PI) ; Langley, P. (PI) ; Lee, P. (PI) ; Lele, S. (PI) ; Leskovec, J. (PI) ; Levinson, D. (PI) ; Levitt, M. (PI) ; Lew, A. (PI) ; Linder, C. (PI) ; Liu, T. (PI) ; Moerner, W. (PI) ; Moin, P. (PI) ; Montanari, A. (PI) ; Motwani, R. (PI) ; Murray, W. (PI) ; Ng, A. (PI) ; Pande, V. (PI) ; Papanicolaou, G. (PI) ; Pitsch, H. (PI) ; Plevritis, S. (PI) ; Poulson, J. (PI) ; Rajagopal, R. (PI) ; Rajaratnam, B. (PI) ; Reed, E. (PI) ; Roughgarden, T. (PI) ; Saberi, A. (PI) ; Salisbury, J. (PI) ; Saunders, M. (PI) ; Shaqfeh, E. (PI) ; Taylor, C. (PI) ; Tchelepi, H. (PI) ; Tibshirani, R. (PI) ; Wein, L. (PI) ; Weissman, T. (PI) ; Wong, W. (PI) ; Xing, L. (PI) ; Ye, Y. (PI) ; Ying, L. (PI)

CME 444: Computational Consulting

Advice by graduate students under supervision of ICME faculty. Weekly briefings with faculty adviser and associated faculty to discuss ongoing consultancy projects and evaluate solutions. May be repeated for credit.
Terms: Aut, Win, Spr | Units: 1-3 | Repeatable for credit
Instructors: Gerritsen, M. (PI)

CME 500: Departmental Seminar

Weekly research lectures by experts from academia, national laboratories, industry, and doctoral students. May be repeated for credit. In autumn and winter 2014-15, this seminar will predominantly feature current graduate students talking about their research.
Terms: Aut, Win, Spr | Units: 1 | Repeatable for credit
Instructors: Gerritsen, M. (PI)
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