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CME 364A: Convex Optimization I (CS 334A, EE 364A)

Convex sets, functions, and optimization problems. The basics of convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications. Least-squares, linear and quadratic programs, semidefinite programming, and geometric programming. Numerical algorithms for smooth and equality constrained problems; interior-point methods for inequality constrained problems. Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering. Prerequisite: linear algebra such as EE263, basic probability.
Terms: Spr, Sum | Units: 3

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.
Last offered: Spring 2015

CME 371: Computational Biology in Four Dimensions (BIOMEDIN 371, BIOPHYS 371, CS 371)

Cutting-edge research on computational techniques for investigating and designing the three-dimensional structure and dynamics of biomolecules, cells, and everything in between. These techniques, which draw on approaches ranging from physics-based simulation to machine learning, play an increasingly important role in drug discovery, medicine, bioengineering, and molecular biology. Course is devoted primarily to reading, presentation, discussion, and critique of papers describing important recent research developments. Prerequisite: CS 106A or equivalent, and an introductory course in biology or biochemistry. Recommended: some experience in mathematical modeling (does not need to be a formal course).
Terms: Win | Units: 3
Instructors: Dror, R. (PI)

CME 372: Applied Fourier Analysis and Elements of Modern Signal Processing (MATH 262)

Introduction to the mathematics of the Fourier transform and how it arises in a number of imaging problems. Mathematical topics include the Fourier transform, the Plancherel theorem, Fourier series, the Shannon sampling theorem, the discrete Fourier transform, and the spectral representation of stationary stochastic processes. Computational topics include fast Fourier transforms (FFT) and nonuniform FFTs. Applications include Fourier imaging (the theory of diffraction, computed tomography, and magnetic resonance imaging) and the theory of compressive sensing.
Last offered: Winter 2016

CME 375: Advanced Topics in Convex Optimization (MATH 301)

Modern developments in convex optimization: semidefinite programming; novel and efficient first-order algorithms for smooth and nonsmooth convex optimization. Emphasis on numerical methods suitable for large scale problems arising in science and engineering. Prerequisites: convex optimization ( EE 364), linear algebra ( Math 104), numerical linear algebra ( CME 302); background in probability, statistics, real analysis and numerical optimization.
Last offered: Winter 2015 | Repeatable 3 times (up to 9 units total)

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)
Instructors: Iaccarino, G. (PI) ; 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) ; Biondi, B. (PI) ; Boahen, K. (PI) ; Boneh, D. (PI) ; Bosagh Zadeh, R. (PI) ; Boyd, S. (PI) ; Bustamante, C. (PI) ; Candes, E. (PI) ; Carlsson, G. (PI) ; Charikar, M. (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) ; Gorle, C. (PI) ; Guibas, L. (PI) ; Hanrahan, P. (PI) ; Hastie, T. (PI) ; Holmes, S. (PI) ; Hong, H. (PI) ; Iaccarino, G. (PI) ; James, D. (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) ; Marsden, A. (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) ; Re, C. (PI) ; Reed, E. (PI) ; Roughgarden, T. (PI) ; Ryzhik, L. (PI) ; Saberi, A. (PI) ; Salisbury, J. (PI) ; Saunders, M. (PI) ; Shaqfeh, E. (PI) ; Sidford, A. (PI) ; Suckale, J. (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

CME 500: Departmental Seminar

Weekly research lectures by doctoral students, experts from academia, national laboratories, and industry. May be repeated for credit. In autumn 2016 this seminar will primarily feature current graduate students talking about their research. In winter and spring 2016-17, this seminar will feature a mix of graduate students and other researchers.
Terms: Aut, Win, Spr | Units: 1 | Repeatable for credit
Instructors: Gerritsen, M. (PI)
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