## CME 103: Introduction to Matrix Methods (EE 103)

Introduction to applied linear algebra with emphasis on applications. Vectors, norm, and angle; linear independence and orthonormal sets; applications to document analysis. Clustering and the k-means algorithm. Matrices, left and right inverses, QR factorization. Least-squares and model fitting, regularization and cross-validation. Constrained and nonlinear least-squares. Applications include time-series prediction, tomography, optimal control, and portfolio optimization. Undergraduate students should enroll for 5 units, and graduate students should enroll for 3 units. Prerequisites:
MATH 51 or
CME 100, and basic knowledge of computing (
CS 106A is more than enough, and can be taken concurrently).
EE103/CME103 and
Math 104 cover complementary topics in applied linear algebra. The focus of EE103 is on a few linear algebra concepts, and many applications; the focus of
Math 104 is on algorithms and concepts.

Terms: Aut, Win, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Nasiri Mahalati, R. (PI)
;
Osgood, B. (PI)
;
Tse, D. (PI)
...
more instructors for CME 103 »

Instructors:
Nasiri Mahalati, R. (PI)
;
Osgood, B. (PI)
;
Tse, D. (PI)
;
Chang, S. (TA)
;
Degleris, A. (TA)
;
Gable, N. (TA)
;
Jani, T. (TA)
;
Lambert, S. (TA)
;
Ramesh, R. (TA)
;
Spear, L. (TA)
;
Toh, E. (TA)
;
Varanasi, V. (TA)
;
Yen, J. (TA)

## CME 106: Introduction to Probability and Statistics for Engineers (ENGR 155C)

Probability: random variables, independence, and conditional probability; discrete and continuous distributions, moments, distributions of several random variables. Topics in mathematical statistics: random sampling, point estimation, confidence intervals, hypothesis testing, non-parametric tests, regression and correlation analyses; applications in engineering, industrial manufacturing, medicine, biology, and other fields. Prerequisite:
CME 100/ENGR154 or
MATH 51 or 52.

Terms: Win, Sum
| Units: 4
| UG Reqs: GER:DB-Math, WAY-AQR, WAY-FR

Instructors:
Khayms, V. (PI)
;
Caron, P. (TA)
;
Lerner, S. (TA)
;
Radif, D. (TA)
;
Rowley, J. (TA)
;
Saad, N. (TA)
;
Veron Vialard, J. (TA)

## CME 108: Introduction to Scientific Computing (MATH 114)

Introduction to Scientific Computing Numerical computation for mathematical, computational, physical sciences and engineering: error analysis, floating-point arithmetic, nonlinear equations, numerical solution of systems of algebraic equations, banded matrices, least squares, unconstrained optimization, polynomial interpolation, numerical differentiation and integration, numerical solution of ordinary differential equations, truncation error, numerical stability for time dependent problems and stiffness. Implementation of numerical methods in MATLAB programming assignments. Prerequisites:
MATH 51, 52, 53; prior programming experience (MATLAB or other language at level of
CS 106A or higher).

Terms: Win, Sum
| Units: 3
| UG Reqs: GER:DB-EngrAppSci, WAY-AQR, WAY-FR

## 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 291: Master's Research

Students require faculty sponsor. (Staff)

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

Instructors:
Aiken, A. (PI)
;
Begenau, J. (PI)
;
Biondi, B. (PI)
;
Brunskill, E. (PI)
;
Bustamante, C. (PI)
;
Darve, E. (PI)
;
Dunham, 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)
;
Pavone, M. (PI)
;
Pelger, M. (PI)
;
Rao, A. (PI)
;
Re, C. (PI)
;
Santucci, A. (PI)
;
Suckale, J. (PI)
;
Tchelepi, H. (PI)
;
Wheeler, M. (PI)
;
Wootters, M. (PI)
;
Ying, L. (PI)

## 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: Win, Sum
| Units: 3

Instructors:
Duchi, J. (PI)
;
Fu, A. (PI)
;
Cauchois, M. (TA)
;
Fu, A. (TA)
;
Kim, J. (TA)
;
Luxenberg, E. (TA)
;
Marsden, A. (TA)

## 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)

## CME 390A: Curricular Practical Training

Educational opportunities in high technology research and development labs in applied mathematics. Qualified ICME Ph.D. 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.

Terms: Sum
| Units: 1

## 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 for credit

## CME 400: Ph.D. Research

Terms: Aut, Win, Spr, Sum
| Units: 1-15
| Repeatable for credit

Instructors:
Aiken, A. (PI)
;
Athey, S. (PI)
;
Basu, S. (PI)
;
Bimpikis, K. (PI)
;
Biondi, B. (PI)
;
Blanchet Mancilla, J. (PI)
;
Bosagh Zadeh, R. (PI)
;
Boyd, S. (PI)
;
Bump, D. (PI)
;
Bustamante, C. (PI)
;
Candes, E. (PI)
;
Carlsson, G. (PI)
;
Chen, J. (PI)
;
Darve, E. (PI)
;
Dror, R. (PI)
;
Farhat, C. (PI)
;
Gerritsen, M. (PI)
;
Giesecke, K. (PI)
;
Goel, S. (PI)
;
Guibas, L. (PI)
;
Hastie, T. (PI)
;
Holmes, S. (PI)
;
Iaccarino, G. (PI)
;
Iancu, D. (PI)
;
James, D. (PI)
;
Johari, R. (PI)
;
Kahn, S. (PI)
;
Khatri, P. (PI)
;
Lai, T. (PI)
;
Lobell, D. (PI)
;
Marsden, A. (PI)
;
Montanari, A. (PI)
;
Owen, A. (PI)
;
Papanicolaou, G. (PI)
;
Pavone, M. (PI)
;
Re, C. (PI)
;
Ryzhik, L. (PI)
;
Saban, D. (PI)
;
Saberi, A. (PI)
;
Sidford, A. (PI)
;
Suckale, J. (PI)
;
Ugander, J. (PI)
;
Wein, L. (PI)
;
Weintraub, G. (PI)
;
Wong, W. (PI)
;
Xing, L. (PI)
;
Ye, Y. (PI)
;
Ying, L. (PI)