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ACM/CMS 104
Linear Algebra and Applied Operator Theory
12 units (309

first term
Prerequisites: Undergraduate prerequistes: Ma 1 abc (analytic track), Ma 2, and ACM 95 abc; or instructor's permission.
This course introduces the theory and applications of linear algebra and linear analysis. Lectures and homework will require the ability to understand and produce mathematical proofs. Theoretical topics may include topology of metric spaces, structure of Banach and Hilbert spaces, examples of normed spaces, duality, structure of linear operators, spectral theory, functional calculus for linear operators, and calculus in Banach spaces. Applications will be drawn from signal processing, numerical analysis, optimization, approximation, differential equations, control, and other areas. Emphasis will be placed on geometry and convexity.
Instructor:
Tropp
ACM/CMS 113
Mathematical Optimization.9
units (306)

first term
Prerequisites: ACM 95/100 abc, ACM 11, or instructor's permission. Corequisite: It is suggested that students take ACM/CMS 104 concurrently.
This class studies mathematical optimization from the viewpoint of convexity. Topics covered include duality and representation of convex sets; linear and semidefinite programming; connections to discrete, network, and robust optimization; relaxation methods for intractable problems; as well as applications to problems arising in graphs and networks, information theory, control, signal processing, and other engineering disciplines.
Instructor:
Chandrasekaran
ACM/EE/CMS 116
Introduction to Stochastic Processes and Modeling.9
units (306)

first term
Prerequisites: Ma 2, Ma 3 or instructor's permission.
Introduction to fundamental ideas and techniques of stochastic analysis and modeling. Random variables, expectation and conditional expectation, joint distributions, covariance, moment generating function, central limit theorem, weak and strong laws of large numbers, discrete time stochastic processes, stationarity, power spectral densities and the WienerKhinchine theorem, Gaussian processes, Poisson processes, Brownian motion. The course develops applications in selected areas such as signal processing (Wiener filter), information theory, genetics, queuing and waiting line theory, and finance.
Instructor:
Owhadi
CS/CMS 139
Analysis and Design of Algorithms
12 units (309)

third term
Prerequisites: Ma 2, Ma 3, Ma/CS 6a, CS 21, CS 38/138, ACM/EE/CMS 116, or instructor's permission.
This course covers advanced topics in the design and analysis of algorithms. Topics are drawn from approximation algorithms, randomized algorithms, online algorithms, streaming algorithms, and other areas of current research interest in algorithms.
Instructor:
Ligett
CS/EE/CMS 144
Networks: Structure Economics
12 units (336)

second term
Prerequisites: Ma 2, Ma 3, Ma/CS 6a, and CS 38, or instructor permission.
Social networks, the web, and the internet are essential parts of our lives and we all depend on them every day, but do you really know what makes them work?This course studies the "big" ideas behind our networked lives. Things like, what do networks actually look like (and why do they all look the same)? How do search engines work? Why do memes spread the way they do? How does web advertising work? For all these questions and more, the course will provide a mixture of both mathematical analysis and handson labs. The course assumes students are comfortable with graph theory, probability, and basic programming.
Instructor:
Wierman
ACM/EE/CMS 170
Mathematics of Signal Processing
12 units (309)

third term
Prerequisites: ACM/CMS 104, ACM/CMS 113, and ACM/EE/CMS 116; or instructor's permission.
This course covers classical and modern approaches to problems in signal processing. Problems may include denoising, deconvolution, spectral estimation, directionofarrival estimation, array processing, independent component analysis, system identification, filter design, and transform coding. Methods rely heavily on linear algebra, convex optimization, and stochastic modeling. In particular, the class will cover techniques based on leastsquares and on sparse modeling. Throughout the course, a computational viewpoint will be emphasized.
Instructor:
Hassibi
ACM/CS/EE/CMS 218
Statistical Inference
9 units (306)

third term
Prerequisites: ACM/CMS 104 and ACM/EE/CMS 116, or instructor's permission.
Fundamentals of estimation theory and hypothesis testing; Bayesian and nonBayesian approaches; minimax analysis, CramerRao bounds, shrinkage in high dimensions; Kalman filtering, basics of graphical models; statistical model selection. Throughout the course, a computational viewpoint will be emphasized.
Instructor:
Chandrasekaran
CMS 290 abc
Computing and Mathematical Sciences Colloquium
1 unit

first, second, third terms
Registration open to graduate students only. This course is a research seminar covering topics at the intersection of mathematics, computation, and their applications. Speakers are internationally recognized researchers from mathematics, applied mathematics, statistics, computer science, electrical engineering, control theory, and related disciplines. Attendance is required. Staff.
Published Date:
July 28, 2022