Linear Analysis with Applications
12 units (3-3-6) | first term
Prerequisites: ACM/IDS 104 or equivalent, Ma 1 b or equivalent.
Covers the basic algebraic, geometric, and topological properties of normed linear spaces, inner-product spaces, and linear maps. Emphasis is placed both on rigorous mathematical development and on applications to control theory, data analysis and partial differential equations.
12 units (3-0-9) | first term
Prerequisites: ACM 11 and ACM 104, or instructor's permission.
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.
Probability Theory and Stochastic Processes
12 units (3-0-9) | first term
Prerequisites: ACM/IDS 104, ACM/EE/IDS 116 or instructor's permission.
This course offers a rigorous introduction to probability and stochastic processes. Emphasis is placed on the interaction between inequalities and limit theorems, as well as contemporary applications in computing and mathematical sciences. Topics include probability measures, random variables and expectation, independence, concentration inequalities, distances between probability measures, modes of convergence, laws of large numbers and central limit theorem, Gaussian and Poisson approximation, conditional expectation and conditional distributions, filtrations, and discrete-time martingales.
Analysis and Design of Algorithms
12 units (3-0-9) | second term
Prerequisites: Ma 2, Ma 3, Ma/CS 6a, CS 21, CS 38/138, and ACM/EE/IDS 116 or CMS/ACM/IDS 113 or equivalent.
This course develops core principles for the analysis and design of algorithms. Basic material includes mathematical techniques for analyzing performance in terms of resources, such as time, space, and randomness. The course introduces the major paradigms for algorithm design, including greedy methods, divide-and-conquer, dynamic programming, linear and semidefinite programming, randomized algorithms, and online learning.
Networks: Structure & Economics
12 units (3-4-5) | second term
Prerequisites: Ma 2, Ma 3, Ma/CS 6 a, and CS 38, or instructor permission.
Social networks, the web, and the internet are essential parts of our lives, and we depend on them every day. This course studies how they work and the "big" ideas behind our networked lives. Questions explored include: 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 hands-on labs. The course expects students to be comfortable with graph theory, probability, and basic programming.
Machine Learning & Data Mining
12 units (3-3-6) | second term
Prerequisites: CS/CNS/EE 156 a.
Having a sufficient background in algorithms, linear algebra, calculus, probability, and statistics, is highly recommended. This course will cover popular methods in machine learning and data mining, with an emphasis on developing a working understanding of how to apply these methods in practice. The course will focus on basic foundational concepts underpinning and motivating modern machine learning and data mining approaches. We will also discuss recent research developments
Advanced Topics in Computing and Mathematical Sciences
Units by arrangement | second term
Advanced topics that will vary according to student and instructor interest. May be repeated for credit.
CMS 290 abc
Computing and Mathematical Sciences Colloquium
1 unit | first, second, third terms
Prerequisites: Registration is limited to graduate students in the CMS department only.
This course is a research seminar course covering topics at the intersection of mathematics, computation, and their applications. Students are asked to attend one seminar per week (from any seminar series on campus) on topics related to computing and mathematical sciences. This course is a requirement for first-year PhD students in the CMS department.
Research in Computing and Mathematical Sciences
Hours and units by arrangement
Research in the field of computing and mathematical science. By arrangement with members of the staff, properly qualified graduate students are directed in research.
Published Date: July 28, 2022