printer friendly pageCME 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)
;
Gurunathan, V. (TA)
;
Hanley, H. (TA)
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Instructors:
Valiant, G. (PI)
;
Gurunathan, V. (TA)
;
Hanley, H. (TA)
;
Pabbaraju, C. (TA)
;
Villa-Renteria, I. (TA)
CME 322: Spectral Methods in Computational Physics (ME 408)
Data analysis, spectra and correlations, sampling theorem, nonperiodic data, and windowing; spectral methods for numerical solution of partial differential equations; accuracy and computational cost; fast Fourier transform, Galerkin, collocation, and Tau methods; spectral and pseudospectral methods based on Fourier series and eigenfunctions of singular Sturm-Liouville problems; Chebyshev, Legendre, and Laguerre representations; convergence of eigenfunction expansions; discontinuities and Gibbs phenomenon; aliasing errors and control; efficient implementation of spectral methods; spectral methods for complicated domains; time differencing and numerical stability.
Last offered: Winter 2023
CME 323: Distributed Algorithms and Optimization
The emergence of clusters of commodity machines with parallel processing units has brought with it a slew of new algorithms and tools. Many fields such as Machine Learning and Optimization have adapted their algorithms to handle such clusters. Topics include distributed and parallel algorithms for: Optimization, Numerical Linear Algebra, Machine Learning, Graph analysis, Streaming algorithms, and other problems that are challenging to scale on a commodity cluster. The class will focus on analyzing parallel and distributed programs, with some implementation using Apache Spark and TensorFlow. Recommended prerequisites: Discrete math at the level of
CS 161 and programming at the level of
CS 106A.
Terms: Spr
| Units: 3
Instructors:
Bosagh Zadeh, R. (PI)
;
YANG, Z. (TA)
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
CME 334: Optimization Algorithms (CS 369O, MS&E 312)
Fundamental theory for solving continuous optimization problems with provable efficiency guarantees. Coverage of both canonical optimization methods and techniques, e.g. gradient descent, mirror descent, stochastic methods, acceleration, higher-order methods, etc. and canonical optimization problems, critical point computation for non-convex functions, smooth-convex function minimization, regression, linear programming, etc. Focus on provable rates for solving broad classes of prevalent problems including both classic problems and those motivated by large-scale computational concerns. Discussion of computational ramifications, fundamental information-theoretic limits, and problem structure. Prerequisite: linear algebra, multivariable calculus, probability, and proofs.
Terms: Win
| Units: 3
Instructors:
Sidford, A. (PI)
;
Graur, A. (TA)
CME 345: Model Reduction (AA 216)
Model reduction is an indispensable tool for computational-based design and optimization, statistical analysis, embedded computing, and real-time optimal control. It is also essential for scenarios where real-time simulation responses are desired. This course presents the basic mathematical theory for projection-based model reduction. It is intended primarily for graduate students interested in computational sciences and engineering. The course material described below is complemented by a balanced set of theoretical, algorithmic, and Matlab computer programming homework assignments. Prerequisites: Solid foundations in numerical linear algebra (
CME 200 or equivalent). Basic numerical methods for ODEs (
CME 206 or equivalent).
Last offered: Spring 2021
CME 350Q: The ABCs of TQC: An introduction to the mathematics of Topological Quantum Computing
Computation is a mechanical process. Computers process information by manipulating physical systems encoding bits, and quantum computers manipulate encodings in quantum mechanical systems. This process is extremely delicate and error-prone, so we must develop fault-tolerant computation protocols to make quantum computers useful. Quantum error-correcting codes provide a means of developing fault-tolerance at the software level. This course will explore Topological Quantum Computing (TQC) as a means of achieving fault-tolerance at the hardware level instead, by encoding information in topological phases of matter that are intrinsically protected from local deformations and interactions. TQC promises scalable quantum computing and it lies at the crossroads of cutting-edge research in Physics, Engineering, and Mathematics. This course will introduce the mathematical machinery modeling TQC. The main players are Anyons, Braids, and Categories: braiding anyons, which are certain quasiparticle
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Computation is a mechanical process. Computers process information by manipulating physical systems encoding bits, and quantum computers manipulate encodings in quantum mechanical systems. This process is extremely delicate and error-prone, so we must develop fault-tolerant computation protocols to make quantum computers useful. Quantum error-correcting codes provide a means of developing fault-tolerance at the software level. This course will explore Topological Quantum Computing (TQC) as a means of achieving fault-tolerance at the hardware level instead, by encoding information in topological phases of matter that are intrinsically protected from local deformations and interactions. TQC promises scalable quantum computing and it lies at the crossroads of cutting-edge research in Physics, Engineering, and Mathematics. This course will introduce the mathematical machinery modeling TQC. The main players are Anyons, Braids, and Categories: braiding anyons, which are certain quasiparticles existing only in two-dimensional systems, results in unitary state transformations implementing logical gates on encoded qubits. The mathematical theory of anyons, which are neither bosons nor fermions, as simple objects in unitary modular tensor categories is quite interesting, and this course will develop it from the ground up.
Last offered: Spring 2022
CME 364A: Convex Optimization I (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
| Units: 3
Instructors:
Ayazifar, B. (PI)
;
Boyd, S. (PI)
;
Bell, L. (TA)
;
Hofgard, J. (TA)
;
Holt, G. (TA)
;
Johansson, K. (TA)
;
Parshakova, T. (TA)
;
Tse, D. (TA)
;
Yang, A. (TA)
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.
Terms: Spr
| Units: 3
Instructors:
Pilanci, M. (PI)
;
Mishkin, A. (TA)
CME 369: Computational Methods in Fluid Mechanics (ME 469)
The last two decades have seen the widespread use of Computational Fluid Dynamics (CFD) for analysis and design of thermal-fluids systems in a wide variety of engineering fields. Numerical methods used in CFD have reached a high degree of sophistication and accuracy. The objective of this course is to introduce 'classical' approaches and algorithms used for the numerical simulations of incompressible flows. In addition, some of the more recent developments are described, in particular as they pertain to unstructured meshes and parallel computers. An in-depth analysis of the procedures required to certify numerical codes and results will conclude the course.
Terms: Spr
| Units: 3
Instructors:
Domino, S. (PI)
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