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1 - 10 of 11 results for: MATH 161

CEE 161I: Atmosphere, Ocean, and Climate Dynamics: The Atmospheric Circulation (CEE 261I, EARTHSYS 146A, ESS 246A)

Introduction to the physics governing the circulation of the atmosphere and ocean and their control on climate with emphasis on the atmospheric circulation. Topics include the global energy balance, the greenhouse effect, the vertical and meridional structure of the atmosphere, dry and moist convection, the equations of motion for the atmosphere and ocean, including the effects of rotation, and the poleward transport of heat by the large-scale atmospheric circulation and storm systems. Prerequisites: MATH 51 or CME100 and PHYSICS 41.
Terms: Aut | Units: 3

CME 251: Geometric and Topological Data Analysis (CS 233)

Mathematical computational tools for the analysis of data with geometric content, such images, videos, 3D scans, GPS traces -- as well as for other data embedded into geometric spaces. Global and local geometry descriptors allowing for various kinds of invariances. The rudiments of computational topology and persistent homology on sampled spaces. Clustering and other unsupervised techniques. Spectral methods for geometric data analysis. Non-linear dimensionality reduction. Alignment, matching, and map computation between geometric data sets. Function spaces and functional maps.Networks of data sets and joint analysis for segmentation and labeling. The emergence of abstractions or concepts from data. Prerequisites: discrete algorithms at the level of 161; linear algebra at the level of CME103.
Terms: Spr | Units: 3
Instructors: Guibas, L. (PI)

CME 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

CS 161: Design and Analysis of Algorithms

Worst and average case analysis. Recurrences and asymptotics. Efficient algorithms for sorting, searching, and selection. Data structures: binary search trees, heaps, hash tables. Algorithm design techniques: divide-and-conquer, dynamic programming, greedy algorithms, amortized analysis, randomization. Algorithms for fundamental graph problems: minimum-cost spanning tree, connected components, topological sort, and shortest paths. Possible additional topics: network flow, string searching. Prerequisite: 103 or 103B; 109 or STATS 116.
Terms: Aut, Win, Sum | Units: 3-5 | UG Reqs: GER:DB-EngrAppSci, WAY-FR

CS 261: Optimization and Algorithmic Paradigms

Algorithms for network optimization: max-flow, min-cost flow, matching, assignment, and min-cut problems. Introduction to linear programming. Use of LP duality for design and analysis of algorithms. Approximation algorithms for NP-complete problems such as Steiner Trees, Traveling Salesman, and scheduling problems. Randomized algorithms. Introduction to sub-linear algorithms and decision making under uncertainty. Prerequisite: 161 or equivalent.
Terms: Win | Units: 3
Instructors: Charikar, M. (PI)

CS 265: Randomized Algorithms and Probabilistic Analysis (CME 309)

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

CS 268: Geometric Algorithms

Techniques for design and analysis of efficient geometric algorithms for objects in 2-, 3-, and higher dimensions. Topics: convexity, triangulations and simplicial complexes, sweeping, partitioning, and point location. Voronoi/Delaunay diagrams and their properties. Arrangements of curves and surfaces. Intersection and visibility problems. Geometric searching and optimization. Random sampling methods. Range searching. Impact of numerical issues in geometric computation. Example applications to robotic motion planning, visibility preprocessing and rendering in graphics, and model-based recognition in computer vision. Prerequisite: discrete algorithms at the level of 161. Recommended: 164.
Last offered: Autumn 2016

ENGR 105: Feedback Control Design

Design of linear feedback control systems for command-following error, stability, and dynamic response specifications. Root-locus and frequency response design techniques. Examples from a variety of fields. Some use of computer aided design with MATLAB. Prerequisites: Dynamics systems ( EE 102B or ME 161), and ordinary differential equations ( CME 102 or Math 53)
Terms: Win, Spr | Units: 3 | UG Reqs: GER:DB-EngrAppSci

MATH 161: Set Theory

Informal and axiomatic set theory: sets, relations, functions, and set-theoretical operations. The Zermelo-Fraenkel axiom system and the special role of the axiom of choice and its various equivalents. Well-orderings and ordinal numbers; transfinite induction and transfinite recursion. Equinumerosity and cardinal numbers; Cantor's Alephs and cardinal arithmetic. Open problems in set theory. Prerequisite: students should be comfortable doing proofs.
Last offered: Winter 2019 | UG Reqs: GER:DB-Math

ME 161: Dynamic Systems, Vibrations and Control

Modeling, analysis, and measurement of mechanical and electromechanical dynamic systems. Closed form solutions of ordinary differential equations governing the behavior of single and multiple-degree-of-freedom systems. Stability, forcing, resonance, and control system design. Prerequisites: Ordinary differential equations ( CME 102 or MATH 53), linear algebra ( CME 104 or MATH 53) and dynamics (E 15) are recommended.
Terms: Aut | Units: 3 | UG Reqs: GER:DB-EngrAppSci
Instructors: Towles, J. (PI)
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