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1 - 10 of 11 results for: Math51

CEE 154: Data Analytics for Physical Systems (CEE 254)

This course introduces practical applications of data analytics and machine learning from understanding sensor data to extracting information and decision making in the context of sensed physical systems. Many civil engineering applications involve complex physical systems, such as buildings, transportation, and infrastructure systems, which are integral to urban systems and human activities. Emerging data science techniques and rapidly growing data about these systems have enabled us to better understand them and make informed decisions. In this course, students will work with real-world data to learn about challenges in analyzing data, applications of statistical analysis and machine learning techniques using MATLAB, and limitations of the outcomes in domain-specific contexts. Topics include data visualization, noise cleansing, frequency domain analysis, forward and inverse modeling, feature extraction, machine learning, and error analysis. Prerequisites: CS106A, CME 100/ Math51, Stats110/101, or equivalent.
Terms: Aut | Units: 3-4
Instructors: Noh, H. (PI)

CEE 254: Data Analytics for Physical Systems (CEE 154)

This course introduces practical applications of data analytics and machine learning from understanding sensor data to extracting information and decision making in the context of sensed physical systems. Many civil engineering applications involve complex physical systems, such as buildings, transportation, and infrastructure systems, which are integral to urban systems and human activities. Emerging data science techniques and rapidly growing data about these systems have enabled us to better understand them and make informed decisions. In this course, students will work with real-world data to learn about challenges in analyzing data, applications of statistical analysis and machine learning techniques using MATLAB, and limitations of the outcomes in domain-specific contexts. Topics include data visualization, noise cleansing, frequency domain analysis, forward and inverse modeling, feature extraction, machine learning, and error analysis. Prerequisites: CS106A, CME 100/ Math51, Stats110/101, or equivalent.
Terms: Aut | Units: 3-4
Instructors: Noh, H. (PI)

CME 200: Linear Algebra with Application to Engineering Computations (ME 300A)

Computer based solution of systems of algebraic equations obtained from engineering problems and eigen-system analysis, Gaussian elimination, effect of round-off error, operation counts, banded matrices arising from discretization of differential equations, ill-conditioned matrices, matrix theory, least square solution of unsolvable systems, solution of non-linear algebraic equations, eigenvalues and eigenvectors, similar matrices, unitary and Hermitian matrices, positive definiteness, Cayley-Hamilton theory and function of a matrix and iterative methods. Prerequisite: familiarity with computer programming, and MATH51.
Terms: Aut | Units: 3

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

Mathematical and 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 graph data. Linear and non-linear dimensionality reduction techniques. 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. Deep learning on irregular geometric data. Prerequisites: discrete algorithms at the level of CS161; linear algebra at the level of Math51 or CME103.
Terms: Spr | Units: 3
Instructors: Guibas, L. (PI)

CS 148: Introduction to Computer Graphics and Imaging

Introductory prerequisite course in the computer graphics sequence introducing students to the technical concepts behind creating synthetic computer generated images. In addition to scanline rendering, ray tracing is introduced at the beginning of the course, since modern consoles now include ray tracing. This is followed by discussions of underlying mathematical concepts including triangles, normals, interpolation, texture/bump mapping, anti-aliasing, acceleration structures, etc. Importantly, the course will discuss handling light/color for image formats, computer displays, printers, etc., as well as how light interacts with the environment, constructing engineering models such as the BRDF, and various simplifications into more basic lighting and shading models. The final class mini-project consists of building out a ray tracer to create visually compelling images. Starter codes and code bits will be provided to aid in development, but this class focuses on what you can do with the code as opposed to what the code itself looks like. Therefore grading is weighted toward in person "demos" of the code in action - creativity and the production of impressive visual imagery are highly encouraged/rewarded. Prerequisites: CS107, MATH51.
Terms: Aut | Units: 3-4 | UG Reqs: GER:DB-EngrAppSci, WAY-CE

CS 229: Machine Learning (STATS 229)

Topics: statistical pattern recognition, linear and non-linear regression, non-parametric methods, exponential family, GLMs, support vector machines, kernel methods, deep learning, model/feature selection, learning theory, ML advice, clustering, density estimation, EM, dimensionality reduction, ICA, PCA, reinforcement learning and adaptive control, Markov decision processes, approximate dynamic programming, and policy search. Prerequisites: knowledge of basic computer science principles and skills at a level sufficient to write a reasonably non-trivial computer program in Python/numpy, familiarity with probability theory to the equivalency of CS109 or STATS116, and familiarity with multivariable calculus and linear algebra to the equivalency of MATH51.
Terms: Aut, Spr, Sum | Units: 3-4

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

Mathematical and 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 graph data. Linear and non-linear dimensionality reduction techniques. 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. Deep learning on irregular geometric data. Prerequisites: discrete algorithms at the level of CS161; linear algebra at the level of Math51 or CME103.
Terms: Spr | Units: 3
Instructors: Guibas, L. (PI)

MATH 51: Linear Algebra, Multivariable Calculus, and Modern Applications

This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion includes orthogonality, linear independence, matrix algebra, and eigenvalues with applications such as least squares, linear regression, and Markov chains (relevant to population dynamics, molecular chemistry, and PageRank); the singular value decomposition (essential in image compression, topic modeling, and data-intensive work in many fields) is introduced in the final chapter of the e-text. The multivariable calculus portion includes unconstrained optimization via gradients and Hessians (used for energy minimization), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning al more »
This course provides unified coverage of linear algebra and multivariable differential calculus, and the free course e-text connects the material to many fields. Linear algebra in large dimensions underlies the scientific, data-driven, and computational tasks of the 21st century. The linear algebra portion includes orthogonality, linear independence, matrix algebra, and eigenvalues with applications such as least squares, linear regression, and Markov chains (relevant to population dynamics, molecular chemistry, and PageRank); the singular value decomposition (essential in image compression, topic modeling, and data-intensive work in many fields) is introduced in the final chapter of the e-text. The multivariable calculus portion includes unconstrained optimization via gradients and Hessians (used for energy minimization), constrained optimization (via Lagrange multipliers, crucial in economics), gradient descent and the multivariable Chain Rule (which underlie many machine learning algorithms, such as backpropagation), and Newton's method (an ingredient in GPS and robotics). The course emphasizes computations alongside an intuitive understanding of key ideas. The widespread use of computers makes it important for users of math to understand concepts: novel users of quantitative tools in the future will be those who understand ideas and how they fit with examples and applications. This is the only course at Stanford whose syllabus includes nearly all the math background for CS 229, which is why CS 229 and CS 230 specifically recommend it (or other courses resting on it). For frequently asked questions about the differences between Math 51 and CME 100, see the FAQ on the placement page on the Math Department website. Prerequisite: Math 21 or the math placement diagnostic (offered through the Math Department website) in order to register for this course.
Terms: Aut, Win, Spr, Sum | Units: 5 | UG Reqs: GER:DB-Math, WAY-FR

MATH 51A: Linear Algebra, Multivariable Calculus, and Modern Applications, ACE

Students attend one of the regular MATH 51 lectures with a longer discussion section of four hours per week instead of two. Active mode: students in small groups discuss and work on problems from a worksheet distributed 2 or 3 days in advance, with a TA providing guidance and answering questions. Application required: https://forms.gle/7Bexo81r9YcZYRW1A
Terms: Aut, Win, Spr | Units: 6 | UG Reqs: GER:DB-Math, WAY-FR

ME 300A: Linear Algebra with Application to Engineering Computations (CME 200)

Computer based solution of systems of algebraic equations obtained from engineering problems and eigen-system analysis, Gaussian elimination, effect of round-off error, operation counts, banded matrices arising from discretization of differential equations, ill-conditioned matrices, matrix theory, least square solution of unsolvable systems, solution of non-linear algebraic equations, eigenvalues and eigenvectors, similar matrices, unitary and Hermitian matrices, positive definiteness, Cayley-Hamilton theory and function of a matrix and iterative methods. Prerequisite: familiarity with computer programming, and MATH51.
Terms: Aut | Units: 3
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