https://math.byu.edu/wiki/index.php?feed=atom&namespace=0&title=Special%3ANewPages 2026-09-04T21:49:51Z From MathWiki MediaWiki 1.26.3 https://math.byu.edu/wiki/index.php/Math_380:_Mathematical_Foundations_of_Data_Science 2024-03-14T17:48:37Z

<p>Ls5: /* Courses for which this course is prerequisite */</p> <hr /> <div>== Catalog Information ==<br /> <br /> === Title ===<br /> Mathematical Foundations of Data Science<br /> <br /> === (Credit Hours:Lecture Hours:Lab Hours) ===<br /> (3:3:0)<br /> <br /> === Offered ===<br /> Contact Department<br /> <br /> === Prerequisite ===<br /> [[Math 112]]<br /> <br /> === Description ===<br /> Mathematical aspects of data science, including high-dimensional geometry and linear algebra, optimization, and probabilistic modeling.<br /> <br /> == Desired Learning Outcomes ==<br /> <br /> === Minimal learning outcomes ===<br /> # Geometry and linear algebra in high-dimensional space<br /> #* Working in high-dimensional space<br /> #* Intro to dimension reduction (including for visualization and computational necessity)<br /> #* Johnson-Lindenstrauss<br /> #* SVD<br /> #** For dimension reduction<br /> #** For data compression<br /> #** PCA<br /> #** Use to solve the normal equation of OLS, even with collinearity<br /> #* More about eigenvalues and eigenvectors and their uses<br /> #* Non-linear dimension reduction (e.g., Isomap/LLE) #* Quotient Groups<br /> # Optimization<br /> #* Motivation: Overview of Machine Learning—it’s all just optimization and sampling<br /> #* Gradients and Hessians and what they tell us about the loss landscape<br /> #* Symbolic and automatic differentiation (sympy and autograd)<br /> #* Gradient descent<br /> #* Newton and Quasi-Newton<br /> #* Regularization<br /> # Probabilistic Modeling<br /> #* Basic distributions, both discrete and continuous<br /> #* MLE is an optimization problem that usually cannot be solved analytically<br /> #* Use modeling and optimization skills to solve an interesting problem:<br /> #** Clustering<br /> #** Prediction<br /> #** Anomaly detection<br /> <br /> === Textbooks ===<br /> <br /> <br /> === Additional topics ===<br /> <br /> === Courses for which this course is prerequisite ===<br /> [[Category:Courses|380]]</div>

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