Advanced Linear Algebra with Applications

Graduate / Professional

This course is a natural continuation of MATH 2220 . The core content includes eigenvectors and the Spectral Theorem for real symmetric matrices; singular value decomposition (SVD) and principle component analysis (PCA); quadratic forms, Rayleigh quotients and generalized eigenvalues. We also consider a number of applications: optimization and stochastic gradient descent (SGD); eigen-decomposition and dimensionality reduction; graph Laplacians and data diffusion; neural networks and machine learning. A main theme of the course is using linear algebra to learn from data. Students complete (computational) projects on topics of their choosing. Prerequisites: MATH 1200 and MATH 2220 , 2250 , or 2260. This is not a proof-based course. May not be taken after MATH 3400 . QR MW 11:35am-12:50pm