Syllabus Detail

Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 270: Mathematics of Data Science

Approved: 2019-04-01, Jesus A. De Loera, Thomas Strohmer
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Bandeira, Singer, Strohmer: Mathematics of Data Science (draft)
127A, 167, 135A or equivalent preparation
Suggested Schedule:
1 Introduction: Basic goals of data science, machine learning, and AI, unsupervised/supervised learning
2 Probability: Curse and blessings of dimensionality, concentration inequalities, strange phenomena in high dimensions
2 Singular Value Decomposition and Principal Component Analysis
2 Clustering: k-means, spectral clustering, graph cuts, community detection
1 Diffusion maps, intrinsic geometry of data
1 Linear dimension reduction, (Fast) Johnson-Lindenstrauss projection
2 Randomized linear algebra: sketching, randomized SVD
2 Optimization: convex vs non-convex problems, Lagrange Duality and KKT optimality conditions, gradient descent algorithms
1 Logistic regression and LASSO
2 Classification/Deep learning: universal approximation theorem, convolutional deep networks, back-propagation, over/underfitting
2 Sparsity and compressive sensing
1 Low-rank matrix models, matrix completion
Additional Notes:
The indicated number of lectures refers to 80-minute lectures. The syllabus accounts for 19 lectures of one quarter.