Topics in Mathematics of Data Science

Lecture Notes

SES #	TOPICS
1	Overview and Two Open Problems (PDF)
2-4	Principal Component Analysis in High Dimensions and the Spike Model (PDF)
5-7	Graphs, Diffusion Maps, and Semi-supervised Learning (PDF)
8-11	Spectral Clustering and Cheeger’s Inequality (PDF)
12-14	Concentration Inequalities, Scalar and Matrix Versions (PDF)
15-16	Johnson-Lindenstrauss Lemma and Gordon’s Theorem (PDF)
17	Local Convergence of Graphs and Enumeration of Spanning Trees (PDF) (Courtesy of Mustazee Rahman. Used with permission.)
18-19	Compressed Sensing and Sparse Recovery (PDF)
20	Group Testing and Error-Correcting Codes (PDF)
21	Approximation Algorithms and Max-Cut (PDF)
22	Community Detection and the Stochastic Block Model (PDF)
23	Synchronization Problems and Alignment (PDF)

Most of the lecture notes were consolidated into a monograph: Ten Lectures and Forty Two Open Problems in the Mathematics of Data Science (PDF - 2.7MB)