Math 89S: The Emerging Science of Complex Data

Time: TH, 10:05-11:20

Location: Physics 205

Instructor: Paul Bendich

Office Hours: Physics 210, T 12-1, F 9-10.

Course Description

Textbooks: There will be many handouts and other xeroxed readings throughout the course of the semester. Assignments: In addition to regularly assigned response writings and problem sets, there will be a substantial research paper, which will be accompanied by several benchmark assignments over the course of the semester.

Date Topics
Jan. 10 Overview, Introduction, Motivating Examples
Jan. 15 No Class
Jan. 17 Intro to SLT
Jan. 22 Basic Probability
Jan. 24 Basic Prob., Intro to Bayesian Analysis
Jan. 29 Bayesian Analysis
Jan. 31 Supervised Learning
Feb. 5 Lecture on Big Data
Feb. 7 NN and Kernel Rules
Feb. 12 Multi-dimensional Scaling
Feb. 14 IsoMap
Feb. 19 Linear Algebra Basics, I
Feb. 21 Linear Algebra Basics, II
Feb. 26 Principal Components Analysis
Feb. 28 PCA: examples
Mar. 5 Random Walks
Mar. 7 PageRank
Mar. 19 Annotated Bibliographies: Class Discussion
Mar. 21 Collaboration in age of big data
Mar. 26 Diffusion Maps: theory
Mar. 28 Diffusion Maps: examples
Apr. 2 Basic Topology
Apr. 4 Basic Homology
Apr. 9 Persistent Homology
Apr. 11 TDA lecture
Apr. 16 Student Presentations
Apr. 18 Student Presentations
Apr. 23 Student Presentations