Math 191. Mathematical Tools for the Information Sciences

Department of Mathematics
University of California, Berkeley
Fall 2009


This class is targeted at anyone who's curious about how mathematics is used by companies like Google, FaceBook, Netflix, etc, for web search, product recommendations, computational advertising, sponsored search auctions, multimedia search, text mining, social network analysis, etc. An alternative course title that would describe 90% of the materials could well have been "The Mathematics of Data Mining, Machine Learning, and Pattern Recognition". The remaining 10% would be on miscellaneous topics like ad auctions.

We will be interested in a handful of mathematical tools for analyzing the sort of complex, high-dimensional, massive datasets that have become ubiquitous in today's world. But this is not a course about statistics. Our tools might well be derived from partial differential equations, harmonic analysis, linear algebra, graph theory, differential geometry, algebraic topology, etc, and they may or may not have obvious interpretations in terms of traditional statistics.

A prerequisite for taking this course is Math 110: Linear Algebra. Knowledge of basic probability theory and multivariate calculus would be helpful. Programming knowledge is useful though not necessary.



Location: Evans Hall, Room 2

Times: 3:00–4:00 PM on Mon/Wed/Fri

Course staff

Instructor: Lek-Heng Lim
Evans Hall, Room 873
(510) 642-8576
Office hours: 12:00–1:00 PM, Mon and Wed, 2:00 AM–3:00 PM, Wed


Here's a list of mathematical topics that we shall examine (some only at a very basic level). Of course everything will be motivated by and made relevant to some cool applications.

Supplementary materials


To be determined. Course grade is likely to be based more on projects/term papers and less on homeworks/exams.


There is no single official textbook for this course but the following are some useful references. It would not be unwise to first discuss with me before deciding which ones to buy (it depends on your interests).