### Lecture notes and tutorials

Topics course on high-dimensional probability and statistics

Graduate course on modern discrete probability

Topics course on stochastic processes in evolutionary genetics

First year of graduate probability theory

Brief survey of mathematical phylogenetics

Summer school slides on probability on graphs with applications to data science

Tutorial slides on mathematical phylogenomics

### This year

Spring 2022: MATH 535 - Mathematical Methods in Data Science

Spring 2020: MATH 535 - Mathematical Methods in Data Science

Spring 2018: MATH 734 - Theory of Probability II

Spring 2015: MATH 632 - Introduction to Stochastic Processes

### Past courses at UCLA, UC-Berkeley and Ecole Polytechnique-Montreal

#### Spring 2012

Description: Prerequisite: course 31B and 32A. Introduction to integral calculus of several variables, line and surface integrals..

Description: Prerequisite: undergraduate probability course will be useful. Overview of Basic Probability: Events; Random variables; Generating functions; Basic limit laws; Simulation. Introduction to Markov Processes: Markov chains; Poisson processes; Branching processes; Continuous-time Markov processes; Diffusion processes and numerical methods (if time permits).

#### Winter 2012

Description: Prerequisite: course 31B and 32A. Introduction to integral calculus of several variables, line and surface integrals..

Description: Prerequisite: course 245A or 265A. Connection between probability theory and real analysis. Weak and strong laws of large numbers, central limit theorem, conditioning, ergodic theory, martingale theory.

#### Spring 2011

Description: Prerequisite: course 3C or 32A. Graphs, greedy algorithms, divide and conquer algorithms, dynamic programming, network flow. Emphasis on designing efficient algorithms useful in diverse areas such as bioinformatics and allocation of resources.

#### Winter 2011

Description: Prerequisite: course 245A or 265A. Connection between probability theory and real analysis. Weak and strong laws of large numbers, central limit theorem, conditioning, ergodic theory, martingale theory.

#### Fall 2010

Description: Prerequisite: course 245A or 265A. Connection between probability theory and real analysis. Weak and strong laws of large numbers, central limit theorem, conditioning, ergodic theory, martingale theory.

#### Spring 2010

Description: Prerequisite: No biology background is required; a graduate course in stochastic processes will be useful. Rigorous mathematical analysis of probabilistic and combinatorial structures arising from biology, mostly in the study of evolution and genetics. See website for details.

#### Winter 2010

Description: Prerequisite: course 245A or 265A. Connection between probability theory and real analysis. Weak and strong laws of large numbers, central limit theorem, conditioning, ergodic theory, martingale theory.

#### Fall 2006

Description: Measure theory concepts needed for probability. Expectation, distributions. Laws of large numbers and central limit theorems for independent random variables. Characteristic function methods. Conditional expectations; martingales and theory convergence.

#### Fall 2002

Description: Elementary Probabilities. Random Variables. Random Vectors. Stochastic Processes. Estimation and Testing. Quality Control.

updated: 12/21/21