Lecture notes

A graduate course in modern discrete probability

A topics course on stochastic processes in evolutionary genetics

The first semester of graduate probability theory


Currently Teaching

[Fall 2017]: MATH 833 - Topics in Probability: Modern Discrete Probability

[Fall 2017]: MATH 431 - Introduction to the Theory of Probability


Past courses at UW-Madison

Fall 2016

MATH 632 - Introduction to Stochastic Processes

Spring 2015

MATH 632 - Introduction to Stochastic Processes

Fall 2014

MATH 632 - Introduction to Stochastic Processes
MATH 833 - Topics in Probability: Essentials of Modern Discrete Probability

Fall 2013

MATH 331 - Introduction to Probability and Markov Chain Modeling
MATH 632 - Introduction to Stochastic Processes
MATH 733 - Theory of Probability I

Fall 2012

MATH 213 - Calculus and Introduction to Differential Equations
MATH 833 - Topics in Probability: Stochastic Processes in Evolution and Genetics


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

Spring 2012

MATH 32B: Calculus of Several Variables (Undergraduate) - UCLA

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

MATH 285J: Applied Probability -- An Introduction (Graduate) - UCLA

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

MATH 32B: Calculus of Several Variables (Undergraduate) - UCLA

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

MATH 275B: Probability Theory (Graduate) - UCLA

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

MATH 182: Algorithms (Undergraduate) - UCLA

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

MATH 275B: Probability Theory (Graduate) - UCLA

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

MATH 275A: Probability Theory (Graduate) - UCLA

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

MATH 285K: Topics in Probability: Stochastic Processes in Evolution and Genetics (Graduate) - UCLA

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

MATH 275B: Probability Theory (Graduate) - UCLA

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

STAT 205A: Probability Theory (Graduate) - UC Berkeley [Teaching Assistant]

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

MTH 2305: Probability for Engineers (Undergraduate) - Ecole Polytechnique, Montreal

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

last modified: jul 20, 2017