From my time at William & Mary
Undergraduate and Master's level, Math department, William & Mary, Spring 2022 - Summer 2023
Analysis of Stochastic Networks
Master’s in Computation in Operations Research (COR), Math department, William & Mary Spring 2022
General description and materials
Analytical properties of the Poisson process and Markov chains, focusing on performance guarantees and applica- tions, are studied. The goal is to answer questions such as how many cashiers are necessary to guarantee that 95% of the customer wait less than 10 minutes? Or, how many parking spaces do we need to create at a store to ensure that at most 5 customers per month have to wait to park? And many more.
We spend an important part of the semester reviewing Markov chains and Poisson processes so that we can speak the same language when we get to analyzing stochastic networks. Also, if you haven’t completed any course that covers these topics, you will get an opportunity to get up to speed in class. After we review these topics, we will focus on analyzing performance measures of a variety of stochastic networks and we will compare theoretical results with simulations.
- Syllabus
- Lecture notes (there might be typos!!)
Applications of Markov Chains
Master’s in Computation in Operations Research (COR), Math department, William & Mary Spring 2023
General description and materials
This course aims to explore some of the (many) applications of Markov chains, focusing on queueing theory and Markov decision processes. The course will be oriented to modeling techniques, analytically computing performance measures, and algorithms to help us estimate these measures when the analysis become intractable.
Specifically, we will learn some of the foundations of reinforcement learning and queueing theory. Our goal this semester is to acquire a broad understanding of these two areas of knowledge and develop intuitions about the performance of various systems and algorithms. We will start the semester reviewing probability and Markov chains, and we will then move on to applications.
- Syllabus
- Lecture notes (there might be typos!!)
Operations Research: Deterministic Models
Undergraduate level, Math department, William & Mary I taught this class in Spring 2022, Fall 2022 and Spring 2023. The materials below are from Spring 2023.
General description and materials
An introduction to operations research - how to use analytics to find the most efficient decision with available data. Focus is on quantitative modeling and formulation of optimization problems, which has been widely applied to management, engineering, and science. Model applications include machine learning, statistics, data science, sports analytics, supply chain, marketing, as well as other domains.
In this course we will use the mathematical tools you have learned in the past to solve and analyze real-life problems. One of the most important skills that you will learn is modeling problems as linear programs. Even though the lectures will focus more on solving and analyzing the solution of these problems, I will encourage you to keep practicing your modeling skills in the homework.
- Syllabus
- Lecture notes (there might be typos!!)
Elementary Probability and Statistics
Undergraduate level, Math department, William & Mary Fall 2022
General description and materials
Introduction to basic concepts and procedures of probability and statistics including descriptive statistics, proba- bility, classical distributions, estimation, hypothesis testing, correlation and regression, in the context of practical applications to data analysis from other disciplines.
This class was planned for students who do not take any other probability and statistics classes in their majors.