Teaching
Current Courses
These are the courses I am teaching this year at the Mathematical Sciences Department, WPI
MA 1024: Multivariate Calculus
Fall A Term 2024, Winter D Term 2025
This course provides an introduction to multivariable calculus. Topics covered include: vector functions, partial derivatives and gradient, multivariable optimization, double and triple integrals, polar coordinates, other coordinate systems and applications. I taught a 35-student section in Fall A Term 2024, where I place a strong emphasis on problem-solving to help students develop an intuitive grasp of these mathematical concepts and their real-world applications.
MA 2621: Probability and Applications
Fall B Term 2024, Spring D Term 2025
This course is an application-oriented course, primarily designed for non-Mathematical Sciences majors, and introduces the student to applied probability. Topics to be covered are: basic probability theory including Bayes theorem; discrete and continuous random variables; special distributions including the Bernoulli, Binomial, Geometric, Poisson, Uniform, Normal, Exponential, Chi-square, Gamma, Weibull, and Beta distributions; multivariate distributions; conditional and marginal distributions; independence; expectation; transformations of univariate random variables.
Past Courses
These courses were taught during my visiting assistant professor position at the PSTAT department, University of California, Santa Barbara. The enrollment numbers for these courses ranged from around 50 students in the more advanced offerings to over 275 students in the introductory probability courses. My goal was to provide a solid mathematical foundation while also emphasizing the practical applications of the concepts covered. I applied a project-based approach whenever possible.
PSTAT 120A: Probability and Statistics I
Fall 2021, Winter 2022, and Summer 2022 • 120-275 students
Concepts of probability; random variables; combinatorial probability; discrete and continuous distributions; joint distributions, expected values; moment generating functions; law of large numbers and central limit theorems. I taught this course over three terms with class sizes ranging from 120 to 275 students. The goal was to provide a strong mathematical foundation that students could build upon in more advanced statistics and data analysis.
PSTAT 120B: Probability and Statistics II
Summer 2023, Fall 2023, Winter 2023 • 60-70 students
Distribution of sample mean and sample variance; t, chi-squared and F distributions; summarizing data by statistics and graphs; estimation theory for single samples: sufficiency, efficiency, consistency, methodof moments, maximum likelihood; hypothesis testing: likelihood ratio test; confidence intervals. I taught this course with class sizes around 60-70 students.
PSTAT 126: Regression Analysis
Spring 2023, Winter 2024, Spring 2024
Linear and multiple regression, analysis of residuals, transformations, variable and model selection including stepwise regression, and analysis of covariance. The course will stress the use of computer packages to solve real-world problems. I followed a project-based approach over a quarter, with presentations at the end.
PSTAT 160A: Applied Stochastic Processes in Discrete Time
Summer 2022
This course covered the theory and applications of discrete-time stochastic processes, including random walks, Markov chains, and simulation techniques. This course has a coding component in Python with emphasis on math finance applications.
PSTAT 160B: Applied Stochastic Processes in Continuous Time
Summer 2023, Winter 2023, Winter 2024
Building on Part A, this course explored continuous-time stochastic processes, such as the Poisson process, continuous-time Markov chains, renewal processes, and Brownian motion. This course has a coding component with emphasis on math finance applications.
PSTAT 171: Mathematics of Fixed Income Markets
Spring 2022, Spring 2023, Spring 2024
This course provided an introduction to fixed income markets, covering topics like interest measurement, annuities, bonds, and depreciation. This course follows the SOA FM exam syllabus.
PSTAT 182T: Mathematics of Fixed Income Markets
Fall 2021, Winter 2022, Spring 2022
This course offered problem-solving sessions to help students prepare for the first two actuarial exams, Probability and FM exams, covering topics in probability and financial mathematics.