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Consulting Courses
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Courses
I typically
teach at least one probability/statistics each semester. Some of the topics
covered in these courses are given below. Computer simulation projects are
included in most of the courses. A project in MATH 4610, for instance, might
involve developing a computer simulation of a random walk on the integers,
initially as a model for the evolution of the fortune of a gambler playing the
game of red-and-black. The simulation could then used in a more serious study
of the properties of Brownian motion. Many of the projects (and some software)
were developed with partial support from an UNT Undergraduate Instructional
Development Grant.
Office
Hours This Semester
Course Notes This Semester
Probability and Statistics
Courses
- MATH 4610 Probability. Senior mathematics major
course covering probability models, limit theorems, and stochastic
processes.
- MATH 4650 Statistics. Senior mathematics major
course covering sampling theory, regression and correlation, ANOVA, and
non-parametric methods.
- MATH 1780 Introduction to Statistical
Analysis.
Introductory course on applications of probability and computer
simulation.
- MATH 6810 (Measure Theoretic)
Probability.
Probability measures, random variables, distributions, weak convergence,
limit theorems, conditional probability and expectation, and stochastic
processes.
- MATH 6350 Martingale Theory. Introduction to martingale
theory, covering conditional expectation, sub and supermartingales,
optional sampling, convergence and decomposition theorems, and
applications.
- MATH 5810 Probability. Theory and applications of
stochastic processes including laws of large numbers, limit theorems,
random walks, Gaussian processes and queueing theory.
- MATH 5350 Markov Processes. Topics include ergodic
theorems, random walks, first passage time results, and applications to
graph theory, genetics, games, and decision theory.
