Probability An introduction to the concepts of probability and their applications, covering both discrete and continuous random variables. Probability spaces, elementary combinatorial analysis, densities and distributions, conditional probabilities, independence, expectation, variance, weak law of large numbers, central limit theorem, and numerous applications.

Advanced Probability Seminar An introduction to the mathematical foundations of Probability for students who have completed work in Probability and Real Analysis.  The central ideas correspond to the Lebesgue theory of measure and integration.  Probability provides additional perspective and motivates intriguing applications of the theory, which students will explore in their final projects.  Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights through expository writing and oral presentations.  This course fulfills the capstone senior work requirement for the mathematics major.

Introduction to Statistical Science A practical introduction to statistical methods and the examination of data sets. Computer software will play a central role in analyzing a variety of real data sets from the natural and social sciences. Topics include descriptive statistics, elementary distributions for data, hypothesis tests, confidence intervals, correlation, regression, contingency tables, and analysis of variance. The course has no formal mathematics prerequisite, and is especially suited to students in the physical, social, environmental, and life sciences who seek an applied orientation to data analysis. (Credit is not given for MATH 0116 if the student has taken ECON 0111 (formerly ECON 0210) or PSYC 0201 previously or concurrently.)

Stochastic Processes Stochastic processes are mathematical models for random phenomena evolving in time or space. This course will introduce important examples of such models, including random walk, branching processes, the Poisson process and Brownian motion. The theory of Markov chains in discrete and continuous time will be developed as a unifying theme. Depending on time available and interests of the class, applications will be selected from the following areas: queuing systems, mathematical finance (Black-Scholes options pricing), probabilistic algorithms, and Monte Carlo simulation.

Linear Algebra Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule.

Bill Peterson

Reviews and ratings for Bill Peterson at Middlebury College.Bill Peterson teaches Probability, Advanced Probability Seminar, Intro to Statistical Science and more.  Explore top rated instructors and find the best for you.Is Bill Peterson good ? Find out on MiddCourses.

Professor Peterson is a very good professor. Very nice, and visibly enthusiastic about the material. His lectures are a bit unstructured but they are not hard to follow. The homework is pretty straightforward and does well to reinforce the learning because it uses the same situations for problems (eg. a lot of problems involve decks of cards or rolling dice).

Bill Peterson is great! I took this class in Spring 2025. He has great enthusiasm for the material and he is a really great person. This class was super hard for me but I am glad I took it and Bill made it fun!

Nice and smart teacher. Similar to Probability, pretty hard tests. Would not take this course again and would switch to econ sophomore year if I had the chance but a little late now considering I'm just trying to pass his class in order to graduate. 