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.

Bill Peterson is a great professor, who is clearly very knowledgeable in this field. The course is a great introduction to probabilistic thinking which is a skill in and of itself. I enjoy Peterson's enthusiasm for the course and his teaching style.

Peterson is fantastic and does a great job explaining everything. The course material is quite interesting on the whole, and the workload is very manageable. Peterson is very helpful at office hours, but he teaches so clearly that you'll rarely have many questions to ask

People used to tell me that Bill was the GOAT professor in Middlebury. I have to agree after taking this course with him. He's invested in his students' success and it inspires you to work your hardest to meet his expectations.