Bill Peterson
Office
Warner 213
Tel
(802) 443-5417
Email
wpeterso@middlebury.edu
Office Hours
Fall 2022: Monday & Wednesday 2:30 PM - 4:00 PM, Tuesday 1:00 PM - 2:30 PM, Friday 11:00 AM - 12:00 PM, and by appointment
Additional Programs
Academic Affairs Mathematics

Courses Taught

Course Description

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.) 3 hrs. lect./1 hr. computer lab.

Terms Taught

Fall 2021, Spring 2023

Requirements

DED

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Course Description

Calculus II
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. 4 hrs. lect.

Terms Taught

Fall 2019, Fall 2020

Requirements

DED

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Course Description

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. (MATH 0121 or by waiver) 3 hrs. lect./disc.

Terms Taught

Fall 2018, Spring 2020, Spring 2021

Requirements

DED

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Course Description

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. (concurrent or prior MATH 0223 or by waiver) 3 hrs. lect./disc.

Terms Taught

Fall 2018, Fall 2019, Fall 2020, Fall 2021, Fall 2022

Requirements

DED

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Course Description

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. (MATH 0310) 3 hrs. lect./disc.

Terms Taught

Spring 2019, Spring 2021, Spring 2023

Requirements

DED

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Course Description

Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Terms Taught

Winter 2019, Fall 2019, Winter 2020, Fall 2020, Winter 2021, Spring 2021, Fall 2021, Winter 2022, Spring 2022, Fall 2022, Winter 2023, Spring 2023

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Course Description

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. (MATH 310 and MATH 323)

Terms Taught

Spring 2019, Spring 2020

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Academic Degrees

A.B., Dartmouth College; M.S., Ph.D., Stanford University;

Applied Probability, Stochastic Processes