# William Peterson

## Professor of Mathematics

wpeterso@middlebury.edu

work(802) 443-5417

Spring 2021: MATH 200 Monday 1:00-2:00, Thursday 10:30-11:30, Fri 1:00-2:00 https://middlebury.zoom.us/j/2057214288?pwd=b28zTHc5bFVMdVkraENKdDc4R21PQT09 MATH 410 Tuesday 1:30-3:00, Wednesday 3:00-4:00, Fri 2:00-3:00. https://middlebury.zoom.us/j/95423783168?pwd=MUEySzBPMGJoQVdWSmVNdmc2dVEwQT09

75 Shannon 102D

**Degrees, Specializations & Interests:**

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

Applied Probability, Stochastic Processes

## Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

▹ *indicates offered in the upcoming term[s]*

##### MATH 0116 - Intro to Statistical Science

**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. **DED**

Fall 2021

##### MATH 0122 - Calculus II

**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. (MATH 0121 or by waiver) 4 hrs. lect. **DED**

Fall 2019, Fall 2020

##### MATH 0200 - Linear Algebra

**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. **DED**

Fall 2018, Spring 2020, Spring 2021

##### MATH 0310 - Probability ▹

**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. **DED**

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

##### MATH 0410 - Stochastic Processes

**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. **DED**

Spring 2019, Spring 2021

##### MATH 0500 - Advanced Study ▲ ▹

**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.

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

##### MATH 0710 - Advanced Probability Seminar

**Advanced Probability Seminar**

This course is a tutorial in Probability Theory for students who have completed work in Probability and Real Analysis. Starting from elementary results about random walks, we will explore the fundamental mathematical ideas underlying measure theoretic probability, martingales, the Weiner process, and the ItÃ´ stochastic calculus. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. This course fulfills the capstone senior work requirement for the mathematics major. (MATH 0310, MATH 0323, and by approval). 3 hrs. sem.

Spring 2019, Spring 2020

#### Math 116

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