# William Peterson

## Professor of Mathematics

wpeterso@middlebury.edu

work(802) 443-5417

Spring 2020: Mondays, Wednesdays, Thursdays 2:00-3:00 PM, Fridays 10:00-11:00 AM, and by appointment

Warner Hall 313

**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 0121 - Calculus I

**Calculus I**

Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. 4 hrs. lect./disc. **DED**

Fall 2016, Fall 2017

##### 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./disc. **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**

Spring 2017, Fall 2018, Spring 2020

##### 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 MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2016, Fall 2017, Fall 2018, Fall 2019, Fall 2020

##### 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 2017, Spring 2019

##### 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.

Fall 2016, Winter 2017, Spring 2017, Winter 2018, Winter 2019, Fall 2019, Winter 2020, Fall 2020

##### 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

webpage