## William Peterson

##### Professor of Mathematics

**Email:** wpeterso@middlebury.edu

**Phone:** work802.443.5417

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**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 0210 or PSYC 0201 previously or concurrently.) 3 hrs. lect./1 hr. computer lab.

**DED**

Fall 2011, Fall 2013

##### 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**

Spring 2011, Fall 2012

##### 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**

Spring 2014

##### 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 2013

##### 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 2010, Fall 2012, Spring 2014, Fall 2014

##### 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 2011, Spring 2013

##### 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 2010, Winter 2011, Spring 2011, Fall 2011, Winter 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014, Fall 2014, Spring 2015

##### MATH 0710 - Advanced Probablility 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.

Fall 2014