William Peterson

Professor of Mathematics

 work(802) 443-5417
 Academic Leave Winter & Spring 2018
 on leave winter/spring

Degrees, Specializations & Interests:
A.B., Dartmouth College; M.S., Ph.D., Stanford University;

Applied Probability, Stochastic Processes




Course List: 

Courses offered in the past four years.
indicates offered in the current term
indicates offered in the upcoming term[s]

FYSE 1025 - Chance      

Chance *
A prominent statistician once wrote, “Statistics exists only at the interfaces of chance and empirical data. But it exists at every such interface.” Are most cancers attributable to bad luck, as Forbes recently suggested? Do fluctuations in US News college rankings reflect educational quality? Is texting while driving riskier than drunk driving? You can't follow the news, choose a college, or even get behind the wheel without encountering statistical claims. Which should you trust? Our readings will include your favorite newspaper, Stephen J. Gould's essays on excellence and variability, and Edward Tufte's critique of data graphics in the popular press.. 3 hrs. sem.

Fall 2015

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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 2015, Fall 2016, Fall 2017

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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 2015

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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

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MATH 0310 - 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 2014, Fall 2016, Fall 2017, Fall 2018

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MATH 0318 - Operations Research      

Operations Research
Operations research is the utilization of quantitative methods as an aid to managerial decisions. In the course, several of these methods will be introduced and studied in both a mathematical context and a physical context. Topics included will be selected from the following: classification of problems and the formulation of models, linear programming, network optimization, transportation problems, assignment problems, integer programming, nonlinear programming, inventory theory, and game theory. (MATH 0200 or waiver) DED

Spring 2016

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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 2015, Spring 2017

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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 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016, Winter 2017, Spring 2017, Winter 2018

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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 Itô 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, Spring 2016

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Math 116


Department of Mathematics

Warner Hall
303 College Street
Middlebury College
Middlebury, VT 05753