Professor of Mathematics
Degrees, Specializations & Interests:
A.B., Dartmouth College; M.S., Ph.D., Stanford University;
Applied Probability, Stochastic Processes
Courses offered in the past four years.
▲ indicates offered in the current term
▹ indicates offered in the upcoming term[s]
FYSE 1025 - Chance
Do movie reviews affect box-office revenues? Do the U.S. News rankings affect the size of Middlebury's applicant pool? In what sense do these assessments reflect "quality"? The Wall Street Journal recently asked, "Can eating breakfast cereal determine the sex of your baby?" Nowadays, you can't read the news, choose a college, or even enjoy breakfast without encountering statistical claims. Which would you trust to inform your life decisions? We will investigate these questions through readings that include your favorite newspaper, paleobiologist Stephen J. Gould's incisive essays on excellence and variability, and statistician Edward Tufte's trenchant critique of data graphics in the popular press. 3 hrs. sem.
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.
Spring 2010, Fall 2011, Fall 2013
MATH 0121 - 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.
Spring 2011, Fall 2012
MATH 0122 - 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.
MATH 0200 - 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.
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.
Fall 2010, Fall 2012, Spring 2014
MATH 0318 - 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)
MATH 0410 - 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.
Spring 2011, Spring 2013
MATH 0500 - 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 2009, Winter 2010, Spring 2010, Fall 2010, Winter 2011, Spring 2011, Fall 2011, Winter 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014, Spring 2014
MATH 0704 - Senior Seminar
Each student will explore in depth a topic in pure or applied mathematics, under one-on-one supervision by a faculty advisor. The course culminates with a major written paper and presentation. This experience emphasizes independent study, library research, expository writing, and oral presentation. The goal is to demonstrate the ability to internalize and organize a substantial piece of mathematics. Class meetings include attendance at a series of lectures designed to introduce and integrate ideas of mathematics not covered in the previous three years. Registration is by permission: Each student must have identified a topic, an advisor, and at least one principal reference source. 3 hrs. lect./disc.