Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
204 Kerchof Hall
81 Hospital DrCharlottesville, Virginia 22903
Scaling Limits for Measure-Valued Processes with Applications to Stochastic Networks
Source: U.S. NSF - Directorate Math. & Physical Sciences
September 15, 2011 – August 31, 2015
A second calculus course for business/biology/and social-science students. Topics include differential equations/infinite series/analysis of functions of several variables/analysis of probability density functions of continuous random variables. The course begins with a review of basic single-variable calculus. Prerequisite: MATH 1210 or equivalent; at most one of MATH 1220 and MATH 1320 may be taken for credit.
Introduces fundamental concepts/techniques of probability/the theory of randomness. Focuses on problem solving/understanding key theoretical ideas. Topics include sample spaces combinatorial analysis/discrete and continuous random variables/classical distributions/expectation/Chebyshev's inequality/independence/central limit theorem/conditional probability/generating functions. Prerequisite: MATH 1320. Recommended: knowledge of double integrals.
Topics in probability selected from Random walks, Markov processes, Brownian motion, Poisson processes, branching processes, stationary time series, linear filtering and prediction, queuing processes, and renewal theory. Prerequisite: MATH 3100 or APMA 3100; and a knowledge of matrix algebra
This class introduces students to the mathematics used in pricing derivative securities. Topics include a review of the relevant probability theory of conditional expectation and martingales/the elements of financial markets and derivatives/pricing contingent claims in the binomial & the finite market model/(time permitting) the Black-Scholes model. Prerequisites: MATH 3100, MATH 3351 and a proof-based course (MATH 3000, MATH 3310 or MATH 3354).
The Pavilion Seminars are open, by instructor permission, to 3rd and 4th year students. They are 3-credit, multidisciplinary seminars, focused on big topics and limited to max. 15 students each. For detailed descriptions of current offerings, see http://college.artsandsciences.virginia.edu/PAVS.
Rigorous introduction to probability, using techniques of measure theory. Includes limit theorems, martingales, and stochastic processes. Prerequisite: 7310 or equivalent.
Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.
For doctoral research, taken before a dissertation director has been selected.
The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.