printer friendly pageMATH 226: Numerical Solution of Partial Differential Equations (CME 306)
Hyperbolic partial differential equations: stability, convergence and qualitative properties; nonlinear hyperbolic equations and systems; combined solution methods from elliptic, parabolic, and hyperbolic problems. Examples include: Burger's equation, Euler equations for compressible flow, Navier-Stokes equations for incompressible flow. Prerequisites:
MATH 220A or
CME 302.
Terms: Spr
| Units: 3
Instructors:
Ying, L. (PI)
MATH 228: Stochastic Methods in Engineering (CME 308)
Review of basic probability; Monte Carlo simulation; state space models and time series; parameter estimation, prediction, and filtering; Markov chains and processes; stochastic control; and stochastic differential equations. Examples from various engineering disciplines. Prerequisites: exposure to probability; background in real variables and analysis.
Terms: Spr
| Units: 3
Instructors:
Papanicolaou, G. (PI)
MATH 230C: Theory of Probability (STATS 310C)
Continuous time stochastic processes: martingales, Brownian motion, stationary independent increments, Markov jump processes and Gaussian processes. Invariance principle, random walks, LIL and functional CLT. Markov and strong Markov property. Infinitely divisible laws. Some ergodic theory. Prerequisite: 310B or
MATH 230B.
Terms: Spr
| Units: 2-4
Instructors:
Chatterjee, S. (PI)
MATH 231: Orthogonal Polynomials and the Moment Problem
Orthogonal polynomials in one variable (three term recurrence, Favard's theorem, distribution of zeros Verblunsky coefficients). Classical examples (Hermite, Chebychev, Jacobi, Meixner, Askey-Wilson). Applications in probability (Markov chains), Statistics (multivariate distributions with given margins), Numerical analysis (Gaussian Quadriture), Combinatorics (combinatorial interpretation of the classical orthogonal polynomials). The moment problem on R (when is a measure determined by its moments, what happens if not?). Multivariate orthogonal polynomials (with an introduction to symmetric function theory). Connections to group representations.
Terms: Spr
| Units: 3
Instructors:
Diaconis, P. (PI)
MATH 237: Default and Systemic Risk
Introduction to mathematical models of complex static and dynamic stochastic systems that undergo sudden regime change in response to small changes in parameters. Examples from materials science (phase transitions), power grid models, financial and banking systems. Special emphasis on mean field models and their large deviations, including computational issues. Dynamic network models of financial systems and their stability.
Terms: Spr
| Units: 3
Instructors:
Papanicolaou, G. (PI)
MATH 239: Computation and Simulation in Finance
Monte Carlo, finite difference, tree, and transform methods for the numerical solution of partial differential equations in finance. Emphasis is on derivative security pricing. Prerequisite: 238 or equivalent.
Terms: Spr
| Units: 3
Instructors:
Menz, G. (PI)
MATH 245C: Topics in Algebraic Geometry
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Li, Z. (PI)
MATH 249C: Topics in Number Theory
Terms: Spr
| Units: 3
| Repeatable
for credit
Instructors:
Conrad, B. (PI)
MATH 257C: Symplectic Geometry and Topology
Continuation of 257B. May be repeated for credit.
Terms: Spr
| Units: 3
Instructors:
Lin, Y. (PI)
MATH 258: Topics in Geometric Analysis
May be repeated for credit.
Terms: Win, Spr
| Units: 3
| Repeatable
for credit
Instructors:
Mazzeo, R. (PI)
;
White, B. (PI)
Filter Results: