Courses

• GRS MA 777: Multiscale Methods for Stochastic Processes and Differential Equations
  Methods and models for the analysis of systems that possess many characteristic length and time scales. Asymptotic expansions, coarse-graining of multiscale stochastic models, mathematical analysis and statistical inference. Balance of theory and concepts illustrated via various applications.
• GRS MA 779: Probability Theory I
  Introduction to probability with measure theoretic foundations. Fundamentals of measure theory. Probability space. Measurable functions and random variables. Expectation and conditional expectation. Zero-one laws and Borel-Cantelli lemmas. Chracteristic functions. Modes of convergence. Uniform integrability. Skorokhod representation theorem. Basic limit theorems.
• GRS MA 780: Probability Theory II
  Probability topics important in applications and research. Laws of large numbers. Three series theorem. Central limit theorems for independent and non-identically distributed random variables. Speed of convergence. Large deviations. Laws of the iterated logarithm. Stable and infinitely divisible distributions. Discrete time martingales and applications.
• GRS MA 781: Estimation Theory
  Review of probability, populations, samples, sampling distributions, and delta theorems. Parametric point estimation. Rao-Cramer inequality, sufficient statistics, Rao-Blackwell theorem, maximum likelihood estimation, least squares estimation, and general linear model of full rank. Confidence intervals. Bayesian analysis and decision theory.
• GRS MA 782: Hypothesis Testing
  Parametric hypothesis testing, uniformly and locally the most powerful tests, similar tests, invariant tests, likelihood ratio tests, linear model testing, asymptotic theory of likelihood ratio, and chi-squared test. Logit and log-lin analysis of contingency tables.
• GRS MA 821: Topics in Geom
  
• GRS MA 822: Topics in Geometry and Topology
  Advanced seminar in topics in differential geometry, topology and mathematical physics of current research interest.
• GRS MA 842: Seminar: Algebra
  
• GRS MA 861: Seminar: Applied Mathematics
  
• GRS MA 871: Seminar: Dynamical Systems
  
• GRS MA 876: Seminar: Partial Differential Equations
  
• GRS MA 881: Seminar: Statistics
  Advanced seminar in topics in statistics of current research interest.
• GRS MA 882: Seminar: Statistics
  Advanced seminar in topics in statistics of current research interest.
• GRS MA 884: Seminar in Probability and Statistics
  Invited speakers from the United States and abroad describe open problems and recent results.
• GRS MA 901: Internship in Statistics
  For masters students in statistics, entailing substantive experience in practical application of statistics in domain areas like biomedicine, finance, marketing, and similar. May be taken only once, with approval of the Director of the MSSP Program. Bi-weekly and final reports required.
• GRS MA 905: Directed Study: History of Mathematics
  
• GRS MA 906: Directed Study: History of Mathematics
  
• GRS MA 911: Directed Study: Real Analysis
  
• GRS MA 912: Directed Study: Real Analysis
  
• GRS MA 913: Directed Study: Complex Analysis
  

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