Metric spaces, uniform convergence, elements of Banach spaces, elements of functions of complex variable. Problem solving and independent proof writing. Review of selected advanced topics in analysis for the PhD preliminary examination.
Instructor: Dr. Stanley Payne
Term: Fall 2010
Final grade: A-

Examines elementary theory of probability, including independence, conditional probability, and Bayes’ theorem; random variables, expectations and probability distributions; joint and conditional distributions; functions of random variables; limit theorems, including the central limit theorem.
Instructor: Dr. Markus Emsermann
Textbook: A First Course in Probability by Sheldon Ross
Term: Summer 2009
Final grade: A

Vector spaces, practical solution of systems of equations, projections, eigenvalues and eigenvectors, unitary transformations, Schur QR, singular value decompositions, similarity transformations, Jordan forms, and positive definite matrices.
Instructor: Dr. Julien Langou
Textbook: Linear Algebra Done Right by Sheldon Jay Axler
Term: Spring 2011
Final grade: A

Markov chains; Poisson processes, continuous time Markov chains, elementary topics in queuing theory, and some mathematical aspects of Monte Carlo simulation, including random variate generation, variance reduction, and output analysis.
Instructor: Dr. Burt Simon
Textbook: Introduction to Probability Models by Sheldon Ross
Term: Fall 2009
Final grade: A

Computationally-intensive methods in statistics, including random number generation and Monte Carlo methods, data partitioning and re-sampling, numerical and graphical methods, nonparametric function estimation, statistical models and data mining methodology, analysis of large data sets.
Instructor: Dr. Steven Culpepper
Textbook: Statistical Computing with R by Maria Rizzo
Term: Spring 2010
Final grade: A

Markov processes in discrete and continuous time, renewal theory, martingales, Brownian motion, branching processes, and stationary processes. Applications include queuing theory, performance evaluation of computer and communication systems and finance.
Instructor: Dr. Burt Simon
Textbook: Introduction to Stochastic Processes by Gregory F. Lawler
Term: Fall 2010
Final grade: A

Mathematical theory of statistics. Parametric inference: discrete and continuous distributions, methods of parameter estimation, confidence intervals.
Instructor: Dr. Stephanie Santorico
Textbook: Statistical Inference by George Casella and Roger L. Berger
Term: Fall 2011
Final grade: Currently in progress

(Continuation of MATH 7381.) Hypothesis testing, robust estimation, tolerance intervals, nonparametric inference, sequential methods.
Instructor: Dr. Stephanie Santorico
Textbook: Statistical Inference by George Casella and Roger L. Berger
Term: Spring 2012
Final grade: Enrolled for next semester

Measurable spaces, probability measures, random variables, conditional expectations and martingales. Convergence in probability, almost sure convergence, convergence in distribution, limit theorems (law of large numbers, central limit theorem, laws of iterated logarithm).
Instructor: Dr. Anatolli Puhalskii
Textbook: First Look at Rigorous Probability Theory by Jeffrey S. Rosenthal
Term: Spring 2010
Final grade: A-

Field theory, Galois theory, Modules over rings, especially over integral domains.
Instructor: Dr. Stanley Payne
Textbook: Abstract Algebra by David S. Dummit and Richard M. Foote
Term: Spring 2011
Final grade: A-