Courses

The listing of a course description here does not guarantee a course’s being offered in a particular term. Please refer to the published schedule of classes on the MyBU Student Portal for confirmation a class is actually being taught and for specific course meeting dates and times.

• CAS MA 779: Probability Theory 1
  Prerequisites: (CASMA 511) or consent of instructor. - 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.
• CAS MA 780: Probability Theory 2
  Prerequisites: (CASMA 711) - 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.
• CAS MA 781: Estimation Theory
  Prerequisites: (CASMA 581) AND (CASMA 582) or consent of instructor. - 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.
• CAS MA 782: Hypothesis Testing
  Prerequisites: (CASMA 781) or consent of instructor. - 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.
• CAS MA 783: Advanced Stochastic Processes
  Prerequisites: (CASMA 779 or CASMA 780) or consent of instructor. - Proof-based approach to stochastic processes. Brownian motion. Continuous martingales. Stochastic integration. Ito formula. Girsanov's Theorem. Stochastic differential equations. Feynman-Kac formula. Markov Processes. Local times. Levy processes. Semimartingales and the general stochastic integral. Stable processes. Fractional Brownian motion.
• CAS MA 821: TOPICS IN GEOM
  TOPICS IN GEOM
• CAS MA 822: Topics in Geometry and Topology
  rerequisites: (CASMA 725) AND (CASMA 728) AND (CASMA 726 or CASMA 727) - Advanced seminar in topics in differential geometry, topology and mathematical physics of current research interest.
• CAS MA 841: Seminar: Algebra
  ALGEBRA SEMINAR
• CAS MA 842: Seminar: Algebra
  ALGEBRA SEMINAR
• CAS MA 861: Seminar: Applied Mathematics
  APP MA SEM
• CAS MA 876: Seminar: Partial Differential Equations
  PDE SEMINAR
• CAS MA 881: Seminar: Statistics
  Prerequisites: (CASMA 782) - Advanced seminar in topics in statistics of current research interest.
• CAS MA 882: Seminar: Statistics
  Prerequisites: (CASMA 782) - Advanced seminar in topics in statistics of current research interest.
• CAS MA 901: Internship in Statistics
  Graduate Prerequisites: master's student standing in statistics in the Department of Mathematics & 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.
• CAS MA 905: Directed Study: History of Mathematics
  DS HIS OF MATH1
• CAS MA 906: Directed Study: History of Mathematics
  DS HIS OF MATH2
• CAS MA 911: Directed Study: Real Analysis
  DS REAL ANALYS1
• CAS MA 912: Directed Study: Real Analysis
  DS REAL ANALYS2
• CAS MA 913: Directed Study: Complex Analysis
  DS COMPLX ANAL1
• CAS MA 914: Directed Study: Complex Analysis 2
  Directed Study: Complex Analysis 2