MAST 687 Control Theory (3 credits)Linear algebraic background material, linear differential and control systems, controllability and observability, properties of the attainable set, the maximal principle and time-optimal control.MAST 681 Optimization (3 credits)Introduction to nonsmooth analysis: generalized directional derivative, generalized gradient, nonsmooth calculus; connections with convex analysis. Mathematical programming: optimality conditions; generalized multiplier approach to constraint qualifications and sensitivity analysis. Application of the theory: functions defined as pointwise maxima of a family of functions; minimizing the maximal eigenvalue of a matrix-valued function; variational analysis of an extended eigenvalue problem.MAST 682 Matrix Analysis (3 credits)Jordan canonical form and applications, Perron-Frobenius theory of nonnegative matrices with applications to economics and biology, generalizations to matrices which leave a cone invariant.MAST 683 Numerical Analysis (3 credits)This course consists of fundamental topics in numerical analysis with a bias towards analytical problems involving optimization integration, differential equations and Fourier transforms. The computer language C++ will be introduced and studied as part of this course; the use of functional programming and graphical techniques will be strongly encouraged. By the end of the course, students should have made a good start on the construction of a personal library of tools for exploring and solving mathematical problems numerically.

MAST 722 Advanced Pension Mathematics (3 credits)Valuation methods, gains and losses, stochastic returns, dynamic control.MAST 723 Portfolio Theory (3 credits)Asset and liability management models, optimal portfolio selection, stochastic returns, special topics.MAST 724 Risk Theory (3 credits)General risk models; renewal processes; Cox processes; surplus control.MAST 725 Credibility Theory (3 credits)Classical, regression and hierarchical Bayes models, empirical credibility, robust credibility, special topics.MAST 726 Loss Distributions (3 credits)Heavy tailed distributions, grouped/censured data, point and interval estimation, goodness-of-fit, model selection.MAST 727 Risk Classification (3 credits)Cluster analysis, principal components, discriminant analysis, Mahalanobis distance, special topics.

MAST 672 Statistical Inference I (3 credits)Order statistics; estimation theory; properties of estimators; maximum likelihood method; Bayes estimation; sufficiency and completeness; interval estimation; shortest length confidence interval; Bayesian intervals; sequential estimation.MAST 673 Statistical Inference II (3 credits)Testing of hypotheses; Neyman-Pearson theory; optimal tests; linear hypotheses; invariance; sequential analysis.MAST 674 Multivariate Analysis (3 credits)An introduction to multivariate distributions will be provided; multivariate normal distribution and its properties will be investigated. Estimation and testing problems related with multivariate normal populations will be discussed with emphasis on Hotellings generalized T2 and Wishart distribution. Other multivariate techniques including MANOVA; canonical correlations and principal components may also be introduced.MAST 670 Mathematical Methods in Statistics (3 credits)This course will discuss mathematical topics which may be used concurrently or subsequently in other statistics stream courses. The topics will come mainly from the following broad categories; 1) geometry of Euclidean space; 2) matrix theory and distribution of quadratic forms; 3) measure theory applications (Reimann-Stieltjes integrals); 4) complex variables (characteristic functions and inversion); 5) inequalities (Cauchy-Schwarz, Holder, Minkowski, etc.) and numerical techniques (Newton-Raphson algorithm, scoring method, statistical differentials); 6) some topics from probability theory.