Courses
MATH-7/8033 - Intelligent Decision Support
Mathematical foundations of decision support systems are addressed. Topics include basic operation research areas of mathematical programming and optimization, such as linear and nonlinear programming, integer and mixed-integer programming, dynamic and approximate dynamic programming, and combinatorial optimization. Mathematical decision theory is addressed, including multistage decisions, Markov chains, decision trees, game theory, and multi-objective optimization. Mathematical models are developed and solved for practical decision support problems, covering business, finance, engineering, cognitive and health applications.
MATH-7/8028 Intelligent Prediction Methods
Theoretical foundations of predictions are described, including deterministic and
stochastic systems, autoregressive (AR), ARMA, and Kalman filtering. Recent developments
are introduced in cognitive prediction, vector prediction, network prediction, time-lagged
recurrent neural networks, and lattice models. Issues of generalization, convergence,
and Lyapunov stability of prediction methods are addressed. Applications in image
processing, in financial systems and in engineering are discussed.
MATH-7/8047 ADP, Stochastic Optimization & Control
Mathematical foundations of neural networks, learning, nonlinear optimization and
control. Exact and approximate optimization of the utility function. Bellman equation,
approximate Bellman equation for solving multivariate optimization problems in real
time. Partially observable variables, with random noise and tactical objectives varying
in time.