Combinatorial problem-solving techniques including the use of generating functions, recurrence relations, Polya theory, combinatorial designs, Ramsey theory, matroids, and asymptotic analysis.
This course is a problem oriented introduction to the basic concepts of probability and statistics, providing a foundation for applications and further study.
Elementary combinatorial techniques used in discrete problem solving: counting methods, solving linear recurrences, graph and network models, related algorithms, and combinatorial designs.
Minimization of functionals, Euler Lagrange equations, sufficient conditions for a minimum, geodesic, isoperimetric and time of transit problems, variational principles of mechanics, applications to control theory.
An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (2nd of two courses in sequence)