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.
Applications of probabilistic techniques in discrete mathematics, including classical ideas using expectation and variance as well as modern tools, such as martingale and correlation inequalities.
Description, institutional features, and mathematical modeling of fixed income securities. Use of both deterministic and stochastic models. Crosslisted with ISYE 6769.
The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.
Continuous time Markov chains. Uniformization, transient and limiting behavior. Brownian motion and martingales. Optional sampling and convergence. Modeling of inventories, finance, flows in manufacturing and computer networks. (Also listed as ISyE 6762)
