Linear Optimization: The object of this course is the understanding of the mathematics of optimization problems with a finite number of variables subject to linear constraints. The primary tool will be linear programming (primarily tucker tableau). We will also consider other kinds of optimization problems (matrix games--game theory, flows in networks, transportation problems, etc,) which have a similar flavor but whose solution is not solely based on linear programming.

Applied Math: Mathematical problems that arise from real-world applications often do not possess exact solutions due to complicating characteristics, such as uncertainty and non-linearities (functions that are not in the form y=kx+b, such as y=x^3). This course will introduce theory and techniques useful for deriving and interpreting approximate, numeric, or probabilistic solutions to mathematical problems. Standard topics include stochastic processes -- probability considering time variable (half of the time) and perturbation methods. Applications will be developed and illustrated on examples drawn from areas such as physics, biology, chemistry, and industry. Notice that we will spend approximately half of the time on probability theory and stochastic process--which doesn’t require any pre-experience but simply basic understanding of probabilities.