"Mathematics is not for spectators. In order to gain in understanding, confidence, and enthusiasm one has to participate." - M.A. Armstrong
Text: Linear Programming: Foundations & Extensions (2nd ed.), Robert J. Vanderbei
Course Description: How do you construct an optimal portfolio while adhering to your covenant? What's the best way to implement a court ordered public school busing program? Given the current market conditions which product line leads to the greatest profitability for our company? These are examples of questions that people are faced with every day and the optimal solutions are usually never clear - if they even exist. One tool that is often implemented to aid in the decision making process is mathematical programming.
Mathematical programming is a method for abstracting the salient features of a problem in a way that makes the scenario amenable to mathematical analysis. In this course we will study mathematical programs of the linear variety. We will begin by learning what a linear program is and how we can convert real world problems into this paradigm. We will then focus on the simplex method - a standard technique for solving linear programs. Our study of the simplex method will lead us into discussions of duality theory, implementation issues, measuring the efficiency of algorithms, and other related topics. After these discussions we will study applications of linear programming to some of the following: game theory, network flows and data enveloping analysis (DEA). If time permits we will also address integer programming and interior point methods.
Target Audience: This course may be of interest to students majoring in mathematics, computer science and the social sciences who would like to explore a mathematical approach to decision making and also have an interest in understanding the theory behind the techniques employed.
Prerequisites: Math 6, 8 or 9, some knowledge of matrix algebra and solving systems of linear equations, and mathematical maturity.
Special Concerns: If you have any special concerns you should speak to me as soon as possible. In particular, if you have a disability and may require disability-related accomodations please speak to me as soon as possible, so we can find a remedy. Also, if you have athletic or other extracurricular committments and hope to accomodate them (i.e., taking mid-terms at alternative times), then you should see me as soon as you are aware of them.