MATH 107-03, Linear Methods, Fall 2004

Abstract

We will begin with a brief review of (systems of) linear equations. Then, we will learn how to solve linear systems using Gauss-Jordan elimination. We sill discuss matrix algebra with applications to input-output analysis and Markov processes Input-output analysis is used to determine how interdependent producers should behave. Markov processes are used to predict long term values of interdependent quantities that vary probabilistically. Next, we will talk about linear programming (LP) problems. An LP problem is on in which you seek to maximize a linear function—profit, for example—subject to certain linear constraints, such as budgetary or workforce limitations. You will learn to solve LP problems geometrically, using the simplex method, and by computer. Integer and 0-1 programming problems, which are closely related to LP problems, are too labor-intensive to solve by hand. We will learn how to solve them using Excel. We will touch briefly on the subject of computational complexity. We will take a look at game theory, the study of strategic interactions between competing interests. We will explore the connection between game theory and LP problems. Finally, we will look at the mathematics of finance. Here we study how different forms of interest can affect loans and investments.