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MATH 107-01, Linear Methods, Fall 2004

Seaton, Christopher
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Seaton, Christopher
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Mathematics and Computer Science, Department of, Syllabus, Curriculum, Academic departments, Text, 2004 Fall
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2004_fall_MATH_107-01_10404.pdf
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http://hdl.handle.net/10267/1418
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. Content: We will briefly review the material in sections 1.1 through 1.4 of the text, although I will assume that you are familiar with this material. Then, we will cover Chapters 2: Systems of Linear Equations and Matrices, Chapter 3: Matrix Algebra and Applications, Chapter 9: Markov Systems, and Chapter 4: Linear Programming, in that order. Time permitting, we will cover Chapter 5: The Mathematics of Finance.
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This syllabus was submitted to the Rhodes College Office of Academic Affairs by the course instructor.