Overview
- Authors:
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Gilbert G. Walter
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Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, USA
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Martha Contreras
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Department of Biometry, Cornell University, Ithaca, USA
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Table of contents (23 chapters)
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Front Matter
Pages i-xviii
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Introduction and Simple Examples
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- Gilbert G. Walter, Martha Contreras
Pages 1-8
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Structure of Models: Directed Graphs
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- Gilbert G. Walter, Martha Contreras
Pages 11-16
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- Gilbert G. Walter, Martha Contreras
Pages 17-24
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- Gilbert G. Walter, Martha Contreras
Pages 25-40
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- Gilbert G. Walter, Martha Contreras
Pages 41-46
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- Gilbert G. Walter, Martha Contreras
Pages 47-51
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- Gilbert G. Walter, Martha Contreras
Pages 53-61
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Digraphs and Probabilities: Markov Chains
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- Gilbert G. Walter, Martha Contreras
Pages 65-69
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- Gilbert G. Walter, Martha Contreras
Pages 71-80
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- Gilbert G. Walter, Martha Contreras
Pages 81-87
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- Gilbert G. Walter, Martha Contreras
Pages 89-99
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- Gilbert G. Walter, Martha Contreras
Pages 101-108
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Compartmental Models: Applications
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Front Matter
Pages 109-109
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- Gilbert G. Walter, Martha Contreras
Pages 111-123
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- Gilbert G. Walter, Martha Contreras
Pages 125-129
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- Gilbert G. Walter, Martha Contreras
Pages 131-139
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- Gilbert G. Walter, Martha Contreras
Pages 141-148
About this book
The subject of mathematical modeling has expanded considerably in the past twenty years. This is in part due to the appearance of the text by Kemeny and Snell, "Mathematical Models in the Social Sciences," as well as the one by Maki and Thompson, "Mathematical Models and Applica tions. " Courses in the subject became a widespread if not standard part of the undergraduate mathematics curriculum. These courses included var ious mathematical topics such as Markov chains, differential equations, linear programming, optimization, and probability. However, if our own experience is any guide, they failed to teach mathematical modeling; that is, few students who completed the course were able to carry out the mod eling paradigm in all but the simplest cases. They could be taught to solve differential equations or find the equilibrium distribution of a regular Markov chain, but could not, in general, make the transition from "real world" statements to their mathematical formulation. The reason is that this process is very difficult, much more difficult than doing the mathemat ical analysis. After all, that is exactly what engineers spend a great deal of time learning to do. But they concentrate on very specific problems and rely on previous formulations of similar problems. It is unreasonable to expect students to learn to convert a large variety of real-world problems to mathematical statements, but this is what these courses require.
Authors and Affiliations
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Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, USA
Gilbert G. Walter
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Department of Biometry, Cornell University, Ithaca, USA
Martha Contreras
