Synopses & Reviews
Learn to build and use mathematical models with MATHEMATICAL MODELING AND COMPUTER SIMULATION! Through the description of mathematical and computer models in a variety of situations, this mathematics text helps you learn that model building is a dynamic process involving simplification, approximation, abstraction, analysis, computation, and comparison. Case studies illustrate how the model building process is applied to real life situations arising in a variety of settings, including business, genetics, population biology, and social science. An appendix on student projects provides you with a selection of classroom-tested projects with hints and suggestions for organizing project work and communicating results.
Review
"I was very impressed with the overall approach to the topic of Mathematical Modeling. I felt that the introduction to the subject of Modeling was one of the best that I have ever read."
Review
"I was very impressed with the overall approach to the topic of Mathematical Modeling. I felt thatthe introduction to the subject of Modeling was one of the best that I have ever read."
Review
"The authors focus on the process of model building and the subsequent analysis and evaluation. They make a clear effort to get the student to think about the material. Also, the exercises are well thought out, and are not simply ones that students can do by mimicking examples provided in the text."
Synopsis
Daniel Maki and Maynard Thompson provide a conceptual framework for the process of building and using mathematical models, illustrating the uses of mathematical and computer models in a variety of situations. This text helps students learn that model building is a dynamic process involving simplification, approximation, abstraction, analysis, computation, and comparison. Students begin the process of model building with a consideration of phenomena arising in another academic area or in the real world.
About the Author
Daniel P. Maki is the Chair of the Department of Mathematics at Indiana University. His research interests include the study of algorithms related to speech recognition by computer, including hidden Markov models, neural networks, and traditional signal processing. He is on the Board of Governors for the MAA and on the MAA Committee on the Undergraduate Program in Mathematics. Maynard Thompson has research interests in the applications of mathematics to problems arising in biology and medicine. He served as Chairman of the CUPM Committee on Applied Mathematics, on the SIAM Education Committee, on the MCM Advisory Board, and as a Visiting Lecturer for the MAA and SIAM. He has written research and expository articles and lectured in workshops and conferences on mathematical modeling in the social and life sciences.
Table of Contents
1. BASIC PRINCIPLES. Overview of the Uses of the Term Model. The Process of Constructing Mathematical Models. Types of Mathematical Models. A Classic Example. Axiom Systems and Models. Simulation Models. Practical Aspects of Model Building. 2. MODEL BUILDING: SELECTED CASE STUDIES. Introduction. Mendelian Genetics. Models for Growth Processes. Social Choice. Moving Mobile Homes. A Stratified Population Model. Selected Simulations. Waiting in Line Again! Estimating Parameters and Testing Hypotheses. 3. MARKOV CHAINS. Introduction. The Setting and Some Examples. Basic Properties of Markov Chains. Regular Markov Chains. Absorbing Chains and Applications. 4. SIMULATION MODELS. Introduction. The Simulation Process. Discrete Random Variables. Discrete Event Simulation. Continuous Random Variables. Applications. 5. LINEAR PROGRAMMING MODELS. Introduction. Formulation of Linear Programming Problems. Linear Programming Problems and Duality. Duality, Sensitivity, and Uncertainty. Job Assignment. Networks and Flows. Appendix A: Projects and Presentations. Introduction. Types of Projects. Examples of Projects. Reports and Presentations. Evaluating Project Reports. Sources of Projects.