Mathematical Modeling in the Social and Life Sciences 1st Edition by Michael Olinick – Ebook PDF Instant Download/Delivery: 978-1118642696, 1118642694
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Product details:
ISBN 10: 1118642694
ISBN 13: 978-1118642696
Author: Michael Olinick
The goal of this book is to encourage the teaching and learning of mathematical model building relatively early in the undergraduate program. The text introduces the student to a number of important mathematical topics and to a variety of models in the social sciences, life sciences, and humanities.
Table of contents:
1. Mathematical Models
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Mathematical Systems and Models
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An Example: Modeling Free Fall
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Discrete Examples: Credit Cards and Populations
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Classification of Mathematical Models
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Uses and Limitations of Mathematical Models
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Exercises
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Suggested Projects
2. Stable and Unstable Arms Races
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The Real-World Setting
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Constructing a Deterministic Model
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A Simple Model for an Arms Race
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The Richardson Model
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Interpreting and Testing the Richardson Model
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Obtaining an Exact Solution
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Exercises
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Suggested Projects
3. Ecological Models: Single Species
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Introduction
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The Pure Birth Process
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Exponential Decay
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Logistic Population Growth
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The Discrete Model of Logistic Growth and Chaos
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The Allee Effect
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Historical and Biographical Notes
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Exercises
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Suggested Projects
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Biographical References
4. Ecological Models: Interacting Species
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Introduction
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Two Real-World Situations
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Autonomous Systems
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The Competitive Hunters Model
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The Predator-Prey Model
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Concluding Remarks on Simple Models in Population Dynamics
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Biographical Sketches
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Exercises
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Suggested Projects
5. Tumor Growth Models
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Introduction
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A General Tumor Growth Model
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The Gompertz Model
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Modeling Colorectal Cancer
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Historical and Biographical Notes
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Exercises
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Suggested Projects
6. Social Choice and Voting Procedures
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Three Voting Situations
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Two Voting Mechanisms
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An Axiomatic Approach
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Arrow’s Impossibility Theorem
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The Liberal Paradox and the Theorem of the Gloomy Alternatives
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Instant Runoff Voting
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Approval Voting
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Topological Social Choice
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Historical and Biographical Notes
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Exercises
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Suggested Projects
7. Foundations of Measurement Theory
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The Registrar’s Problem
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What Is Measurement?
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Simple Measures on Finite Sets
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Perception of Differences
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An Alternative Approach
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Some Historical Notes
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Exercises
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Suggested Projects
8. Introduction to Utility Theory
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Introduction
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Gambles
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Axioms of Utility Theory
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Existence and Uniqueness of Utility
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Classification of Scales
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Interpersonal Comparison of Utility
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Historical and Biographical Notes
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Exercises
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Suggested Projects
9. Equilibrium in an Exchange Economy
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Introduction
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A Two-Person Economy with Two Commodities
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An m-Person Economy
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Existence of Economic Equilibrium
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Some Remaining Questions
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Historical and Biographical Notes
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Exercises
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Suggested Projects
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Additional Historical and Biographical Notes
10. Elementary Probability
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The Need for Probability Models
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What Is Probability?
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A Probabilistic Model
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Stochastic Processes
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Exercises
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Suggested Projects
11. Markov Processes
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Markov Chains
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Matrix Operations and Markov Chains
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Regular Markov Chains
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Absorbing Markov Chains
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Historical and Biographical Notes
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Exercises
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Suggested Projects
12. Two Models of Cultural Stability
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Introduction
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The Gadaa System
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A Deterministic Model
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A Probabilistic Model
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Criticisms of the Models
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Hans Hoffmann
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Exercises
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Suggested Projects
13. Paired-Associate Learning
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The Learning Problem
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The Model
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Testing the Model
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Historical and Biographical Notes
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Exercises
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Suggested Projects
14. Epidemics
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Introduction
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Deterministic Models
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A Probabilistic Approach
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Historical and Biographical Notes
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Exercises
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Suggested Projects
15. Roulette Wheels and Hospital Beds: A Computer Simulation of Operating and Recovery Room Usage
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Introduction
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The Problems of Interest
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Projecting the Number of Surgical Procedures
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Estimating Operating Room Demands
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The Simulation Model
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Other Examples of Simulation
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Historical and Biographical Notes
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Exercises
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Suggested Projects
16. Game Theory
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Two Difficult Decisions
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Game Theory Basics
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The Binding of Isaac
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Tosca and the Prisoners’ Dilemma
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Nash Equilibrium
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Dynamic Solutions
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Historical and Biographical Notes
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Exercises
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Suggested Projects
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