Mathematical Modeling in the Social and Life Sciences

Contents

Preface

Acknowledgements

1   Mathematical Models

I. Mathematical Systems and Models

II. An Example: Modeling Free Fall

III. Discrete Examples: Credit Cards and Populations

IV. Classification of Mathematical Models

V. Uses and Limitations of Mathematical Models

Exercises

Suggested Projects

2   Stable and Unstable Arms Races

I. The Real-World Setting

II. Constructing a Deterministic Model

III. A Simple Model for an Arms Race

IV. The Richardson Model

V. Interpreting and Testing the Richardson Model

VI. Obtaining an Exact Solution

Exercises

Suggested Projects

3   Ecological Models: Single Species

I. Introduction

II. The Pure Birth Process

III. Exponential Decay

IV. Logistic Population Growth

V. The Discrete Model of Logistic Growth and Chaos

VI. The Allee Effect

VII. Historical and Biographical Notes

Exercises

Suggested Projects

Biographical References

4   Ecological Models: Interacting Species

I. Introduction

II. Two Real-World Situations

III. Autonomous Systems

IV. The Competitive Hunters Model

V. The Predator-Prey Model

VI. Concluding Remarks on Simple Models in Population Dynamics

VII. Biographical Sketches

Exercises

Suggested Projects

5   Tumor Growth Models

I. Introduction

II. A General Tumor Growth Model

III. The Gompertz Model

IV. Modeling Colorectal Cancer

V. Historical and Biographical Notes

Exercises

Suggested Projects

6   Social Choice and Voting Procedures

I. Three Voting Situations

II. Two Voting Mechanisms

III. An Axiomatic Approach

IV. Arrow's Impossibility ...