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Mathematical Modeling in the Social and Life Sciences 1st Edition by Michael Olinick ISBN 978-1118642696 1118642694

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Mathematical Modeling in the Social and Life Sciences 1st Edition Michael Olinick Digital Instant Download

Author(s): Michael Olinick
ISBN(s): 9781118642696, 1118642694
Edition: 1
File Details: PDF, 18.47 MB
Year: 2014
Language: english
SKU: EB-4941698 Category: Tag:

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

  • Mathematical Systems and Models

  • An Example: Modeling Free Fall

  • Discrete Examples: Credit Cards and Populations

  • Classification of Mathematical Models

  • Uses and Limitations of Mathematical Models

  • Exercises

  • Suggested Projects

2. Stable and Unstable Arms Races

  • The Real-World Setting

  • Constructing a Deterministic Model

  • A Simple Model for an Arms Race

  • The Richardson Model

  • Interpreting and Testing the Richardson Model

  • Obtaining an Exact Solution

  • Exercises

  • Suggested Projects

3. Ecological Models: Single Species

  • Introduction

  • The Pure Birth Process

  • Exponential Decay

  • Logistic Population Growth

  • The Discrete Model of Logistic Growth and Chaos

  • The Allee Effect

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

  • Biographical References

4. Ecological Models: Interacting Species

  • Introduction

  • Two Real-World Situations

  • Autonomous Systems

  • The Competitive Hunters Model

  • The Predator-Prey Model

  • Concluding Remarks on Simple Models in Population Dynamics

  • Biographical Sketches

  • Exercises

  • Suggested Projects

5. Tumor Growth Models

  • Introduction

  • A General Tumor Growth Model

  • The Gompertz Model

  • Modeling Colorectal Cancer

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

6. Social Choice and Voting Procedures

  • Three Voting Situations

  • Two Voting Mechanisms

  • An Axiomatic Approach

  • Arrow’s Impossibility Theorem

  • The Liberal Paradox and the Theorem of the Gloomy Alternatives

  • Instant Runoff Voting

  • Approval Voting

  • Topological Social Choice

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

7. Foundations of Measurement Theory

  • The Registrar’s Problem

  • What Is Measurement?

  • Simple Measures on Finite Sets

  • Perception of Differences

  • An Alternative Approach

  • Some Historical Notes

  • Exercises

  • Suggested Projects

8. Introduction to Utility Theory

  • Introduction

  • Gambles

  • Axioms of Utility Theory

  • Existence and Uniqueness of Utility

  • Classification of Scales

  • Interpersonal Comparison of Utility

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

9. Equilibrium in an Exchange Economy

  • Introduction

  • A Two-Person Economy with Two Commodities

  • An m-Person Economy

  • Existence of Economic Equilibrium

  • Some Remaining Questions

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

  • Additional Historical and Biographical Notes

10. Elementary Probability

  • The Need for Probability Models

  • What Is Probability?

  • A Probabilistic Model

  • Stochastic Processes

  • Exercises

  • Suggested Projects

11. Markov Processes

  • Markov Chains

  • Matrix Operations and Markov Chains

  • Regular Markov Chains

  • Absorbing Markov Chains

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

12. Two Models of Cultural Stability

  • Introduction

  • The Gadaa System

  • A Deterministic Model

  • A Probabilistic Model

  • Criticisms of the Models

  • Hans Hoffmann

  • Exercises

  • Suggested Projects

13. Paired-Associate Learning

  • The Learning Problem

  • The Model

  • Testing the Model

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

14. Epidemics

  • Introduction

  • Deterministic Models

  • A Probabilistic Approach

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

15. Roulette Wheels and Hospital Beds: A Computer Simulation of Operating and Recovery Room Usage

  • Introduction

  • The Problems of Interest

  • Projecting the Number of Surgical Procedures

  • Estimating Operating Room Demands

  • The Simulation Model

  • Other Examples of Simulation

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

16. Game Theory

  • Two Difficult Decisions

  • Game Theory Basics

  • The Binding of Isaac

  • Tosca and the Prisoners’ Dilemma

  • Nash Equilibrium

  • Dynamic Solutions

  • Historical and Biographical Notes

  • Exercises

  • Suggested Projects

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Tags: Michael Olinick, Mathematical Modeling, the Social