book

Mathematical Modeling in the Social and Life Sciences

by Michael Olinick

May 2014

Intermediate to advanced

588 pages

19h 30m

English

Wiley

Read now

Unlock full access

Structure of the BookConcluding Remarks
I. Mathematical Systems and ModelsII. An Example: Modeling Free FallIII. Discrete Examples: Credit Cards and PopulationsIV. Classification of Mathematical ModelsV. Uses and Limitations of Mathematical ModelsEXERCISESSUGGESTED PROJECTS
I. The Real-World SettingII. Constructing a Deterministic ModelIII. A Simple Model for an Arms RaceIV. The Richardson ModelV. Interpreting and Testing the Richardson ModelVI. Obtaining an Exact SolutionEXERCISESSUGGESTED PROJECTS
I. IntroductionII. The Pure Birth ProcessIII. Exponential DecayIV. Logistic Population GrowthV. The Discrete Model of Logistic Growth and ChaosVI. The Allee EffectVII. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTSBIOGRAPHICAL REFERENCES

I. IntroductionII. Two Real-World SituationsIII. Autonomous SystemsIV. The Competitive Hunters ModelV. The Predator-Prey ModelVI. Concluding Remarks on Simple Models in Population DynamicsVII. Biographical SketchesEXERCISESSUGGESTED PROJECTS
I. IntroductionII. A General Tumor Growth ModelIII. The Gompertz ModelIV. Modeling Colorectal CancerV. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
I. Three Voting SituationsII. Two Voting MechanismsIII. An Axiomatic ApproachIV. Arrow's Impossibility TheoremV. The Liberal Paradox and the Theorem of the Gloomy AlternativesVI. Instant Runoff VotingVII. Approval VotingVIII. Topological Social ChoiceIX. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
I. The Registrar's ProblemII. What Is Measurement?III. Simple Measures on Finite SetsIV. Perception of DifferencesV. An Alternative ApproachVI. Some Historical NotesEXERCISESSUGGESTED PROJECTS
I. IntroductionII. GamblesIII. Axioms of Utility TheoryIV. Existence and Uniqueness of UtilityV. Classification of ScalesVI. Interpersonal Comparison of UtilityVII. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
I. IntroductionII. A Two-Person Economy with Two CommoditiesIII. An m -Person EconomyIV. Existence of Economic EquilibriumV. Some Remaining QuestionsVI. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTSVII. Additional Historical and Biographical Notes
I. The Need for Probability ModelsII. What Is Probability?III. A Probabilistic ModelIV. Stochastic ProcessesEXERCISESSUGGESTED PROJECTS
I. Markov ChainsII. Matrix Operations and Markov ChainsIII. Regular Markov ChainsIV. Absorbing Markov ChainsV. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
I. IntroductionII. The Gadaa SystemIII. A Deterministic ModelIV. A Probabilistic ModelV. Criticisms of the ModelsVI. Hans HoffmannEXERCISESSUGGESTED PROJECTS
I. The Learning ProblemII. The ModelIII. Testing the ModelIV. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
I. IntroductionII. Deterministic ModelsIII. A Probabilistic ApproachIV. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
I. IntroductionII. The Problems of InterestIII. Projecting the Number of Surgical ProceduresIV. Estimating Operating Room DemandsV. The Simulation ModelVI. Other Examples of SimulationVII. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
I. Two Difficult DecisionsII. Game Theory BasicsIII. The Binding of IsaacIV. Tosca and the Prisoners' DilemmaV. Nash EquilibriumVI. Dynamic SolutionsVII. Historical and Biographical NotesEXERCISESSUGGESTED PROJECTS
EXERCISES
EXERCISES
Computing the Inverse of a Square MatrixEXERCISES
EXERCISES
EXERCISES

Overview

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.