{"product_id":"mathematical-modeling-in-the-social-and-life-sciences-9781118642696","title":"Mathematical Modeling in the Social and Life","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eThe 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.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface viii\u003c\/p\u003e \u003cp\u003eAcknowledgements xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Mathematical Models 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Mathematical Systems and Models 1\u003c\/p\u003e \u003cp\u003eII. An Example: Modeling Free Fall 4\u003c\/p\u003e \u003cp\u003eIII. Discrete Examples: Credit Cards and Populations 10\u003c\/p\u003e \u003cp\u003eIV. Classification of Mathematical Models 16\u003c\/p\u003e \u003cp\u003eV. Uses and Limitations of Mathematical Models 18\u003c\/p\u003e \u003cp\u003eExercises 19\u003c\/p\u003e \u003cp\u003eSuggested Projects 21\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Stable and Unstable Arms Races 23\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. The Real-World Setting 23\u003c\/p\u003e \u003cp\u003eII. Constructing a Deterministic Model 25\u003c\/p\u003e \u003cp\u003eIII. A Simple Model for an Arms Race 25\u003c\/p\u003e \u003cp\u003eIV. The Richardson Model 28\u003c\/p\u003e \u003cp\u003eV. Interpreting and Testing the Richardson Model 45\u003c\/p\u003e \u003cp\u003eVI. Obtaining an Exact Solution 53\u003c\/p\u003e \u003cp\u003eExercises 59\u003c\/p\u003e \u003cp\u003eSuggested Projects 63\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Ecological Models: Single Species 65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 65\u003c\/p\u003e \u003cp\u003eII. The Pure Birth Process 65\u003c\/p\u003e \u003cp\u003eIII. Exponential Decay 71\u003c\/p\u003e \u003cp\u003eIV. Logistic Population Growth 72\u003c\/p\u003e \u003cp\u003eV. The Discrete Model of Logistic Growth and Chaos 80\u003c\/p\u003e \u003cp\u003eVI. The Allee Effect 87\u003c\/p\u003e \u003cp\u003eVII. Historical and Biographical Notes 89\u003c\/p\u003e \u003cp\u003eExercises 100\u003c\/p\u003e \u003cp\u003eSuggested Projects 104\u003c\/p\u003e \u003cp\u003eBiographical References 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Ecological Models: Interacting Species 106\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 106\u003c\/p\u003e \u003cp\u003eII. Two Real-World Situations 106\u003c\/p\u003e \u003cp\u003eIII. Autonomous Systems 108\u003c\/p\u003e \u003cp\u003eIV. The Competitive Hunters Model 116\u003c\/p\u003e \u003cp\u003eV. The Predator-Prey Model 123\u003c\/p\u003e \u003cp\u003eVI. Concluding Remarks on Simple Models in Population Dynamics 131\u003c\/p\u003e \u003cp\u003eVII. Biographical Sketches 133\u003c\/p\u003e \u003cp\u003eExercises 137\u003c\/p\u003e \u003cp\u003eSuggested Projects 139\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Tumor Growth Models 141\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 141\u003c\/p\u003e \u003cp\u003eII. A General Tumor Growth Model 142\u003c\/p\u003e \u003cp\u003eIII. The Gompertz Model 145\u003c\/p\u003e \u003cp\u003eIV. Modeling Colorectal Cancer 155\u003c\/p\u003e \u003cp\u003eV. Historical and Biographical Notes 167\u003c\/p\u003e \u003cp\u003eExercises 176\u003c\/p\u003e \u003cp\u003eSuggested Projects 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Social Choice and Voting Procedures 179\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Three Voting Situations 179\u003c\/p\u003e \u003cp\u003eII. Two Voting Mechanisms 180\u003c\/p\u003e \u003cp\u003eIII. An Axiomatic Approach 185\u003c\/p\u003e \u003cp\u003eIV. Arrow’s Impossibility Theorem 187\u003c\/p\u003e \u003cp\u003eV. The Liberal Paradox and the Theorem of the Gloomy Alternatives 191\u003c\/p\u003e \u003cp\u003eVI. Instant Runoff Voting 197\u003c\/p\u003e \u003cp\u003eVII. Approval Voting 203\u003c\/p\u003e \u003cp\u003eVIII. Topological Social Choice 207\u003c\/p\u003e \u003cp\u003eIX. Historical and Biographical Notes 212\u003c\/p\u003e \u003cp\u003eExercises 224\u003c\/p\u003e \u003cp\u003eSuggested Projects 229\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Foundations of Measurement Theory 232\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. The Registrar’s Problem 232\u003c\/p\u003e \u003cp\u003eII. What Is Measurement? 233\u003c\/p\u003e \u003cp\u003eIII. Simple Measures on Finite Sets 238\u003c\/p\u003e \u003cp\u003eIV. Perception of Differences 240\u003c\/p\u003e \u003cp\u003eV. An Alternative Approach 242\u003c\/p\u003e \u003cp\u003eVI. Some Historical Notes 245\u003c\/p\u003e \u003cp\u003eExercises 245\u003c\/p\u003e \u003cp\u003eSuggested Projects 247\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Introduction to Utility Theory 249\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 249\u003c\/p\u003e \u003cp\u003eII. Gambles 250\u003c\/p\u003e \u003cp\u003eIII. Axioms of Utility Theory 251\u003c\/p\u003e \u003cp\u003eIV. Existence and Uniqueness of Utility 254\u003c\/p\u003e \u003cp\u003eV. Classification of Scales 257\u003c\/p\u003e \u003cp\u003eVI. Interpersonal Comparison of Utility 259\u003c\/p\u003e \u003cp\u003eVII. Historical and Biographical Notes 261\u003c\/p\u003e \u003cp\u003eExercises 265\u003c\/p\u003e \u003cp\u003eSuggested Projects 266\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Equilibrium in an Exchange Economy 268\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 268\u003c\/p\u003e \u003cp\u003eII. A Two-Person Economy with Two Commodities 268\u003c\/p\u003e \u003cp\u003eIII. An m-Person Economy 276\u003c\/p\u003e \u003cp\u003eIV. Existence of Economic Equilibrium 283\u003c\/p\u003e \u003cp\u003eV. Some Remaining Questions 293\u003c\/p\u003e \u003cp\u003eVI. Historical and Biographical Notes 294\u003c\/p\u003e \u003cp\u003eExercises 298\u003c\/p\u003e \u003cp\u003eSuggested Projects 301\u003c\/p\u003e \u003cp\u003eVII. Additional Historical and Biographical Notes 302\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Elementary Probability 303\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. The Need for Probability Models 303\u003c\/p\u003e \u003cp\u003eII. What Is Probability? 304\u003c\/p\u003e \u003cp\u003eIII. A Probabilistic Model 322\u003c\/p\u003e \u003cp\u003eIV. Stochastic Processes 325\u003c\/p\u003e \u003cp\u003eExercises 331\u003c\/p\u003e \u003cp\u003eSuggested Projects 335\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Markov Processes 336\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Markov Chains 336\u003c\/p\u003e \u003cp\u003eII. Matrix Operations and Markov Chains 341\u003c\/p\u003e \u003cp\u003eIII. Regular Markov Chains 347\u003c\/p\u003e \u003cp\u003eIV. Absorbing Markov Chains 357\u003c\/p\u003e \u003cp\u003eV. Historical and Biographical Notes 369\u003c\/p\u003e \u003cp\u003eExercises 371\u003c\/p\u003e \u003cp\u003eSuggested Projects 374\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Two Models of Cultural Stability 375\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 375\u003c\/p\u003e \u003cp\u003eII. The Gadaa System 375\u003c\/p\u003e \u003cp\u003eIII. A Deterministic Model 378\u003c\/p\u003e \u003cp\u003eIV. A Probabilistic Model 381\u003c\/p\u003e \u003cp\u003eV. Criticisms of the Models 383\u003c\/p\u003e \u003cp\u003eVI. Hans Hoffmann 384\u003c\/p\u003e \u003cp\u003eExercises 386\u003c\/p\u003e \u003cp\u003eSuggested Projects 387\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Paired-Associate Learning 388\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. The Learning Problem 388\u003c\/p\u003e \u003cp\u003eII. The Model 389\u003c\/p\u003e \u003cp\u003eIII. Testing the Model 397\u003c\/p\u003e \u003cp\u003eIV. Historical and Biographical Notes 401\u003c\/p\u003e \u003cp\u003eExercises 404\u003c\/p\u003e \u003cp\u003eSuggested Projects 406\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Epidemics 407\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 407\u003c\/p\u003e \u003cp\u003eII. Deterministic Models 411\u003c\/p\u003e \u003cp\u003eIII. A Probabilistic Approach 449\u003c\/p\u003e \u003cp\u003eIV. Historical and Biographical Notes 455\u003c\/p\u003e \u003cp\u003eExercises 459\u003c\/p\u003e \u003cp\u003eSuggested Projects 463\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Roulette Wheels and Hospital Beds: A Computer Simulation of Operating and Recovery Room Usage 464\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Introduction 464\u003c\/p\u003e \u003cp\u003eII. The Problems of Interest 468\u003c\/p\u003e \u003cp\u003eIII. Projecting the Number of Surgical Procedures 468\u003c\/p\u003e \u003cp\u003eIV. Estimating Operating Room Demands 469\u003c\/p\u003e \u003cp\u003eV. The Simulation Model 474\u003c\/p\u003e \u003cp\u003eVI. Other Examples of Simulation 480\u003c\/p\u003e \u003cp\u003eVII. Historical and Biographical Notes 484\u003c\/p\u003e \u003cp\u003eExercises 487\u003c\/p\u003e \u003cp\u003eSuggested Projects 488\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Game Theory 490\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eI. Two Difficult Decisions 490\u003c\/p\u003e \u003cp\u003eII. Game Theory Basics 492\u003c\/p\u003e \u003cp\u003eIII. The Binding of Isaac 502\u003c\/p\u003e \u003cp\u003eIV. Tosca and the Prisoners’ Dilemma 507\u003c\/p\u003e \u003cp\u003eV. Nash Equilibrium 511\u003c\/p\u003e \u003cp\u003eVI. Dynamic Solutions 515\u003c\/p\u003e \u003cp\u003eVII. Historical and Biographical Notes 519\u003c\/p\u003e \u003cp\u003eExercises 522\u003c\/p\u003e \u003cp\u003eSuggested Projects 526\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendices\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAppendix I: Sets 613\u003c\/p\u003e \u003cp\u003eAppendix II: Matrices 617\u003c\/p\u003e \u003cp\u003eAppendix III: Solving Systems of Equations 631\u003c\/p\u003e \u003cp\u003eAppendix IV: Functions of Two Variables 645\u003c\/p\u003e \u003cp\u003eAppendix V: Differential Equations 648\u003c\/p\u003e \u003cp\u003eIndex 657\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406899093847,"sku":"9781118642696","price":164.3,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118642696.jpg?v=1730497488","url":"https:\/\/bookcurl.com\/products\/mathematical-modeling-in-the-social-and-life-sciences-9781118642696","provider":"Book Curl","version":"1.0","type":"link"}