Finite Mathematics

Preface ix About the Authors xi 1 Linear Equations and Mathematical Concepts 1 1.1 Solving Linear Equations 2 1.2 Equations of Lines and Their Graphs 7 1.3 Solving Systems of Linear Equations 15 1.4 The Numbers pi and e 21 1.5 Exponential and Logarithmic Functions 24 1.6 Variation 32 1.7 Unit Conversions and Dimensional Analysis 38 2 Mathematics of Finance 47 2.1 Simple and Compound Interest 47 2.2 Ordinary Annuity 55 2.3 Amortization 59 2.4 Arithmetic and Geometric Sequences 63 3 Matrix Algebra 71 3.1 Matrices 72 3.2 Matrix Notation, Arithmetic, and Augmented Matrices 78 3.3 Gauss-Jordan Elimination 89 3.4 Matrix Inversion and Input-Output Analysis 100 4 Linear Programming - Geometric Solutions 116 Introduction 116 4.1 Graphing Linear Inequalities 117 4.2 Graphing Systems of Linear Inequalities 121 4.3 Geometric Solutions to Linear Programs 125 5 Linear Programming - Simplex Method 136 5.1 The Standard Maximization Problem (SMP) 137 5.2 Tableaus and Pivot Operations 142 5.3 Optimal Solutions and the Simplex Method 149 5.4 Dual Programs 161 5.5 Non-SMP Linear Programs 167 6 Linear Programming - Application Models 182 7 Set and Probability Relationships 203 7.1 Sets 204 7.2 Venn Diagrams 210 7.3 Tree Diagrams 216 7.4 Combinatorics 221 7.5 Mathematical Probability 231 7.6 Bayes' Rule and Decision Trees 245 8 Random Variables and Probability Distributions 259 8.1 Random Variables 259 8.2 Bernoulli Trials and the Binomial Distribution 265 8.3 The Hypergeometric Distribution 273 8.4 The Poisson Distribution 279 9 Markov Chains 285 9.1 Transition Matrices and Diagrams 286 9.2 Transitions 291 9.3 Regular Markov Chains 295 9.4 Absorbing Markov Chains 304 10 Mathematical Statistics 314 10.1 Graphical Descriptions of Data 315 10.2 Measures of Central Tendency and Dispersion 323 10.3 The Uniform Distribution 331 10.4 The Normal Distribution 334 10.5 Normal Distribution Applications 348 10.6 Developing and Conducting a Survey 363 11 Enrichment in Finite Mathematics 371 11.1 Game Theory 372 11.2 Applications in Finance and Economics 385 11.3 Applications in Social and Life Sciences 394 11.4 Monte Carlo Method 403 11.5 Dynamic Programming 422 Answers to Odd Numbered Exercises 439 Using Technology 502 Glossary 506 Index 513