Finite Mathematics

Carla C. Morris, PhD,?is Assistant Professor of Mathematics in the Associate in Arts Program at the University of Delaware. A member of The Institute for Operations Research and the Management Sciences and the Mathematical Association of America, Dr. Morris teaches courses ranging from college algebra to calculus and statistics. Robert M. Stark, PhD,?is Professor Emeritus in the Departments of Mathematical Sciences and Civil and Environmental Engineering at the University of Delaware. Dr. Stark's teaching and research interests include applied probability, mathematical optimization, operations research, and mathematics education.

• Preface ixAbout the Authors xi1 Linear Equations and Mathematical Concepts 11.1 Solving Linear Equations 21.2 Equations of Lines and Their Graphs 71.3 Solving Systems of Linear Equations 151.4 The Numbers 𝜋 and e 211.5 Exponential and Logarithmic Functions 241.6 Variation 321.7 Unit Conversions and Dimensional Analysis 382 Mathematics of Finance 472.1 Simple and Compound Interest 472.2 Ordinary Annuity 552.3 Amortization 592.4 Arithmetic and Geometric Sequences 633 Matrix Algebra 713.1 Matrices 723.2 Matrix Notation, Arithmetic, and Augmented Matrices 783.3 Gauss–Jordan Elimination 893.4 Matrix Inversion and Input–Output Analysis 1004 Linear Programming – Geometric Solutions 116Introduction 1164.1 Graphing Linear Inequalities 1174.2 Graphing Systems of Linear Inequalities 1214.3 Geometric Solutions to Linear Programs 1255 Linear Programming – Simplex Method 1365.1 The Standard Maximization Problem (SMP) 1375.2 Tableaus and Pivot Operations 1425.3 Optimal Solutions and the Simplex Method 1495.4 Dual Programs 1615.5 Non-SMP Linear Programs 1676 Linear Programming – Application Models 1827 Set and Probability Relationships 2037.1 Sets 2047.2 Venn Diagrams 2107.3 Tree Diagrams 2167.4 Combinatorics 2217.5 Mathematical Probability 2317.6 Bayes’ Rule and Decision Trees 2458 Random Variables and Probability Distributions 2598.1 Random Variables 2598.2 Bernoulli Trials and the Binomial Distribution 2658.3 The Hypergeometric Distribution 2738.4 The Poisson Distribution 2799 Markov Chains 2859.1 Transition Matrices and Diagrams 2869.2 Transitions 2919.3 Regular Markov Chains 2959.4 Absorbing Markov Chains 30410 Mathematical Statistics 31410.1 Graphical Descriptions of Data 31510.2 Measures of Central Tendency and Dispersion 32310.3 The Uniform Distribution 33110.4 The Normal Distribution 33410.5 Normal Distribution Applications 34810.6 Developing and Conducting a Survey 36311 Enrichment in Finite Mathematics 37111.1 Game Theory 37211.2 Applications in Finance and Economics 38511.3 Applications in Social and Life Sciences 39411.4 Monte Carlo Method 40311.5 Dynamic Programming 422Answers to Odd Numbered Exercises 439Using Technology 502Glossary 506Index 513