Finite Mathematics

PART I: Probability Models Chapter 1: Sets, Partitions, and Tree Diagrams 1-0 The Setting and Overview 1-1 Review of Sets and Set Operations 1-2 Venn Diagrams and Partitions 1-3 Sizes of Sets 1-4 Sets of Outcomes and Trees Important Terms and Concepts Review Exercises Chapter 2: Probabilities, Counting, and Equally Likely Outcomes 2-0 The Setting and Overview 2-1 Probabilities, Events, and Equally Likely Outcomes 2-2 Counting Arrangements: Permutations 2-3 Counting Partitions: Combinations 2-4 Computing Probabilities: Using Equally Likely Outcomes Important Terms and Concepts Review Exercises Chapter 3: Probability 3-0 The Setting and Overview 3-1 Probability Measures: Axioms and Properties 3-2 Conditional Probability and Independence 3-3 Stochastic Processes and Trees 3-4 Bayes Probabilities 3-5 Bernoulli Trials Important Terms and Concepts Review Exercises Chapter 4: Random Variables, Averages, and Statistics 4-0 The Setting and Overview 4-1 Random Variables and Probability Density Functions 4-2 Expected Values and Standard Deviations of Random Variables 4-3 Normal Random Variables and the Normal Approximation to the Binomial Important Terms and Concepts Review Exercises Part II: Linear Models Chapter 5: Systems of Linear Equations 5-0 The Setting and Overview: Linear Models 5-1 Review of Equations and Graphs of Lines 5-2 Formulation and Solution of Systems of Linear Equations in Two Variables 5-3 Forumulation and Solution of Systems of Linear Equations in Three or More Variables Important Terms and Concepts Review Exercises Chapter 6: Matrix Algebra and Applications 6-0 The Setting and Overview 6-1 Matrix Notation and Algebra 6-2 Matrix Inverses 6-3 A Linear Economic Model Important Terms and Concepts Review Exercises Chapter 7: Linear Programming: Modeling and Graphical Solution 7-0 The Setting and Overview: Linear Optimization Models 7-1 Formulation of Linear Programming Problems 7-2 Systems of Linear Inequalities in Two Variables 7-3 Graphical Solution of Linear Programming Problems with Two Variables Important Terms and Concepts Review Exercises PART III: Applications and Related Topics Chapter 8: Markov Chains 8-0 The Setting and Overview 8-1 States, Transitions, Transition Diagrams, and Transition Matrices 8-2 Basic Properties of Markov Chains 8-3 Regular Markov Chains 8-4 Absorbing Markov Chains 8-5 A Markov Chain Model for Plant Succession Important Terms and Concepts Review Exercises Chapter 9: Interest, Mortgages, and Financial Decision Making 9-0 The Setting and Overview 9-1 Interest 9-2 The Present Value of Future Payments 9-3 Time Payments, Amortization, and Mortgages 9-4 Evaluating Investment Options and Financial Decision Making Important Terms and Concepts Review Exercises Chapter 10: Linear Programming: Simplex Method 10-0 The Setting and Overview 10-1 Standard Maximum Problems, Slack Variables, and Basic Solutions 10-2 Tableaus and the Pivot Operation 10-3 Optimal Vectors via the Simplex Method 10-4 Dual Programming Problems and Minimum Problems Important Terms and Concepts Review Exercises Chapter 11: Two-Person Zero-Sum Games 11-0 The Setting and Overview 11-1 Two Simple Games 11-2 Saddle Points and Dominance 11-3 Solving 2 X n and m X 2 Games 11-4 Solving m X n Games using the Simplex Method Important Terms and Concepts Review Exercises Chapter 12: Logic for Finite Mathematics 12-0 The Setting and Overview 12-1 Statements, Connectives, and Negation 12-2 Truth Tables 12-3 Equivalence, Implication, and Deduction Important Terms and Concepts APPENDICES: A: Logic for Finite Mathematics B: Areas under the Standard Normal Curve C: Success Probabilities for Bernoulli Processes GLOSSARY INDEX