Finite Mathematics & Its Applications, 13th edition

PART ONE

1. Linear Equations and Straight Lines
   • 1.1 Coordinate Systems and Graphs
   • 1.2 The Slope of a Line
   • 1.3 The Intersection Point of a Pair of Lines
   • 1.4 The Method of Least Squares
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Break-Even Analysis
2. Matrices
   • 2.1 Systems of Linear Equations with Unique Solutions
   • 2.2 General Systems of Linear Equations
   • 2.3 Arithmetic Operations on Matrices
   • 2.4 The Inverse of a Matrix
   • 2.5 The Gauss-Jordan Method for Calculating Inverses
   • 2.6 Input-Output Analysis
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Population Dynamics
3. Linear Programming, A Geometric Approach
   • 3.1 Linear Inequalities
   • 3.2 A Linear Programming Problem
   • 3.3 Fundamental Theorem of Linear Programming
   • 3.4 Linear Programming
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Shadow Prices
4. The Simplex Method
   • 4.1 Slack Variables and the Simplex Tableau
   • 4.2 The Simplex Method I: Maximum Problems
   • 4.3 The Simplex Method II: Nonstandard and Minimum Problems
   • 4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems
   • 4.5 Duality
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Shadow Prices Revisited

PART TWO

5. Sets and Counting
   • 5.1 Sets
   • 5.2 A Fundamental Principle of Counting
   • 5.3 Venn Diagrams and Counting
   • 5.4 The Multiplication Principle
   • 5.5 Permutations and Combinations
   • 5.6 Further Counting Techniques
   • 5.7 The Binomial Theorem
   • 5.8 Multinomial Coefficients and Partitions
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Pascal's Triangle
6. Probability
   • 6.1 Experiments, Outcomes, Sample Spaces, and Events
   • 6.2 Assignment of Probabilities
   • 6.3 Calculating Probabilities of Events
   • 6.4 Conditional Probability and Independence
   • 6.5 Tree Diagrams
   • 6.6 Bayes' Theorem, Natural Frequencies
   • 6.7 Simulation
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Two Paradoxes
7. Probability and Statistics
   • 7.1 Visual Representations of Data
   • 7.2 Frequency and Probability Distributions
   • 7.3 Binomial Trials
   • 7.4 The Mean
   • 7.5 The Variance and Standard Deviation
   • 7.6 The Normal Distribution
   • 7.7 Normal Approximation to the Binomial Distribution
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: An Unexpected Expected Value

PART THREE

8. Markov Processes
   • 8.1 The Transition Matrix
   • 8.2 Regular Stochastic Matrices
   • 8.3 Absorbing Stochastic Matrices
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Doubly Stochastic Matrices
9. The Theory of Games
   • 9.1 Games and Strategies
   • 9.2 Mixed Strategies
   • 9.3 Determining Optimal Mixed Strategies
   • Chapter Summary and Chapter Review Exercises
   • Chapter Project: Simulating The Outcomes of Mixed-Strategy Games

PART FOUR

10. The Mathematics of Finance
    • 10.1 Interest
    • 10.2 Annuities
    • 10.3 Amortization of Loans
    • 10.4 Personal Financial Decisions
    • 10.5 A Unifying Equation
    • Chapter Summary and Chapter Review Exercises
    • Chapter Project: Two Items of Interest
11. Logic
    • 11.1 Introduction to Logic
    • 11.2 Truth Tables
    • 11.3 Implication
    • 11.4 Logical Implication and Equivalence
    • 11.5 Valid Argument
    • 11.6 Predicate Calculus
    • 11.7 Logic Circuits
    • Chapter Summary and Chapter Review Exercises
    • Chapter Project: A Logic Puzzle
12. Difference Equations and Mathematical Models (online)
    • 12.1 Introduction to Difference Equations
    • 12.2 Difference Equations and Interest
    • 12.3 Graphing Difference Equations
    • 12.4 Mathematics of Personal Finance
    • 12.5 Modeling with Difference Equations
    • Chapter Summary and Chapter Review Exercises
    • Chapter Project: Connections to Markov Processes

APPENDICES

1. Areas Under the Standard Normal Curve
2. The TI-83/84 Plus Graphing Calculator
3. Spreadsheet Fundamentals
4. Wolfram Alpha

Learning Objectives

Index of Applications

Index