PART ONELinear Equations and Straight Lines1.1 Coordinate Systems and Graphs1.2 The Slope of a Line1.3 The Intersection Point of a Pair of Lines1.4 The Method of Least SquaresChapter Summary and Chapter Review ExercisesChapter Project: Break-Even AnalysisMatrices2.1 Systems of Linear Equations with Unique Solutions2.2 General Systems of Linear Equations2.3 Arithmetic Operations on Matrices2.4 The Inverse of a Matrix2.5 The Gauss-Jordan Method for Calculating Inverses2.6 Input-Output AnalysisChapter Summary and Chapter Review ExercisesChapter Project: Population DynamicsLinear Programming, A Geometric Approach3.1 Linear Inequalities3.2 A Linear Programming Problem3.3 Fundamental Theorem of Linear Programming3.4 Linear ProgrammingChapter Summary and Chapter Review ExercisesChapter Project: Shadow PricesThe Simplex Method4.1 Slack Variables and the Simplex Tableau4.2 The Simplex Method I: Maximum Problems4.3 The Simplex Method II: Nonstandard and Minimum Problems4.4 Sensitivity Analysis and Matrix Formulations of Linear Programming Problems4.5 DualityChapter Summary and Chapter Review ExercisesChapter Project: Shadow Prices RevisitedPART TWOSets and Counting5.1 Sets5.2 A Fundamental Principle of Counting5.3 Venn Diagrams and Counting5.4 The Multiplication Principle5.5 Permutations and Combinations5.6 Further Counting Techniques5.7 The Binomial Theorem5.8 Multinomial Coefficients and PartitionsChapter Summary and Chapter Review ExercisesChapter Project: Pascal’s TriangleProbability6.1 Experiments, Outcomes, Sample Spaces, and Events6.2 Assignment of Probabilities6.3 Calculating Probabilities of Events6.4 Conditional Probability and Independence6.5 Tree Diagramsv6.6 Bayes’ Theorem, Natural Frequencies6.7 SimulationChapter Summary and Chapter Review ExercisesChapter Project: Two ParadoxesProbability and Statistics7.1 Visual Representations of Data7.2 Frequency and Probability Distributions7.3 Binomial Trials7.4 The Mean7.5 The Variance and Standard Deviation7.6 The Normal Distribution7.7 Normal Approximation to the Binomial DistributionChapter Summary and Chapter Review ExercisesChapter Project: An Unexpected Expected ValuePART THREEMarkov Processes8.1 The Transition Matrix8.2 Regular Stochastic Matrices8.3 Absorbing Stochastic MatricesChapter Summary and Chapter Review ExercisesChapter Project: Doubly Stochastic MatricesThe Theory of Games9.1 Games and Strategies9.2 Mixed Strategies9.3 Determining Optimal Mixed StrategiesChapter Summary and Chapter Review ExercisesChapter Project: Simulating The Outcomes of Mixed-Strategy GamesPART FOURThe Mathematics of Finance10.1 Interest10.2 Annuities10.3 Amortization of Loans10.4 Personal Financial Decisions10.5 A Unifying EquationChapter Summary and Chapter Review ExercisesChapter Project: Two Items of InterestLogic11.1 Introduction to Logic11.2 Truth Tables11.3 Implication11.4 Logical Implication and Equivalence11.5 Valid Argument11.6 Predicate Calculus11.7 Logic CircuitsChapter Summary and Chapter Review ExercisesChapter Project: A Logic PuzzleDifference Equations and Mathematical Models (online)12.1 Introduction to Difference Equations12.2 Difference Equations and Interest12.3 Graphing Difference Equations12.4 Mathematics of Personal Finance12.5 Modeling with Difference EquationsChapter Summary and Chapter Review ExercisesChapter Project: Connections to Markov ProcessesAPPENDICESAreas Under the Standard Normal CurveThe TI-83/84 Plus Graphing CalculatorSpreadsheet FundamentalsWolfram Alpha

Learning ObjectivesIndex of Applications

Index