Finite Mathematics
Note: Each chapter concludes with a Chapter Summary with Hints and Suggestions and Review Exercises. 1. Functions Application Preview: World Record Mile Runs 1.1 Real Numbers, Inequalities, and Lines 1.2 Exponents 1.3 Functions 1.4 Functions, Continued 1.5 Exponential Functions 1.6 Logarithmic Functions 2. Mathematics of Finance Application Preview: Musical Instruments as Investments 2.1 Simple Interest 2.2 Compound Interest 2.3 Annuities 2.4 Amortization 3. Systems of Equations and Matrices Application Preview: A "Taxing" Problem 3.1 Systems of Two Linear Equations in Two Variables 3.2 Matrices and Linear Equations in Two Variables 3.3 Systems of Linear Equations and the Gauss-Jordan Method 3.4 Matrix Arithmetic 3.5 Inverse Matrices and Systems of Linear Equations 3.6 Introduction to Modeling: Leontief Models and Least Squares 4. Linear Programming Application Preview: Managing an Investment Portfolio 4.1 Linear Inequalities 4.2 Two-Variable Linear Programming Problems 4.3 The Simplex Method for Standard Maximum Problems 4.4 Standard Minimum Problems and Duality 4.5* Nonstandard Problems: The Dual Pivot Element and the Two-Stage Method 4.6* Nonstandard Problems: Artificial Variables and the Big-M Method * These two sections provide alternate methods for solving the same types of problems. The choice of which to cover is left to the Instructor. 5. Probability Application Preview: The Chevalier de Mere 5.1 Sets, Counting, and Venn Diagrams 5.2 Permutations and Combinations 5.3 Probability Spaces 5.4 Conditional Probability and Independence 5.5 Bayes' Formula 5.6 Random Variables and Distributions 6. Statistics Application Preview: Household Income 6.1 Random Samples and Data Organization 6.2 Measures of Central Tendency 6.3 Measures of Variation 6.4 Normal Distributions and Binomial Approximation 7. Markov Chains Application Preview: Weather in Sri Lanka 7.1 States and Transitions 7.2 Regular Markov Chains 7.3 Absorbing Markov Chains 8. Game Theory Application Preview: Sherlock Holmes and James Moriarty 8.1 Two-Person Games and Saddle Points 8.2 Mixed Strategies 8.3 Games and Linear Programming Appendix: Normal Probabilities Using Tables Answers to Selected Exercises Index Available on the Web L. Logic L.1 Statements and Connectives Application Preview: Grammar, Logic, and Rhetoric L.2 Truth Tables Application Preview: Circuits L.3 Implications Application Preview: "If..., then..." as a Computer Instruction L.4 Valid Arguments Application Preview: Fuzzy Logic and Artificial Intelligence L.5 Quantifiers and Euler Diagrams Application Preview: The Dog Walking Ordinance Chapter Projects and Essays