Finite Mathematics

Geoffrey C. Berresford; Andrew Mansfield Rockett

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This engaging new text for the one-semester finite mathematics course uses intriguing real-world applications to capture business, economics, life, and social science majors' interest and show them the practical side of mathematics. The text naturally integrates graphing calculator and spreadsheet explorations to expose students to the tools they will encounter in their future careers.

• Application Previews at the beginning of most sections include in-depth real-world applications that motivate students to focus on the section material.
• A wealth of pedagogy includes the following distinctive features: Worked-out Examples with Annotations to help students through the more challenging concepts; Practice Problems, offered as extra exercises after the more difficult worked-out examples; Section Summaries, briefly restating essential formulas and key concepts; Chapter Summary with Hints and Suggestions included at the end of every chapter to unify the chapter, give specific reminders, and reference problems in the review exercises suitable for a practice test; and Cumulative Review Exercises appearing at the end of groups of chapters to reinforce previously learned concepts and skills.

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Dr. Berresford received his Ph.D. from the Courant Institute of Mathematical Sciences at New York University and taught at the State University of New York at Purchase before joining the faculty at the C.W. Post campus of Long Island University. Besides co-authoring four textbooks with Dr. Rockett, he has published papers in differential equations, linear programming, logic, and probability, and has received several teaching awards and the Distinguished Service Award from The Metropolitan New York Section of the Mathematical Association of America.

Review:

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

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