Finite mathematics, 4th ed.

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Language: Anglais

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656 p.
Finite Mathematics is designed for the one-term course in finite math taken primarily by students majoring in business, economics, life sciences, and the social sciences. The mathematical integrity of the previous edition has been maintained in the new edition. The core topics and their applications are presented in Parts One and Two of this text, and additional applications are developed in
Part Three. Parts One and Two are independent of one another, thus either probability or linear mathematics may be studied first. The authors' emphasis is on developing and testing the student's problem-solving ability. They use discussions and examples to illustrate ideas and techniques to aid the student in acquiring these skills. Some examples and exercises are straightforward computation, while others require that the problem be solved by combining several techniques. Since it is impossible to provide examples of every type of problem the student will encounter in the text, the authors have identified and treated the fundamental principles that should be used in unfamiliar situations.

Part 1: 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 2: 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 3: 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