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# Finite Mathematics & Its Applications

## byLarry J. Goldstein, David I. Schneider, Martha J. Siegel

### Hardcover | January 18, 2017

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*For Finite Math courses for students majoring in business, economics, life science, or social sciences*

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** Finite Mathematics ** is a comprehensive yet flexible text for students majoring in business, economics, life science, or social sciences. Its varied and relevant applications are designed to pique and hold student interest, and the depth of coverage provides a solid foundation for students’ future coursework and careers. Built-in, optional instruction for the latest technology—graphing calculators, spreadsheets, and WolframAlpha—gives instructors flexibility in deciding how to integrate these tools into their course. Thousands of well-crafted exercises–a hallmark of this text–are available in print and online in MyLab™ Math to enable a wide range of practice in skills, applications, concepts, and technology.

In the **12th Edition**, new co-author Steve Hair (Pennsylvania State University) brings a fresh eye to the content and MyLab™ Math course based on his experience in the classroom. In addition to its updated applications, exercises, and technology coverage, the revision infuses modern topics such as health statistics and content revisions based on user feedback. The authors relied on aggregated student usage and performance data from MyLab™ Math to improve the quality and quantity of exercises.

**Also available with MyLab Math**

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. In the new edition, MyLab Math has expanded to include a suite of new videos, Interactive Figures, exercises that require step-by-step solutions, support for the graphing calculator, and more.

**Note:** You are purchasing a standalone product; MyLab does not come packaged with this content. Students, if interested in purchasing this title with MyLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

If you would like to purchase both the physical text and MyLab, search for:

**0134768639 / 9780134768632 Finite Mathematics & Its Applications plus MyLab Math with Pearson eText -- Title-Specific Access Card Package, 12/e**

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- 0134437764 / 9780134437767 Finite Mathematics & Its Applications
- 0134765729 / 9780134765723 MyLab Math plus Pearson eText -- Standalone Access Card -- for Finite Mathematics & Its Applications

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ISBN - 10:0134437764

ISBN - 13:9780134437767

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Table of Contents

Preface

1. Linear Equations and Straight Lines

1.1 Coordinate Systems and Graphs

1.2 The Slope of a Straight Line

1.3 The Intersection Point of a Pair of Lines

1.4 The Method of Least Squares

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 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 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 Project: Shadow Prices

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 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 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 Project: An Unexpected Expected Value

8. Markov Processes

8.1 The Transition Matrix

8.2 Regular Stochastic Matrices

8.3 Absorbing Stochastic Matrices

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 Project: Simulating The Outcomes of Mixed-Strategy Games

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 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 Project: A Logic Puzzle

**12. Difference Equations and Mathematical Models (Online at www.pearsonhighered.com/mathstatsresources)**

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 Project: Connections to Markov Processes

Appendix A. Areas Under the Standard Normal Curve

Appendix B. The TI-83/84 Plus Graphing Calculators

Appendix C. Spreadsheet Fundamentals

Appendix D. Wolfram Alpha

Answers to Odd-Numbered Exercises

Index