Finite Mathematics & Its Applications

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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 Wolfram|Alpha–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.

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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.

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Larry Goldstein has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming.  He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.

David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT.  He is currently an emeritus professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematical software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.

Martha Siegel holds a BA from Russell Sage College, attended Rensselaer Polytechnic Institute as a special student, and received her PhD at the University of Rochester. From 1966 until 1971 she taught at Goucher University in Baltimore. Since 1971 she has been a professor at Towson State University, also in Maryland. Professor Siegel has been on the writing team of this book since the fifth edition and is also the co-author of a precalculus reform book.

Steven Hair holds a BS from Virginia Tech and a PhD from Penn State University. He is currently a lecturer and course coordinator at Penn State, where he develops traditional and digital content for finite math and precalculus courses. In his free time, Steven enjoys spending time with his family, playing the saxophone, and fly fishing.

Preface

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

2.1 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

3.1 Linear Inequalities

3.2 A Linear Programming Problem

3.3 Fundamental Theorem of Linear Programming

3.4 Linear Programming

            Chapter Project: Shadow Prices

4.1 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

5.1 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

6.1 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

7.1 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

8.1 The Transition Matrix

8.2 Regular Stochastic Matrices

8.3 Absorbing Stochastic Matrices

            Chapter Project: Doubly Stochastic Matrices

9.1 Games and Strategies

9.2 Mixed Strategies

9.3 Determining Optimal Mixed Strategies

            Chapter Project: Simulating The Outcomes of Mixed-Strategy Games

10.1 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

11.1 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

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