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More About This Textbook
Overview
Editorial Reviews
From The Critics
This college textbook is for a oneterm course for students who have had oneandahalf years of high school algebra or the equivalent. the book is designed to give students substantial experience in modeling and solving realworld problems, to increase their understanding of the applicability of mathematics to everyday life. the text contains over 260 completely worked problems, each followed by a similar matched problem for the student to work. The exercise sets have a range of degree of difficulty, to ensure all levels of students are challenged but also able to experience success. Activities are included to encourage verbalization of mathematical concepts, results and processes. Specific changes made to the ninth edition are not stated. Annotation c. Book News, Inc., Portland, OR (booknews.com)Booknews
Written for students with a background in high school algebra, this text explains finite mathematics with an emphasis on applications to the business and finance worlds. Topics covered include linear inequalities, probability, data description, and Markov chains. Annotation c. by Book News, Inc., Portland, Or.Product Details
Related Subjects
Table of Contents
I. A LIBRARY OF ELEMENTARY FUNCTIONS.
2. Additional Elementary Functions.
II. FINITE MATHEMATICS.
4. Systems of Linear Equations; Matrices.
5. Linear Inequalities and Linear Programming.
6. Probability.
7. Data Description and Probability Distributions.
8. Games and Decisions.
9. Markov Chains.
APPENDICES.
B. Special Topics.
C. Tables.
Answers.
Index.
Library of Elementary Functions.
Applications Index.
Preface
Improvements in this edition evolved out of the generous response from a large number of users of the last and previous editions as well as survey results from instructors, mathematics departments, course outlines, and college catalogs. Fundamental to a book's growth and effectiveness is classroom use and feedback. Now in its ninth edition, Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences has had the benefit of having a substantial amount of both.
Emphasis and Style
The text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible to students. Emphasis is on computational skills, ideas, and problem solving rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed.
Examples and Matched Problems
Over 260 completely worked examples are used to introduce concepts and to demonstrate problemsolving techniques. Many examples have multiple parts, significantly increasing the totalnumber of worked examples. Each example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process. The answers to these matched problems are included at the end of each section for easy reference.
Exploration and Discussion
Every section contains ExploreDiscuss problems interspersed at appropriate places to encourage the student to think about a relationship or process before a result is stated, or to investigate additional consequences of a development in the text. Verbalization of mathematical concepts, results, and processes is encouraged in these ExploreDiscuss problems, as well as in some matched problems, and in some problems in almost every exercise set. The ExploreDiscuss material also can be used as inclass or outofclass group activities. In addition, at the end of every chapter, we have included two special chapter group activities that involve several of the concepts discussed in the chapter. Problems in the exercise sets that require verbalization are indicated by color problem numbers.
Exercise Sets
The book contains over 3,500 problems. Many problems have multiple parts, significantly increasing the total number of problems. Each exercise set is designed so that an average or belowaverage student will experience success and a very capable student will be challenged. Exercise sets are mostly divided into A (routine, easy mechanics), B (more difficult mechanics), and C (difficult mechanics and some theory) levels.
Applications
A major objective of this book is to give the student substantial experience in modeling and solving realworld problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful (see the Applications Index inside the back cover). Worked examples involving applications are identified by an icon. Almost every exercise set contains application problems, usually divided into business and economics, life science, and social science groupings. An instructor with students from all three disciplines can let them choose applications from their own field of interest; if most students are from one of the three areas, then special emphasis can be placed there. Most of the applications are simplified versions of actual realworld problems taken from professional journals and books. No specialized experience is required to solve any of the applications.
Internet Connections
The Internet provides a wealth of material that can be related to this book, from sources for the data in application problems to interactive exercises that provide additional insight into various mathematical processes. Every section of the book contains Internet connections identified by a www icon. Links to the related web sites can be found at the PH Companion Website discussed later in this preface: www.prenhall.com/barnett
Technology
The generic term graphing utility is used to refer to any of the various graphing calculators or computer software packages that might be available to a student using this book. (See the description of the software accompanying this book later in this Preface.) Although access to a graphing utility is not assumed, it is likely that many students will want to make use of one of these devices. To assist these students, optional graphing utility activities are included in appropriate places in the book. These include brief discussions in the text, examples or portions of examples solved on a graphing utility, problems for the student to solve, and a group activity that involves the use of technology at the end of each chapter. In the group activity at the end of Chapter 1, and continuing through Chapter 2, linear regression on a graphing utility is used at appropriate points to illustrate mathematical modeling with real data. All the optional graphing utility material is clearly identified by calculator icons and can be omitted without loss of continuity, if desired.
Graphs
All graphs are computergenerated to ensure mathematical accuracy. Graphing utility screens displayed in the text are actual output from a graphing calculator.
Additional Pedagogical Features
Annotation of examples and developments, in small color type, is found throughout the text to help students through critical stages (see Sections 11 and 42). Think boxes (dashed boxes) are used to enclose steps that are usually performed mentally (see Sections 11 and 41). Boxes are used to highlight important definitions, results, and stepbystep processes (see Sections 11 and 14). Caution statements appear throughout the text where student errors often occur (see Sections 43 and 45). Functional use of color improves the clarity of many illustrations, graphs, and developments, and guides students through certain critical steps (see Sections 11 and 42). Boldface type is used to introduce new terms and highlight important comments. Chapter review sections include a review of all important terms and symbols and a comprehensive review exercise. Answers to most review exercises, keyed to appropriate sections, are included in the back of the book. Answers to all other oddnumbered problems are also in the back of the book. Answers to application problems in linear programming include both the mathematical model and the numeric answer.
Content
The text begins with the development of a library of elementary functions in Chapters 1 and 2, including their properties and uses. We encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. This development lays a firm foundation for studying mathematics both in this book and in future endeavors. Depending on the syllabus for the course and the background of the students, some or all of this material can be covered at the beginning of a course, or selected portions can be referred to as needed later in the course.
The material in Part Two (Finite Mathematics) can be thought of as four units: mathematics of finance (Chapter 3); linear algebra, including matrices, linear systems, and linear programming (Chapters 4 and 5); probability and statistics (Chapters 6 and 7); and applications of linear algebra and probability to game theory and Markov chains (Chapters 8 and 9). The first three units are independent of each other, while the last two chapters are dependent on some of the earlier chapters (see the Chapter Dependency Chart preceding this Preface).
Chapter 3 presents a thorough treatment of simple and compound interest and present and future value of ordinary annuities. Appendix B contains a section on arithmetic and geometric sequences that can be covered in conjunction with this chapter, if desired.
Chapter 4 covers linear systems and matrices with an emphasis on using row operations and GaussJordan elimination to solve systems and to find matrix inverses. This chapter also contains numerous applications of mathematical modeling utilizing systems and matrices. To assist students in formulating solutions, all the answers in the back of the book to application problems in Exercises 43, 45, and the chapter Review Exercise contain both the mathematical model and its solution. The row operations discussed in Sections 42 and 43 are required for the simplex method in Chapter 5. Matrix multiplication, matrix inverses, and systems of equations are required for Markov chains in Chapter 9.
Chapter 5 provides broad and flexible coverage of linear programming. The first two sections cover twovariable graphing techniques. Instructors who wish to emphasize techniques can cover the basic simplex method in Sections 53 and 54 and then discuss any or all of the following: the dual method (Section 55), the big M method (Section 56), or the twophase simplex method (Group Activity 1). Those who want to emphasize modeling can discuss the formation of the mathematical model for any of the application examples in Sections 54, 55, and 56, and either omit the solution or use software to find the solution (see the description of the software that accompanies this text later in this Preface). To facilitate this approach, all the answers in the back of the book to application problems in Exercises 54, 55, 56, and the chapter Review Exercise contain both the mathematical model and its solution. Geometric, simplex, and dual solution methods are required for portions of Chapter 8.
Chapter 6 covers counting techniques and basic probability, including Bayes' formula and random variables. Appendix A contains a review of basic set theory and notation to support the use of sets in probability. Some of the topics discussed in Chapter 6 are required for Chapter 7.
Chapter 7 deals with basic descriptive statistics and more advanced probability distributions, including the important normal distribution. Appendix B contains a short discussion of the binomial theorem that can be used in conjunction with the development of the binomial distribution in Section 75.
Each of the last two chapters ties together concepts developed in earlier chapters and applies them to two interesting topics: game theory (Chapter 8) and Markov chains (Chapter 9). Either chapter provides an excellent unifying conclusion to a finite mathematics course.
Appendix A contains a selftest and a concise review of basic algebra that also may be covered as part of the course or referred to as needed. As mentioned above, Appendix B contains additional topics that can be covered in conjunction with certain sections in the text, if desired.
Supplements for the Student
Supplements for the Instructor
For a summary of all available supplementary materials and detailed information regarding examination copy requests and orders, see page xix.
Error Check
Because of the careful checking and proofing by a number of mathematics instructors (acting independently), the authors and publisher believe this book to be substantially errorfree. For any errors remaining, the authors would be grateful if they were sent to: Karl E. Byleen, 9322 W Garden Court, Hales Corners, WI 53130; or by email, to: byleen@execpc.com
Acknowledgments
In addition to the authors, many others are involved in the successful publication of a book.
We wish to thank the following reviewers of the eighth edition:
Thomas Riedel, University of Louisville
Linda M. Neal, Southern Methodist University
Beverly Vredevelt, Spokane Falls Community College
J. Sriskandarajah, University of WisconsinRichland
Cathleen A. ZuccoTevelot, Trinity College
We also wish to thank our colleagues who have provided input on previous editions:
Chris Boldt, Bob Bradshaw, Bruce Chaffee, Robert Chaney, Dianne Clark, Charles E. Cleaver, Barbara Cohen, Richard L. Conlon, Catherine Cron, Lou D'Alotto, Madhu Deshpande, Kenneth A. Dodaro, Michael W. Ecker, Jerry R. Ehman, Lucina Gallagher, Martha M. Harvey, Sue Henderson, Lloyd R. Hicks, Louis F. Hoelzle, Paul Hutchins, K. Wayne James, Robert H. Johnston, Robert Krystock, Inessa Levi, James T. Loats, Frank Lopez, Roy H. Luke, Wayne Miller, Mel Mitchell, Ronald Persky, Kenneth A. Peters, Jr., Dix Petty, Tom Plavchak, Bob Prielipp, Stephen Rodi, Arthur Rosenthal, Sheldon Rothman, Elaine Russell, John Ryan, Daniel E. Scanlon, George R. Schriro, Arnold L. Schroeder, Hari Shanker, Joan Smith, Steven Terry, Delores A. Williams, Caroline Woods, Charles W. Zimmerman, and Pat Zrolka.
We also express our thanks to:
Hossein Hamedani, Carolyn Meitler, Stephen Merrill, Robert Mullins, and Caroline Woods for providing a careful and thorough check of all the mathematical calculations in the book, and to Priscilla Gathoni for checking the Student Solutions Manual, and the Instructor's Solutions Manual (a tedious but extremely important job).
Garret Etgen, Hossein Hamedani, Carolyn Meitler, and David Schneider for developing the supplemental manuals that are so important to the success of a text.
Jeanne Wallace for accurately and efficiently producing most of the manuals that supplement the text. George Morris and his staff at Scientific Illustrators for their effective illustrations and accurate graphs. All the people at Prentice Hall who contributed their efforts to the production of this book, especially Quincy McDonald, our acquisitions editor, and Lynn Savino Wendel, our production editor.
Producing this new edition with the help of all these extremely competent people has been a most satisfying experience.
R. A. Barnett
M. R. Ziegler
K. E. Byleen
Introduction
Improvements in this edition evolved out of the generous response from a large number of users of the last and previous editions as well as survey results from instructors, mathematics departments, course outlines, and college catalogs. Fundamental to a book's growth and effectiveness is classroom use and feedback. Now in its ninth edition, Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences has had the benefit of having a substantial amount of both.
Emphasis and Style
The text is written for student comprehension. Great care has been taken to write a book that is mathematically correct and accessible to students. Emphasis is on computational skills, ideas, and problem solving rather than mathematical theory. Most derivations and proofs are omitted except where their inclusion adds significant insight into a particular concept. General concepts and results are usually presented only after particular cases have been discussed.
Examples and Matched Problems
Over 260 completely worked examples are used to introduce concepts and to demonstrate problemsolving techniques. Many examples have multiple parts, significantly increasing the totalnumber of worked examples. Each example is followed by a similar matched problem for the student to work while reading the material. This actively involves the student in the learning process. The answers to these matched problems are included at the end of each section for easy reference.
Exploration and Discussion
Every section contains ExploreDiscuss problems interspersed at appropriate places to encourage the student to think about a relationship or process before a result is stated, or to investigate additional consequences of a development in the text. Verbalization of mathematical concepts, results, and processes is encouraged in these ExploreDiscuss problems, as well as in some matched problems, and in some problems in almost every exercise set. The ExploreDiscuss material also can be used as inclass or outofclass group activities. In addition, at the end of every chapter, we have included two special chapter group activities that involve several of the concepts discussed in the chapter. Problems in the exercise sets that require verbalization are indicated by color problem numbers.
Exercise Sets
The book contains over 3,500 problems. Many problems have multiple parts, significantly increasing the total number of problems. Each exercise set is designed so that an average or belowaverage student will experience success and a very capable student will be challenged. Exercise sets are mostly divided into A (routine, easy mechanics), B (more difficult mechanics), and C (difficult mechanics and some theory) levels.
Applications
A major objective of this book is to give the student substantial experience in modeling and solving realworld problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful (see the Applications Index inside the back cover). Worked examples involving applications are identified by an icon. Almost every exercise set contains application problems, usually divided into business and economics, life science, and social science groupings. An instructor with students from all three disciplines can let them choose applications from their own field of interest; if most students are from one of the three areas, then special emphasis can be placed there. Most of the applications are simplified versions of actual realworld problems taken from professional journals and books. No specialized experience is required to solve any of the applications.
Internet Connections
The Internet provides a wealth of material that can be related to this book, from sources for the data in application problems to interactive exercises that provide additional insight into various mathematical processes. Every section of the book contains Internet connections identified by a www icon. Links to the related web sites can be found at the PH Companion Website discussed later in this preface: www.prenhall.com/barnett
Technology
The generic term graphing utility is used to refer to any of the various graphing calculators or computer software packages that might be available to a student using this book. (See the description of the software accompanying this book later in this Preface.) Although access to a graphing utility is not assumed, it is likely that many students will want to make use of one of these devices. To assist these students, optional graphing utility activities are included in appropriate places in the book. These include brief discussions in the text, examples or portions of examples solved on a graphing utility, problems for the student to solve, and a group activity that involves the use of technology at the end of each chapter. In the group activity at the end of Chapter 1, and continuing through Chapter 2, linear regression on a graphing utility is used at appropriate points to illustrate mathematical modeling with real data. All the optional graphing utility material is clearly identified by calculator icons and can be omitted without loss of continuity, if desired.
Graphs
All graphs are computergenerated to ensure mathematical accuracy. Graphing utility screens displayed in the text are actual output from a graphing calculator.
Additional Pedagogical Features
Annotation of examples and developments, in small color type, is found throughout the text to help students through critical stages (see Sections 11 and 42). Think boxes (dashed boxes) are used to enclose steps that are usually performed mentally (see Sections 11 and 41). Boxes are used to highlight important definitions, results, and stepbystep processes (see Sections 11 and 14). Caution statements appear throughout the text where student errors often occur (see Sections 43 and 45). Functional use of color improves the clarity of many illustrations, graphs, and developments, and guides students through certain critical steps (see Sections 11 and 42). Boldface type is used to introduce new terms and highlight important comments. Chapter review sections include a review of all important terms and symbols and a comprehensive review exercise. Answers to most review exercises, keyed to appropriate sections, are included in the back of the book. Answers to all other oddnumbered problems are also in the back of the book. Answers to application problems in linear programming include both the mathematical model and the numeric answer.
Content
The text begins with the development of a library of elementary functions in Chapters 1 and 2, including their properties and uses. We encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. This development lays a firm foundation for studying mathematics both in this book and in future endeavors. Depending on the syllabus for the course and the background of the students, some or all of this material can be covered at the beginning of a course, or selected portions can be referred to as needed later in the course.
The material in Part Two (Finite Mathematics) can be thought of as four units: mathematics of finance (Chapter 3); linear algebra, including matrices, linear systems, and linear programming (Chapters 4 and 5); probability and statistics (Chapters 6 and 7); and applications of linear algebra and probability to game theory and Markov chains (Chapters 8 and 9). The first three units are independent of each other, while the last two chapters are dependent on some of the earlier chapters (see the Chapter Dependency Chart preceding this Preface).
Chapter 3 presents a thorough treatment of simple and compound interest and present and future value of ordinary annuities. Appendix B contains a section on arithmetic and geometric sequences that can be covered in conjunction with this chapter, if desired.
Chapter 4 covers linear systems and matrices with an emphasis on using row operations and GaussJordan elimination to solve systems and to find matrix inverses. This chapter also contains numerous applications of mathematical modeling utilizing systems and matrices. To assist students in formulating solutions, all the answers in the back of the book to application problems in Exercises 43, 45, and the chapter Review Exercise contain both the mathematical model and its solution. The row operations discussed in Sections 42 and 43 are required for the simplex method in Chapter 5. Matrix multiplication, matrix inverses, and systems of equations are required for Markov chains in Chapter 9.
Chapter 5 provides broad and flexible coverage of linear programming. The first two sections cover twovariable graphing techniques. Instructors who wish to emphasize techniques can cover the basic simplex method in Sections 53 and 54 and then discuss any or all of the following: the dual method (Section 55), the big M method (Section 56), or the twophase simplex method (Group Activity 1). Those who want to emphasize modeling can discuss the formation of the mathematical model for any of the application examples in Sections 54, 55, and 56, and either omit the solution or use software to find the solution (see the description of the software that accompanies this text later in this Preface). To facilitate this approach, all the answers in the back of the book to application problems in Exercises 54, 55, 56, and the chapter Review Exercise contain both the mathematical model and its solution. Geometric, simplex, and dual solution methods are required for portions of Chapter 8.
Chapter 6 covers counting techniques and basic probability, including Bayes' formula and random variables. Appendix A contains a review of basic set theory and notation to support the use of sets in probability. Some of the topics discussed in Chapter 6 are required for Chapter 7.
Chapter 7 deals with basic descriptive statistics and more advanced probability distributions, including the important normal distribution. Appendix B contains a short discussion of the binomial theorem that can be used in conjunction with the development of the binomial distribution in Section 75.
Each of the last two chapters ties together concepts developed in earlier chapters and applies them to two interesting topics: game theory (Chapter 8) and Markov chains (Chapter 9). Either chapter provides an excellent unifying conclusion to a finite mathematics course.
Appendix A contains a selftest and a concise review of basic algebra that also may be covered as part of the course or referred to as needed. As mentioned above, Appendix B contains additional topics that can be covered in conjunction with certain sections in the text, if desired.
Supplements for the Student
Supplements for the Instructor
For a summary of all available supplementary materials and detailed information regarding examination copy requests and orders, see page xix.
Error Check
Because of the careful checking and proofing by a number of mathematics instructors (acting independently), the authors and publisher believe this book tm be substantially errorfree. For any errors remaining, the authors would be grateful if they were sent to: Karl E. Byleen, 9322 W Garden Court, Hales Corners,, WI 53130; or by email, to: byleen@execpc.com
Acknowledgments
In addition to the authors, many others are involved in the successful publication of a book.
We wish to thank the following reviewers of the eighth edition:
Thomas Riedel, University of Louisville
Linda M. Neal, Southern Methodist University
Beverly Vredevelt, Spokane Falls Community College
J. Sriskandarajah, University of WisconsinRichland
Cathleen A. ZuccoTevelot, Trinity College
We also wish to thank our colleagues who have provided input on previous editions:
Chris Boldt, Bob Bradshaw, Bruce Chaffee, Robert Chaney, Dianne Clark, Charles E. Cleaver, Barbara Cohen, Richard L. Conlon, Catherine Cron, Lou D'Alotto, Madhu Deshpande, Kenneth A. Dodaro, Michael W. Ecker, Jerry R. Ehman, Lucina Gallagher, Martha M. Harvey, Sue Henderson, Lloyd R. Hicks, Louis F. Hoelzle, Paul Hutchins, K. Wayne James, Robert H. Johnston, Robert Krystock, Inessa Levi, James T. Loats, Frank Lopez, Roy H. Luke, Wayne Miller, Mel Mitchell, Ronald Persky, Kenneth A. Peters, Jr., Dix Petty, Tom Plavchak, Bob Prielipp, Stephen Rodi, Arthur Rosenthal, Sheldon Rothman, Elaine Russell, John Ryan, Daniel E. Scanlon, George R. Schriro, Arnold L. Schroeder, Hari Shanker, Joan Smith, Steven Terry, Delores A. Williams, Caroline Woods, Charles W. Zimmerman, and Pat Zrolka.
We also express our thanks to:
Hossein Hamedani, Carolyn Meitler, Stephen Merrill, Robert Mullins, and Caroline Woods for providing a careful and thorough check of all the mathematical calculations in the book, and to Priscilla Gathoni for checking the Student Solutions Manual, and the Instructor's Solutions Manual (a tedious but extremely important job).
Garret Etgen, Hossein Hamedani, Carolyn Meitler, and David Schneider for developing the supplemental manuals that are so important to the success of a text.
Jeanne Wallace for accurately and efficiently producing most of the manuals that supplement the text. George Morris and his staff at Scientific Illustrators for their effective illustrations and accurate graphs. All the people at Prentice Hall who contributed their efforts to the production of this book, especially Quincy McDonald, our acquisitions editor, and Lynn Savino Wendel, our production editor.
Producing this new edition with the help of all these extremely competent people has been a most satisfying experience.
R. A. Barnett
M. R. Ziegler
K. E. Byleen