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More About This Textbook
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Preface
This work is the seventh edition of our text for the traditional finite mathematics course taught to first and secondyear college students, especially those majoring in business and the social and biological sciences. Finite mathematics courses exhibit tremendous diversity with respect to both content and approach. Therefore, in revising this book, we incorporated a wide range of topics from which an instructor may design a curriculum, as well as a high degree of flexibility in the order in which the topics may be presented. For the mathematics of finance, we even allow for flexibility in the approach of the presentation.
In this edition we attempt to maintain our popular studentoriented approach throughout and, in particular, through the use of the following features:
Applications
We provide realistic applications that illustrate the uses of finite mathematics in other disciplines. The reader may survey the variety of applications by referring to the Index of Applications located on the front endpapers. Wherever possible, we attempt to use applications to motivate the mathematics. For example, the concept of linear programming is introduced in Chapter 3 via a discussion of production options for a factory with a labor limitation.
Examples
We include many more worked examples than is customary in textbooks. Furthermore, we include computational details to enhance comprehension by students whose basic skills are weak.
Exercises
More than 2200 exercises comprise about onequarter of the book, the most important part of the text in our opinion. The exercises at the ends of thesections are usually arranged in the order in which the text proceeds, so that homework assignments may be easily made after only part of a section is discussed. Interesting applications and more challenging problems tend to be located near the ends of the exercise sets. Supplementary exercises at the end of each chapter amplify the other exercise sets and provide cumulative exercises that require skills acquired from earlier chapters. Answers to the oddnumbered exercises are included at the back of the book.
Practice Problems
The practice problems are a popular and useful feature of the book. They are carefully selected exercises located at the end of each section, just before the exercise set. Complete solutions follow the exercise set. The practice problems often focus on points that are potentially confusing or are likely to be overlooked. We recommend that the reader seriously attempt to do the practice problems and study their solutions before moving on to the exercises.
Use of Technology
Although the use of technology is optional for this text, many of the topics can be enhanced with graphing calculators and computers. Also, each year more students own graphing calculators that they have used in their high school mathematics courses. Therefore, whenever relevant, we explicitly show the student how to use graphing calculators effectively to assist in understanding the fundamental concepts of the course. In addition, the text contains an appendix on the use of graphing calculators and about 200 specially designated "calculator and computer" exercises. Such exercises are denoted by GC.
In our discussions of graphing calculators, we specifically refer to the TI82 and TI83 since these are the two most popular graphing calculators. Therefore, most students will have a book customized to their calculator. Students with other graphing calculators can consult their guidebooks to learn how to make adjustments. Had the calculator material been written generically, every student would have to make adjustments.
Examples from Professional Exams
We have included questions similar to those found on CPA and GMAT exams to further illustrate the relevance of the material in the course. These multiplechoice questions are identified with the notation PE.
Review of Fundamental Concepts
Near the end of each chapter is a set of questions that help the student recall the key ideas of the chapter and focus on the relevance of these concepts.
New in This Edition
Among the changes in this edition, the following are the most significant.
Minimal Prerequisites
Because of the great variation in student preparation, we keep formal prerequisites to a minimum. We assume only a first year of high school algebra. Furthermore, we review, as needed, those topics that are typically weak spots for students.
Topics Included
This edition has more material than can be covered in most onesemester courses. Therefore, the instructor can structure the course to the students' needs and interests. The book divides naturally into four parts. The first part consists of linear mathematics: linear equations, matrices, and linear programming (Chapters 14); the second part is devoted to probability and statistics (Chapters 57); the third part covers topics utilizing the ideas of the other parts (Chapters 810); and the fourth part explores key topics from discrete mathematics that are sometimes included in the modern finite mathematics curriculum (Chapters 1113). We prefer to begin with linear mathematics since it makes for a smooth transition from high school mathematics and leads quickly to interesting applications, especially linear programming. Our preference notwithstanding, the instructor may begin this book with Chapter 5 (Sets and Counting) and then do either the linear mathematics or the probability and statistics.
Supplements
Table of Contents
1. Linear Equations and Straight Lines.
2. Matrices.
3. Linear Programming, A Geometric Approach.
4. The Simplex Method.
5. Sets and Counting.
6. Probability.
7. Probability and Statistics.
8. Markov Processes.
9. The Theory of Games.
10. The Mathematics of Finance.
11. Difference Equations and Mathematical Models.
12. Logic.
13. Graphs.
Appendix A. Tables.
Appendix B. Using the TI82 and TI83 Graphing Calculators.
Appendix C. Spreadsheet Fundamentals.
Answers to Exercises.
Index.
Preface
Preface
This work is the seventh edition of our text for the traditional finite mathematics course taught to first and secondyear college students, especially those majoring in business and the social and biological sciences. Finite mathematics courses exhibit tremendous diversity with respect to both content and approach. Therefore, in revising this book, we incorporated a wide range of topics from which an instructor may design a curriculum, as well as a high degree of flexibility in the order in which the topics may be presented. For the mathematics of finance, we even allow for flexibility in the approach of the presentation.
In this edition we attempt to maintain our popular studentoriented approach throughout and, in particular, through the use of the following features:
Applications
We provide realistic applications that illustrate the uses of finite mathematics in other disciplines. The reader may survey the variety of applications by referring to the Index of Applications located on the front endpapers. Wherever possible, we attempt to use applications to motivate the mathematics. For example, the concept of linear programming is introduced in Chapter 3 via a discussion of production options for a factory with a labor limitation.
Examples
We include many more worked examples than is customary in textbooks. Furthermore, we include computational details to enhance comprehension by students whose basic skills are weak.
Exercises
More than 2200 exercises comprise about onequarter of the book, the most important part of the text in our opinion. The exercises at the ends ofthesections are usually arranged in the order in which the text proceeds, so that homework assignments may be easily made after only part of a section is discussed. Interesting applications and more challenging problems tend to be located near the ends of the exercise sets. Supplementary exercises at the end of each chapter amplify the other exercise sets and provide cumulative exercises that require skills acquired from earlier chapters. Answers to the oddnumbered exercises are included at the back of the book.
Practice Problems
The practice problems are a popular and useful feature of the book. They are carefully selected exercises located at the end of each section, just before the exercise set. Complete solutions follow the exercise set. The practice problems often focus on points that are potentially confusing or are likely to be overlooked. We recommend that the reader seriously attempt to do the practice problems and study their solutions before moving on to the exercises.
Use of Technology
Although the use of technology is optional for this text, many of the topics can be enhanced with graphing calculators and computers. Also, each year more students own graphing calculators that they have used in their high school mathematics courses. Therefore, whenever relevant, we explicitly show the student how to use graphing calculators effectively to assist in understanding the fundamental concepts of the course. In addition, the text contains an appendix on the use of graphing calculators and about 200 specially designated "calculator and computer" exercises. Such exercises are denoted by GC.
In our discussions of graphing calculators, we specifically refer to the TI82 and TI83 since these are the two most popular graphing calculators. Therefore, most students will have a book customized to their calculator. Students with other graphing calculators can consult their guidebooks to learn how to make adjustments. Had the calculator material been written generically, every student would have to make adjustments.
Examples from Professional Exams
We have included questions similar to those found on CPA and GMAT exams to further illustrate the relevance of the material in the course. These multiplechoice questions are identified with the notation PE.
Review of Fundamental Concepts
Near the end of each chapter is a set of questions that help the student recall the key ideas of the chapter and focus on the relevance of these concepts.
New in This Edition
Among the changes in this edition, the following are the most significant.
Minimal Prerequisites
Because of the great variation in student preparation, we keep formal prerequisites to a minimum. We assume only a first year of high school algebra. Furthermore, we review, as needed, those topics that are typically weak spots for students.
Topics Included
This edition has more material than can be covered in most onesemester courses. Therefore, the instructor can structure the course to the students' needs and interests. The book divides naturally into four parts. The first part consists of linear mathematics: linear equations, matrices, and linear programming (Chapters 14); the second part is devoted to probability and statistics (Chapters 57); the third part covers topics utilizing the ideas of the other parts (Chapters 810); and the fourth part explores key topics from discrete mathematics that are sometimes included in the modern finite mathematics curriculum (Chapters 1113). We prefer to begin with linear mathematics since it makes for a smooth transition from high school mathematics and leads quickly to interesting applications, especially linear programming. Our preference notwithstanding, the instructor may begin this book with Chapter 5 (Sets and Counting) and then do either the linear mathematics or the probability and statistics.
Supplements