Finite Mathematics : Solving Problems in Business, Economics, and the Social and Behavioral Sciences

by Armstrong, Bill; Davis, Don

• ISBN13: 9780130199584
• ISBN10: 0130199583
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Pearson College Div

Summary

This book, modern in its writing style as well as in its applications, contains numerous exercises--both skill oriented and applications--, real data problems, and a problem solving method. The book features exercises based on data form the World Wide Web, technology options for those who wish to use a graphing calculator, review boxes, strategic checkpoints, interactive activities, section summaries and projects, and chapter openers and reviews. For anyone who wants to see and understand how mathematics are used in everyday life.

Table of Contents

Preface	xiii
Linear Models and Systems of Linear Equations	1	(70)
Problem Solving: Linear Equations	2	(9)
Introduction to Linear Functions	11	(13)
Linear Models	24	(12)
Solving Systems of Linear Equations Graphically	36	(15)
Solving Systems of Linear Equations Algebraically	51	(20)
Chapter Review Exercises	65	(5)
Chapter 1 Project	70	(1)
Systems of Linear Equations and Matrices	71	(68)
Matrices and Gauss-Jordan	72	(13)
Matrices and Operations	85	(10)
Matrix Multiplication	95	(13)
Matrix Inverses and Solving Systems of Linear Equations	108	(15)
Leontief Input-Output Models	123	(16)
Chapter Review Exercises	131	(6)
Chapter 2 Project	137	(2)
Linear Programming: The Graphical Method	139	(52)
Problem Solving: Linear Inequalities	140	(11)
Graphing Systems of Linear Inequalities	151	(12)
Solving Linear Programming Problems Graphically	163	(10)
Applications of Linear Programming	173	(18)
Chapter Review Exercises	186	(4)
Chapter 3 Project	190	(1)
Linear Programming: The Simplex Method	191	(64)
Introduction to the Simplex Method	192	(13)
Simplex Method: Standard Maximum Form Problems	205	(15)
Simplex Method: Standard Minimum Form Problems and Duality	220	(14)
Simplex Method: Nonstandard Problems	234	(21)
Chapter Review Exercises	247	(6)
Chapter 4 Project	253	(2)
Mathematics of Finance	255	(52)
Simple Interest	256	(10)
Compound Interest	266	(14)
Future Value of an Annuity	280	(10)
Present Value of an Annuity	290	(17)
Chapter Review Exercises	302	(3)
Chapter 5 Project	305	(2)
Sets and the Fundamentals of Probability	307	(90)
Problem Solving: Probability and Statistics	308	(11)
Sets and Set Operations	319	(11)
Principles of Counting	330	(10)
Introduction to Probability	340	(13)
Computing Probabilities Using the Addition Rule	353	(12)
Computing Probabilities Using the Multiplication Rule	365	(11)
Bayes' Theorem and Its Applications	376	(21)
Chapter Review Exercises	389	(7)
Chapter 6 Project	396	(1)
Graphical Data Description	397	(64)
Graphing Qualitative Data	398	(14)
Graphing Quantitative Data	412	(16)
Measures of Centrality	428	(14)
Measures of Dispersion	442	(19)
Chapter Review Exercises	454	(5)
Chapter 7 Project	459	(2)
Probability Distributions	461	(64)
Discrete Random Variables	462	(13)
Expected Value and Standard Deviation of a Discrete Random Variable	475	(14)
The Binomial Distribution	489	(13)
The Normal Distribution	502	(23)
Chapter Review Exercises	519	(5)
Chapter 8 Project	524	(1)
Markov Chains	525	(42)
Introduction to Markov Chains	526	(12)
Regular Markov Chains	538	(11)
Absorbing Markov Chains	549	(18)
Chapter Review Exercises	562	(3)
Chapter 9 Project	565	(2)
Game Theory	567	(35)
Strictly Determined Games	568	(8)
Mixed Strategies	576	(10)
Game Theory and Linear Programming	586	(16)
Chapter Review Exercises	596	(4)
Chapter 10 Project	600	(2)
Appendix A Prerequisites for Finite Mathematics	602	(11)
A.1 Percents, Decimals and Fractions	602	(3)
A.2 Evaluating Expressions and Order of Operations	605	(2)
A.3 Properties of Integer Exponents	607	(4)
A.4 Rational Exponents and Radicals	611	(2)
Appendix B Algebra Review	613	(24)
B.1 Multiplying Polynomial Expressions	613	(3)
B.2 Factoring Trinomials	616	(5)
B.3 Solving Linear Equations	621	(3)
B.4 Solving Quadratic Equations	624	(5)
B.5 Properties of Logarithms	629	(3)
B.6 Geometric Sequence and Series	632	(5)
Appendix C Calculator Programs	637	(5)
Appendix D Standard Normal Table	642
Answers to Odd-Numbered Exercises	1	(1)
Index	1

Excerpts

Audience In preparing to write this text, we talked with many of our colleagues who teach a finite math course to find out if they experienced the same difficulties in teaching this course. What we learned is that while there is very little similarity in the topics covered or in how much time is spent on each area, there is remarkable uniformity in the needs of students who enroll in these diverse courses. Professors at Community Colleges, Universities, and Liberal Arts Colleges all told us that their students are generally unmotivated, unsure of their algebra skills, and uncomfortable with translating English into mathematics and knowing how to set up problems for solution. Armed with this knowledge, we set out to write a new Finite Math text that would address these fundamental needs. As with other Finite Mathematics textbooks, our text may be used in either a one or two term course for students majoring in economics, business, social, or behavioral sciences. We have organized the topics for maximum flexibility so that the text may be adapted to any college or university's curriculum. However, that is where the similarity ends. We have crafted this book around six key principles designed to address student's needs: Present the mathematics in language that students can read and understand Teach good problem solving techniques and provide ample practice Use real data applications to keep it interesting Provide timely reinforcement of algebra and other essential skills Let Instructor's decide whether to incorporate technology Present Probability and Statistics with clarity and precision Present the Mathematics in Language That Students Can Read and Understand By writing this text in a conversational, easy-to-read style, we strive to evoke the one-on-one communication of a tutorial session. When students find that they can understand the clear presentation and follow the interesting, real world examples, we believe they will get into the habit of reading the text. Although we have written a text that is accessible, we have been careful not to sacrifice the proper depth of coverage and necessary rigor required of finite mathematics. We are confident both objectives have been met. Teach Good Problem Solving Techniques and Provide Ample Practice Problem Solving Sections Before explaining how to solve an entire class of problems, we provide a special section that demonstrates how to apply the appropriate mathematical tools to analyze a given type of problem. For example, the first section of the book,Problem Solving: Linear Equations,introduces our general approach to problem solving and then addresses the challenge of analyzing a word problem and translating the words into mathematical expressions; after which we examine the more complex situation of writing a word problem as a system of linear, equations. The other dedicated problem solving sections introduce strategies and techniques for solving each type of problem. Section 3.1,Problem Solving: Linear Inequalitiesreviews writing linear models and solving linear inequalities, both of which are vital skills for solving linear programming problems. Section 6.1,Problem Solving: Probability and Statisticsexplains some basic concepts in probability and statistics such as probability experiment, mutual exclusivity, and ordered samples. Many of the exercises in these problem solving sections prepare students for subsequent sections because they introduce exercises that are solved later in the textbook. Reviewer feedback was enthusiastic on these sections which indicated to us that we were pursuing an approach that many felt was lacking in this area. Problem Solving Method To help students solve problems in finite mathematics, we developed a problem solving method that is used throughout the entire text. Many revie