Finite Mathematics

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9780130199584: Finite Mathematics

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.

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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 Inequalities reviews 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 Statistics explains 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 reviewers commented that this is the single most distinctive and user-friendly feature of our book that provides students a tool in their learning and understanding of the mathematics at hand. Frequently, applied mathematics instructors hear students comment that "I don't even know how to begin this problem." or "If the problem was just set up for me, I could solve it." Because skills such as setting up problems and writing the solution in its proper context can be a major challenge for finite mathematics students, we have integrated a problem solving method throughout the text. The steps of the problem solving method are used throughout the text. We use the phrases "Understand the Situation" and "Interpret the Solution" to identify two critical steps in problem solving.

  • When solving an application example, we first need to Understand the Situation. In these clearly labeled paragraphs we state the quantity we are trying to determine and identify the method used to determine the solution. Frequently we reveal the thought processes necessary to attack the problem.
  • After determining a numerical solution in a traditional solution step, we Interpret the Solution. In the interpretation step, we write a concluding sentence that conveys the meaning of the numerical answer in the context of the application. To reinforce these techniques, we often ask students to solve and interpret the solution to various applied problems in the exercise sets.

Exercises

A typical section exercise set contains numerous skill builder problems, a generous selection of applications from many different disciplines, and an abundant supply of real data modeling applications, which are denoted by a symbol. We have included more applications based on real data in our textbook than in any other finite mathematics book on the market. Another lesson learned from our market research is that many finite mathematics textbooks fail to provide enough exercises for the student to grasp the course content. With more than 3200 exercises, we are confident our textbook has more than enough exercises to meet student's needs.

Use Real Data Applications to Keep It Interesting

Students in this course tend to be very pragmatic; they want to know why they must learn the mathematical content in this course. Including many real data modeling applications (denoted in text by a symbol) helps to answer their unstated question and provides motivation and interest. Many of the models, parameters, and scenarios in the examples and exercises are based on data gathered from the U.S. Statistical Abstract, the Census Bureau, and other reliable sources for which URLs are always given. For example, we include real data modeling applications such as determining planting schedules in California (Source: U.S. Department of Agriculture, www.usda.gov/nass) in the linear programming chapters. Other examples include:

  • The out-of-pocket hospital care and physician services expenditures by patients and by Medicare used as an application of matrix operations (Source: U.S. Census Bureau, www.census.gov).
  • The percentage of American adults who exercised for 30 minutes or more at least 5 times per week, classified by gender, as an application of conditional probability. (Source: National Center for Chronic Disease Prevention, www.cdc.gov/nccdphp).
  • The typical amount of financial debt held by American families, classified by age group, as an application of frequency distributions (Source: U.S. Census Bureau, www.census.gov).

The quantity, quality, and variation of these types of applications are simply not found in other finite mathematics textbooks. We believe that real data modeling applications not only keep the course content relevant and fresh, but compel students to interpret the numerical solution in the context of the problem they have solved.

Provide Timely Reinforcement of Algebra and Other Essential Skills

One of the major challenges faced by students, and frustrations encountered by instructors, is weak preparation in algebra and other essential skills. Even students who have proficient algebra skills are often rusty and unsure of which algebraic tool to apply. Further, the content demands of a finite mathematics course does not allow for extensive time spent on review. In an effort to address this pervasive problem, we have developed the "From Your Toolbox" feature in the body of the text and also in the MathPro for Finite Math software.

From Your Toolbox

When appropriate, the "From Your Toolbox" feature directs students to read background material in the Algebra Review or other appendices. In addition, this feature is used to review previously introduced definitions, theorems, or properties as needed. By providing a brief review when it is needed, students stay on task and do not need to flip back to hunt through previous sections for key information.

MathPro5 for Finite Math. Powered by Prentice Hall's celebrated MathPro engine, this unique new program is keyed section by section to our text. MathPro5 is online, customizable tutorial and assessment software that is fully integrated with Finite Math at the section level for anytime, anywhere learning. Students access multiple types of help while working algorithmically-generated tutorial exercises for review and concept mastery.

Let Instructor's Decide Whether to Incorporate Technology

As graduates and instructors of The Ohio State University, we began using graphing calculator technology in the classroom long before it was fashionable to do so. Based on our years of experience in this area, we have seen the strengths of using a graphing calculator and the drawbacks as well. Our philosophy is to let the instructor, rather than the textbook, determine how much or how little graphing calculators, spreadsheets, or other desktop applications are used in classroom. Since our goal was to write a text where graphing calculator t...

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