# Understanding Our Quantitative World

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*Janet Andersen; Todd Swanson*

MAA Press: An Imprint of the American Mathematical Society

This book is intended for a general education
mathematics course. The authors focus on the topics that they believe
students will likely encounter after college. These topics fall into
the two main themes of functions and statistics. After the concept of
a function is introduced and various representations are explored,
specific types of functions (linear, exponential, logarithmic,
periodic, power, and multi-variable) are investigated. These functions
are explored symbolically, graphically, and numerically and are used
to describe real world phenomena. On the theme of statistics, the
authors focus on different types of statistical graphs and simple
descriptive statistics. Linear regression, as well as exponential and
power regression, is also introduced. Simple types of probability
problems as well as the idea of sampling and confidence intervals are
the last topics covered in the text. The book is written in a
conversational tone. Each section begins by setting the mathematics
within a context and ends with an application. The questions at the
end of each section are called "Reading Questions" because students
are expected to be able to answer most of these after carefully
reading the text. "Activities and Class Exercises" are also found at
the end of each section. These activities are taken from public
sources such as newspapers, magazines, and the Internet. Doing these
activities demonstrates that mathematics can be used as a tool in
interpreting quantitative information encountered in everyday
life. The text assumes that students will have access to some type of
technology such as a graphing calculator.

An instructor's manual for this title is available to those
instructors who have adopted the textbook for classroom use. Please
send email to textbooks@ams.org
for more information.

#### Reviews & Endorsements

This text is part of the Mathematical Association of America's "Classroom Resource materials" series, which provides students with supplementary classroom materials. While the majority of the text's exposition includes many basic yet appropriate examples of the topic at hand, the authors explain in the preface that they expect the majority of course class time to be spent working with students on the more applied "Activities and Class Exercises" in a group setting. Each chapter includes example activities that incorporate public source data and ask students to think about relevant topics. Examples of these applied activities include analysis of credit card debt, tuition rates, textbook prices, car loans, and the destruction of the ozone layer. These topics and the mathematics that students would use to analyze them address the question, "What mathematical skills and concepts are useful for informed citizens?" This is the query upon which the authors base their text. The average student would find this book easy to read. There are many examples in every section, and tables and figures are clear and readily interpreted. Each section of reading includes one application problem and a number of reading questions. While many of these reading questions are quantitative in nature, the majority of the numerically based problems require some form of interpretation on the student's part. Generally, students should be able to answer the reading questions if they read the text, and these problems will allow students to delve deeper into the "Class Exercises" that are the richest aspect of the book. Three main topics addressed in the text are the application and interpretation of graphs; simple functions; and statistical information. the chapters are arranged such that these three main topics are scattered throughout the book. However, an instructor could easily choose the order in which to study the different topics. Chapter 6 focuses on multi-variable functions and contour diagrams, topics that students often find confusing, but Andersen and Swanson provide concrete examples that are well-written and easy to understand. At several points in the text, the authors use technology to help solve problems or display data. Instructions for using the TI-83 calculator are provided in an appendix and short supplementary directions can be found within the text. I recommend this text for college algebra instructors who would like to see their students use their mathematical skills to analyze and interpret real-world problems. The variety of data and applications will also inspire many curious students to think mathematically beyond the classroom.

-- Hilary Fletcher, Mathematics and Computer Education

# Table of Contents

## Understanding Our Quantitative World

- Understanding our Quantitative World iii4
- Preface vii8
- Contents xi12
- 1 Functions 114
- 2 Graphical Representations of Functions 2134
- 3 Applications of Graphs 4558
- 4 Displaying Data 6780
- 5 Describing Data: Mean, Median, and Standard Deviation 8598
- 6 Multivariable Functions and Contour Diagrams 105118
- 7 Linear Functions 123136
- 8 Regression and Correlation 145158
- 9 Exponential Functions 161174
- 10 Logarithmic Functions 195208
- 11 Periodic Functions 213226
- 12 Power Functions 233246
- 13 Probability 255268
- 14 Random Samples 273286
- Appendix: Instructions for the TI-83 Graphing Calculator 287300
- Index 301314
- About the Authors 303316