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Understanding Our Quantitative World

Understanding Our Quantitative World

By Janet Andersen and Todd Swanson

Print ISBN: 978-0-88385-738-0
320 pp., Hardbound, 2005
List Price: $58.00
MAA Member: $43.50
Series: MAA Textbooks

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This text 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 multivariable) 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 text 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 Web. Doing these activities demonstrates to students that they can use mathematics as a tool in interpreting quantitative information they encounter outside of academics. The course is designed to allow students to spend most of their time in class working in groups on the activities. Rather than having students passively listen, this approach requires students to read, discuss, and apply mathematics. The text assumes that students will have access to some type of technology such as a graphing calculator.

Table of Contents

Graphical Representations of Functions
Applications of Graphs
Displaying Data
Describing Data: Mean, Median, and Standard Deviation
Multivariable Functions and Contour Diagrams
Linear Functions
Regression and Correlation
Exponential Functions
Logarithmic Functions
Periodic Functions
Power Functions
Random Samples
Appendix: Instructions for the TI-83 Graphing Calculator
About the Authors

About the Authors

Janet Andersen has been a member of the Hope College Mathematics Department since 1991, Director o the Pew Midstates Science and Mathematics Consortium since 2002, Chair of the Mathematics Department from 2000 to 2004, GEMS (General Education Mathematics & Science courses) Coordinator from 1996 to 2001, and Director of General Education from 1998 to 2000. She taught high school in East Texas for four years before attending graduate school at the University of Minnesota.

She has been the Principal Investigator from three NSF curriculum grants. The second grant, awarded in 1997, led to the development of a general education mathematics course tied to two general education science courses at Hope College. Her co-author, Todd Swanson (Mathematics) collaborated with her on this project, along with, Ed Hansen (Geological and Environmental Science), and Kathy Winnent-Murray (Biology). The materials from the mathematics course are contained in Understanding our Quantitative World. The first NSF grant, awarded in 1993, resulted in Projects for Precalculus and Precalculus: A Study of Functions and Their Applications. Her third grant, awarded in 2000, resulted in the development of a co-taught mathematical biology course. She also enjoys being with her family, contra dancing, playing Euro board games, and reading mysteries.

Todd Swanson received a BS in mathematics from Grand Valley State University in 1985 and then taught high school mathematics for two years. He received an MA in mathematics from Michigan State University in 1989 (where he received the Excellence in Teaching Award for Senior Graduate Students). He has taught at the college level since 1989 and has been at Hope College since 1995.

His other books, Projects for Precalculus (published in 1997 and awarded the Innovative Programs Using Technology Award) and Precalculus: A Study of Functions and Their Applications were co-authored with Janet Andersen (Hope College) and Robert Keeley (Calvin College).

Much of Todd Swanson’s teaching time at Hope is devoted to Introductory Statistics. He has written numerous laboratories that involve the incorporation of Minitab and are aimed at trying to get students to understand the concepts while exploring real world data. He has also taught liberal arts mathematics, precalculus, calculus, mathematics education courses, and an introduction to writing proofs. Outside of work he can be found working around the hose, transporting one of his children to soccer or baseball practice, and participating in some outdoor activity.