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Using and Understanding Mathematics: A Quantitative Reasoning Approach, 3/E
Jeffrey O. Bennett, University of Colorado at Boulder
William Briggs, University of Colorado at Denver

ISBN-10: 0321227735
ISBN-13: 9780321227737

Publisher: Pearson
Copyright: 2005
Format: Cloth; 800 pp
Published: 02/17/2004

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Description

With all of the topics needed to fulfill a general education requirement, this text, one of the few for the emerging Quantitative Literacy/Quantitative Reasoning Course, helps to reduce mathematical anxiety and focuses on the practicality of mathematics in college, career, and life.

Features

Time Out to Think. Appearing throughout the book, the “Time Out to Think“ features pose short conceptual questions designed to help students reflect on important new ideas. They also serve as excellent starting points for classroom discussions.

Margin Features. This book includes a wide margin so that students have room to make notes while studying. The margin also contains material that should spur student interest but is peripheral to the main discussion. This material comes in three basic forms:
- By the Way features contain interesting notes and asides relevant to the topic at hand.
- Historical Note remarks give historical context to the ideas presented in the chapter.
- Technical Notes contain details that are important mathematically, but generally do not affect students' understanding of the material.

A Brief Review. These boxed features review key mathematical skills that students should have learned previously, but in which many students still need review and practice. They appear in the book wherever a particular skill is first needed, and exercises based on the review boxes can be found at the end of the unit.

Practical Matters. These boxed features focus on topics of particularly high practical importance, such as how to watch out for bad deals on telephone service, how to avoid credit card trouble, and how to save money and energy at the same time.

Thinking About. These boxed features build upon ideas in the main narrative but go somewhat beyond the level of other material in the book. Examples include boxes on the proof of the Pythagorean theorem and on Zeno's paradox.

Basic Skills and Concepts. These questions offer practice with the concepts covered in the unit. The exercises can be used for homework assignments or for self-study (answers to most odd-numbered exercises appear in the back of the book).

Web Projects. The Web Projects require searching for data or other information on the Web. They can be used for extended projects, discussion, group activities, or essays.

In the News. These questions ask students to find examples from the news or from daily life of the ideas presented in the unit. These questions may be assigned as homework or used for class discussions.

New To This Edition

We have expanded our coverage of geometry with our new Chapter 10, called Modeling with Geometry. This chapter contains two full units of basic geometry and its applications, as well as a unit on fractal geometry.

NEW! Further Applications. These exercises extend the ideas and techniques covered in the text through additional applications.

NEW! Now Try Exercises. At the end of every in-text example students are directed to “Now Try” a specific exercise. This new feature allows students to immediately test their comprehension of the material.

NEW! Does It Make Sense? These qualitative questions test conceptual understanding by asking whether given statements are sensible and asking students to explain why or why not.

Table of Contents

I. LOGIC AND PROBLEM SOLVING.

1. Thinking Critically.

Recognizing Fallacies.

Propositions and Truth Values.

Sets and Venn Diagrams.

A Brief Review: Sets of Numbers.

Analyzing Arguments.

Critical Thinking in Everyday Life.

2. Approaches to Problem Solving.

The Problem-Solving Power of Units.

A Brief Review: Working with Fractions.

Standardized Units: More Problem-Solving Power.

A Brief Review: Powers of 10.

Problem-Solving Guidelines and Hints.

II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE.

3. Numbers in the Real World.

Uses and Abuses of Percentages.

A Brief Review: Percentages.

A Brief Review: What is ratio?.

Putting Numbers in Perspective.

A Brief Review: Working with Scientific Notation.

Dealing with Uncertainty.

A Brief Review: Rounding.

Index Numbers: The CPI and Beyond.

How Numbers Deceive: Polygraphs, Mammograms, and More.

4. Financial Management.

The Power of Compounding.

A Brief Review: Three Basic Rules of Algebra.

Savings Plans and Investments.

A Brief Review: Algebra with Powers and Roots.

Loan Payments, Credit Cards, and Mortgages.

Income Taxes.

Understanding the Federal Budget.

III. PROBABILITY AND STATISTICS.

5. Statistical Reasoning.

Fundamentals of Statistics.

Should You Believe a Statistical Study?

Statistical Tables and Graphs.

Graphs in the Media.

Correlation and Causality.

6. Putting Statistics to Work.

Characterizing a Data Distribution.

Measures of Variation.

The Normal Distribution.

Statistical Inference.

7. Probability: Living with the Odds.

Fundamentals of Probability.

A Brief Review: The Multiplication Principle.

Combining Probabilities.

The Law of Large Numbers.

Assessing Risk.

Counting and Probability.

A Brief Review: Factorials.

IV. MODELING.

8. Exponential Astonishment.

Growth: Linear Versus Exponential.

Doubling Time and Half-Life.

A Brief Review: Logarithms.

Real Population Growth.

Logarithmic Scales: Earthquakes, Sounds, and Acids.

9. Modeling Our World.

Functions: The Building Blocks of Mathematical Models.

A Brief Review: The Coordinate Plane.

Linear Modeling.

Exponential Modeling.

A Brief Review: Algebra with Logarithms.

10. Modeling with Geometry.

Fundamentals of Geometry.

Problem Solving with Geometry.

Fractal Geometry.

V. FURTHER APPLICATIONS.

11. Mathematics and the Arts.

Mathematics and Music.

Perspective and Symmetry.

Proportion and the Golden Ration.

12. Mathematics and Politics.

Voting: Does the Majority Always Rule?

Theory of Voting.

Apportionment: The House of Representatives and Beyond.

13. Mathematics and Business.

Network Analysis.

The Traveling Salesman Problem.

Scheduling Problems.

Credits.

Answers.

Index.

Courses

Quantitative Literacy (Mathematics)
Liberal Arts Mathematics (Mathematics)

Next Edition(s)

Using and Understanding Mathematics: A Quantitative Reasoning Approach, 5/E
Bennett & Briggs
©2011 | Pearson | Cloth; 744 pp | Instock
ISBN-10: 0321652797 | ISBN-13: 9780321652799
Net price: $115.00 (What's this?)Brief Description |

Using and Understanding Mathematics: A Quantitative Reasoning Approach increases students‘ mathematical literacy so that they better understand the mathematics used in their daily lives.

Ideal for courses that emphasize quantitative reasoning, Bennett and Briggs prepare students to use math effectively to make better decisions throughout their lives. Contents are organized with that in mind, with engaging coverage in sections like Taking Control of Your Finances, Dividing the Political Pie, and a full chapter about Mathematics and the Arts.

This Fifth Edition offers new hands-on Activities for use with students in class, new ways for students to check their understanding through Quick Quizzes, and a new question type in MyMathLab that applies math to recent events in the news. In addition, the authors increase their coverage of consumer math, and provide a stronger emphasis on technology through new Using Technology features and exercises. The new Insider's Guide provides instructors with tips and ideas for effective use of the text in teaching the course.

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Author Bios

Jeffrey O. Bennett¿s academic home is the University of Colorado at Boulder, where he has been teaching on and off since 1983 and from which he received his Ph.D. in Astrophysics in 1987. During this time, he¿s taught more than 50 college courses in subjects including mathematics, astronomy, physics, environmental science, and science education. He began work on Using and Understanding Mathematics because he is particularly interested in helping students overcome difficulties with mathematics. For similar reasons, he has recently completed a textbook for introductory astronomy (The Cosmic Perspective, with M. Donahue, N. Schneider, and G.M. Voit, Addison Wesley Longman, 1999).

He is also working on several books about mathematics and science for the general public. In addition, he is now working on science books for children. Jeff is perhaps best known for his role in creating the Voyage Scale Model Solar System on the National Mall in Washington, DC (opening October 2001); he proposed the project and worked on the team that developed it as a collaborative effort between the Challenger Center for Space Science Education, the Smithsonian Institution, and NASA.

When not working, he enjoys participating in masters swimming and hiking the trails of Boulder, Colorado, with his family.

William L. Briggs has been on the mathematics faculty at the University of Colorado at Denver for 17 years. He teaches throughout the undergraduate and graduate curriculum with a special interest in teaching mathematical modeling as it applies to problems in biology and medicine. He developed the quantitative reasoning course for liberal arts students at CU-Denver supported by the textbook Using and Understanding Mathematics, which he co-authored with Jeff Bennett. He has written two other tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform.

He is a University of Colorado President's Teaching Scholar, an Outstanding Teacher awardee of the Rocky Mountain Section of the MAA, and the recipient of a Fulbright Fellowship to Ireland. Bill lives with his wife, Julie, his daughter, Katie, and two dogs, Midnight and Seamus, in Boulder, Colorado. He loves to bake bread, as well as run trails and rock climb in the mountains near his home.

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Using and Understanding Mathematics: A Quantitative Reasoning Approach, 3/E