Addison-Wesley / Prentice Hall

Mathematics

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Using and Understanding Mathematics: A Quantitative Reasoning Approach, 4/E
Jeffrey O. Bennett, University of Colorado at Boulder
William L. Briggs, University of Colorado at Denver

ISBN-10: 0321458206
ISBN-13: 9780321458209

Publisher: Addison-Wesley
Copyright: 2008
Format: Cloth; 848 pp
Published: 01/22/2007

Suggested retail price: $126.67
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Most students taking this course do so to fulfill a requirement, but the true benefit of the course is learning how to use and understand mathematics in daily life. This quantitative reasoning text is written expressly for those students, providing them with the mathematical reasoning and quantitative literacy skills they'll need to make good decisions throughout their lives. Common-sense applications of mathematics engage students while underscoring the practical, essential uses of math.

  • Practical Matters. Focusing on matters of high practical importance, this feature highlights common-sense applications of math such as avoiding credit card trouble and spotting a bad cell phone deal.
  • A Brief Review. This feature reviews key mathematical skills students should have learned previously, but 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.
  • Thinking About. Building upon the main narrative, this feature reaches beyond to a deeper level of mathematical understanding. Examples include boxes on the proof of the Pythagorean theorem and on Zeno's paradox.
  • 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. A wide margin leaves room for students to make notes while studying. The margin also contains material that spurs student interest 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 for students looking for more depth
  • Now Try Exercises. At the end of every in-text example students are directed to Now Try a specific exercise, immediately testing their comprehension of the material.
  • Does It Make Sense? These qualitative exercise questions test conceptual understanding by asking whether given statements are sensible and asking students to explain why or why not.  
  • Basic Skills and Concepts. Covering concepts from the unit, these 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 students to search for data or other information online. They can be used for extended projects, discussions, group activities, or essays.
  • In the News. In these exercises, students are challenged to find examples of unit concepts in the news or in their daily lives. These questions may be assigned as homework or used for class discussions.

  • Two new units increase students’ understanding of how math applies to daily life. New Unit 4A: Taking Control of Your Finances provides an introduction to the personal budgeting issues presented in Chapter 4. In addition, a new unit on redistricting and what it means has been added as Unit 12D: Dividing the Political Pie, to show students how math affects their day-to-day life with a topic that is especially important in the upcoming elections.
  • Each set of exercises now begins with a Quick Quiz to test students’ conceptual understanding. These multiple choice questions are designed to be answered with an explanation on why a particular answer was selected, and will help students prepare for the rest of the exercise set.
  • All of the Applications Exercises are updated or revised with more current data or more relevant information for students.
  • New Art Annotations have been included to make the art a more useful learning tool.
  • Over 500 new exercises have been added, wtih more exercises focusing on basic skills. Over 50% of the exercises are new or have been revised and improved for better student understanding.

Preface

Prologue: Literacy for the Modern World

 

Part 1 Logic and Problem Solving            

Chapter 1      Thinking Critically

1A       Recognizing Fallacies

1B       Propositions and Truth Values

1C       Sets and Venn Diagrams

1D       Analyzing Arguments

1E       Critical Thinking in Everyday Life

 

Chapter 2      Approaches to Problem Solving

2A       The Problem-Solving Power of Units

2B       Standardized Units: More Problem-Solving Power

2C       Problem-Solving Guidelines and Hints

 

Part 2 Quantitative Information in Everyday Life            

Chapter 3      Numbers in the Real World

3A       Uses and Abuses of Percentages

3B       Putting Numbers in Perspective

3C       Dealing with Uncertainty

3D       Index Numbers: The CPI and Beyond

3E       How Numbers Deceive: Polygraphs, Mammograms, and More

 

Chapter 4      Managing Your Money

4A       Taking Control of Your Finances

4B       The Power of Compounding

4C       Savings Plans and Investments

4D       Loan Payments, Credit Cards, and Mortgages

4E       Income Taxes

4F       Understanding the Federal Budget

 

Part 3 Probability and Statistics

Chapter 5      Statistical Reasoning

5A       Fundamentals of Statistics

5B       Should You Believe a Statistical Study?

5C       Statistical Tables and Graphs

5D       Graphics in the Media

5E       Correlation and Causality

 

Chapter 6      Putting Statistics to Work

6A       Characterizing a Data Distribution

6B       Measures of Variation

6C       The Normal Distribution

6D       Statistical Inference

 

Chapter 7      Probability: Living with the Odds

7A       Fundamentals of Probability

7B       Combining Probabilities

7C       The Law of Large Numbers

7D       Assessing Risk

7E       Counting and Probability

 

Part 4 Modeling

Chapter 8      Exponential Astonishment

8A       Growth: Linear versus Exponential

8B       Doubling Time and Half-Life

8C       Real Population Growth

8D       Logarithmic Scales: Earthquakes, Sounds, and Acids

 

Chapter 9      Modeling Our World

9A       Functions: The Building Blocks of Mathematical Models

9B       Linear Modeling

9C       Exponential Modeling

 

Chapter 10   Modeling with Geometry

10A     Fundamentals of Geometry

10B     Problem Solving with Geometry

10C     Fractal Geometry

 

Part 5 Further Applications

Chapter 11   Mathematics and the Arts

11A     Mathematics and Music

11B     Perspective and Symmetry

11C     Proportion and the Golden Ratio

 

Chapter 12   Mathematics and Politics

12A     Voting: Does the Majority Always Rule?

12B     Theory of Voting

12C     Apportionment: The House of Representatives and Beyond

12D     Dividing the Political Pie

 

Chapter 13   Mathematics and Business

13A     Network Analysis

13B     The Traveling Salesman Problem

13C     Scheduling Problems

 

Credits

Answers

Index

 

 

Jeffrey Bennett specializes in mathematics and science education. He has taught at every level, from pre-school through graduate school, including more than 50 college courses in mathematics, physics, astronomy, and education. His work on Using and Understanding Mathematics began in 1987, when he helped create a new mathematics course for the University of Colorado’s core curriculum. Variations on this course, with its quantitative reasoning approach, are now taught at hundreds of colleges nationwide. In addition to his work in mathematics, Dr. Bennett (whose PhD is in astrophysics) has written leading college-level textbooks in astronomy, statistics, and the new science of astrobiology, as well as books for the general public. He also proposed and developed both the Colorado Scale Model Solar System on the University of Colorado at Boulder campus and the Voyage Scale Model Solar System, a permanent, outdoor exhibit on the National Mall in Washington, DC. He has recently begun writing science books for children, including the award-winning Max Goes to the Moon and Max Goes to Mars. When not working, he enjoys 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 22 years. He teaches numerous courses within the undergraduate and graduate curriculum, and has special interest in teaching calculus, differential equations, and mathematical modeling. He developed the quantitative reasoning course for liberal arts students at University of Colorado at Denver supported by his textbook Using and Understanding Mathematics. He has written two other tutorial monographs, The Multigrid Tutorial and The DFT: An Owner's Manual for the Discrete Fourier Transform, as well as Ants, Bikes, Clocks, a mathematical problem solving text for undergraduates. 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, and their gordon setter, Seamus, in Boulder, Colorado. He loves to bake bread, run trails, and rock climb in the mountains near his home.

View a Sample Chapter PDF:

For Liberal Arts Mathematics


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