Using & Understanding Mathematics: A Quantitative Reasoning Approach, 9th edition
- Jeffrey O. Bennett |
- William L. Briggs |
Title overview
For courses in Liberal Arts Mathematics and Quantitative Reasoning.
Mathematics for college, career, and life
Using & Understanding Mathematics: A Quantitative Reasoning Approach prepares students for the math they’ll encounter in future courses and everyday life. The authors' context-driven approach motivates students and helps them develop the skills needed to think critically about quantitative issues in contemporary society. With a modular structure and consistent Brief Review features, this text can be used by students with a wide range of mathematical backgrounds.
The 9th Edition incorporates new and updated data throughout, along with many expanded and new examples. New Math for Life features tie concepts directly to real-world issues and topics; a new emphasis on AI asks students to make use of AI tools and to evaluate their reliability.
Hallmark features of this title
- Material is organized by real-world context versus mathematical content, with current applications throughout.
- In Your World boxes focus on topics that students are likely to encounter in the news, consumer decisions, or political discussions. Corresponding exercises and videos are available.
- Brief Reviews summarize key skills and appear where first needed. Assignable exercises are available.
- Using Technology boxes highlight Excel, graphing calculators, apps, and more that can be used for the corresponding concept.
- A wide range of exercises in each chapter include Review Questions, Does It Make Sense? exercises, Basic Skills & Concepts, Further Applications, In Your World exercises, and Technology Exercises.
New and updated features of this title
- AI emphasis addresses the prevalence of artificial intelligence in student lives. Numerous examples and exercises (particularly in the “In Your World” exercise sections) ask students to make use of AI tools and to evaluate their reliability.
- New Math for Life sections near the start of each chapter are adapted from the Activity sections in prior editions, but are reframed to help students connect the chapter material more strongly with issues that will affect them in real life.
- Example topics include public health, thinking about big numbers, and more.
- Substantially revised chapter on Numbers in the Real World (Ch. 3) contains extensive examples and discussion related to economic and demographic data, including material that relies on the Consumer Price Index.
- Updated discussion involving probability and population data (Chs. 8-9) reflects the latest global demographic data.
- Discussion of the 2024 election and the new congressional apportionment based on the 2020 census are covered in Ch.12; Unit 12A explores the basics of voting.
Key features
Features of MyLab Math for the 9th Edition
- Updated Lecture videos: Lecture videos for every example in the text have been updated based on text updates. Corresponding video assessment questions make it easy to assign videos and check students’ understanding.
- New Interactive Figures illustrate key concepts and allow students to visualize topics to enhance learning.
- Updated Integrated Review offers content built specifically to support a corequisite course for quantitative reasoning or liberal arts math.
- In Your World videos are "movie trailer” videos based on the In Your World book feature. They’re a fun way to introduce topics, engage students, and show the relevancy of math in their daily lives.
- StatCrunch® is powerful, web-based statistical software integrated into the MyLab course that allows users to collect data, perform analyses, and generate compelling results. Exercises labeled with “SC” ask students to use StatCrunch to complete the exercise, getting hands-on with data.
- Interactive Concept videos provide a brief explanation, then pause to ask students to try a problem on their own. Incorrect answers are followed by further explanation. Dynamic Lightboard videos use a modern and visual "lightboard" format to cover some of the most challenging topics.
Table of contents
(Note: Each chapter concludes with Summary and Review Questions.)
I. LOGIC AND PROBLEM SOLVING
- 0. Getting Started: Literacy for the Modern World
- Math for Life: Job Satisfaction
- What Is Quantitative Reasoning?
- Quantitative Reasoning and Culture
- Quantitative Reasoning in the Work Force
- Misconceptions About Mathematics
- What Is Mathematics?
- How to Succeed in Mathematics
- 1. Thinking Critically
- Math for Life: Math and Public Health
- Living in the Media Age
- In Your World: Fact Checking on the Web
- Propositions and Truth Values
- Sets and Venn Diagrams
- Brief Review: Sets of Numbers
- Analyzing Arguments
- Mathematical Insight: Deductive Proof of the Pythagorean Theorem
- Critical Thinking in Everyday Life
- In Your World: Beware of “Up to” Deals
- 2. Approaches to Problem Solving
- Math for Life: Global Melting
- Understand, Solve, and Explain
- Brief Review: Common Fractions
- Brief Review: Decimal Fractions
- Using Technology: Currency Conversions
- In Your World: Changing Money in Foreign Countries
- Extending Unit Analysis
- Brief Review: Powers of 10
- In Your World: Gems and Gold Jewelry
- Using Technology: Metric Conversions
- In Your World: Save Money and Save the Earth
- Problem-Solving Hints
- Mathematical Insight: Zeno’s Paradox
II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE
- 3. Numbers in the Real World
- Math for Life: Big Numbers
- Uses and Abuses of Percentages
- Brief Review: Percentages
- Brief Review: What Is a Ratio?
- Putting Numbers in Perspective
- Brief Review: Working with Scientific Notation
- Using Technology: Scientific Notation
- Dealing with Uncertainty
- Brief Review: Rounding
- Using Technology: Rounding in Excel
- Index Numbers: The CPI and Beyond
- In Your World: The Chained CPI, Taxes, and Social Security
- Numerical Surprises: Polygraphs, Mammograms, and More
- 4. Managing Money
- Math for Life: Student Loans
- Taking Control of Your Finances
- The Power of Compounding
- Brief Review: Powers and Roots
- Using Technology: Powers
- Using Technology: The Compound Interest Formula
- Using Technology: The Compound Interest Formula for Interest Paid More Than Once a Year
- Using Technology: APY in Excel
- Brief Review: Four Basic Rules of Algebra
- Using Technology: Powers of e
- In Your World: Effects of Low Interest Rates
- Savings Plans and Investments
- Mathematical Insight: Derivation of the Savings Plan Formula
- Using Technology: The Savings Plan Formula
- Using Technology: Fractional Powers (Roots)
- In Your World: Building a Portfolio
- Loan Payments, Credit Cards, and Mortgages
- Using Technology: The Loan Payment Formula (Installment Loans)
- Mathematical Insight: Derivation of the Loan Payment Formula
- Using Technology: Principal and Interest Portions of Loan Payments
- In Your World: Avoiding Credit Card Trouble
- In Your World: Choosing or Refinancing a Loan
- Personal Income Taxes
- Understanding the Federal Budget
III. STATISTICS AND PROBABILITY
- 5. Statistical Reasoning
- Math for Life: Cellphones and Driving
- Fundamentals of Statistics
- Using Technology: Random Numbers
- Should You Believe a Statistical Study?
- In Your World: The Gun Debate: Defensive Gun Use
- Statistical Tables and Graphs
- Using Technology: Frequency Tables in Spreadsheets
- Using Technology: Bar Graphs and Pie Charts
- Using Technology: Line Charts
- Graphics in the Media
- Using Technology: Graphs with Multiple Data Sets
- Correlation and Causality
- Using Technology: Scatterplots
- 6. Putting Statistics to Work
- Math for Life: Are We Smarter Than Our Parents?
- Characterizing Data
- Using Technology: Mean, Median, and Mode
- Measures of Variation
- Using Technology: Calculating the Standard Deviation
- The Normal Distribution
- Using Technology: Standard Scores and Percentiles
- Statistical Inference
- 7. Probability: Living With the Odds
- Math for Life: Lotteries
- Fundamentals of Probability
- Combining Probabilities
- The Law of Large Numbers
- Assessing Risk
- In Your World: Terrorism, Risk, and Human Psychology
- Counting and Probability
- Using Technology: Factorials
- Brief Review: Factorials
- Using Technology: Permutations
- Using Technology: Combinations
IV. MODELING
- 8. Probability: Exponential Astonishment
- Math for Life: Towers of Hanoi
- Growth: Linear versus Exponential
- Doubling Time and Half-Life
- Brief Review: Logarithms
- Using Technology: Logarithms
- Real Population Growth
- In Your World: Choosing Our Fate
- Logarithmic Scales: Earthquakes, Sounds, and Acids
- In Your World: Ocean Acidification
- 9. Modeling Our World
- Math for Life: Climate Modeling
- Functions: The Building Blocks of Mathematical Models
- Brief Review: The Coordinate Plane
- Linear Modeling
- Using Technology: Graphing Functions
- In Your World: Algebra’s Origins in Baghdad
- Exponential Modeling
- Brief Review: Algebra with Logarithms
- In Your World: Changing Rates of Change
- 10. Modeling with Geometry
- Math for Life: Eyes in the Sky
- Fundamentals of Geometry
- Mathematical Insight: Archimedes and Pi
- In Your World: Plato, Geometry, and Atlantis
- Problem Solving with Geometry
- Fractal Geometry
V. FURTHER APPLICATIONS
- 11. Mathematics and the Arts
- Math for Life: Digital Music Files
- Mathematics and Music
- In Your World: Music Just for You
- Perspective and Symmetry
- Proportion and the Golden Ratio
- 12. Mathematics and the Arts
- Math for Life: Partisan Redistricting
- Voting: Does the Majority Always Rule?
- In Your World: Counting Votes - Not as Easy as It Sounds
- Theory of Voting
- In Your World: The Electoral College and the Presidency
- Apportionment: The House of Representatives and Beyond
- Dividing the Political Pie
- 13. Mathematics and Business (ONLINE ONLY)
- Math for Life: Remodeling a House
- Network Analysis
- The Traveling Salesperson Problem
- In Your World: Artificial Intelligence (AI) and Network Problems
- Scheduling Problems
- Answers to Quick Quizzes Odd-Numbered Exercises, and Chapter Review Questions
- Credits
- Index
- Index of Applications
Author bios
About our authors
Jeffrey Bennett served as the first director of the program “Quantitative Reasoning and Mathematical Skills” at the University of Colorado at Boulder, where he developed the groundbreaking curriculum that became the basis of this textbook. He holds a BA in biophysics (University of California, San Diego) and an MS and a PhD in astrophysics (University of Colorado), and has focused his career on math and science education.
In addition to co-authoring this textbook, he is also the lead author of best-selling college textbooks on statistical reasoning, astronomy, and astrobiology, and of more than a dozen books for children and adults. Among other projects, Dr. Bennett proposed and co-led the development of the Voyage Scale Model Solar System on the National Mall in Washington, DC; created the free Totality app to help people learn about total solar eclipses; developed a free, online curriculum for middle school Earth and Space Science; and wrote an online primer on global warming. He has received numerous awards, including the American Institute of Physics Science Communication award and the American Association of Physics Teachers Klopsteg Education Award. Learn more at his website.
William Briggs was on the mathematics faculty at Clarkson University for 6 years and at the University of Colorado at Denver for 23 years, where he taught both undergraduate and graduate courses, with a special interest in applied mathematics. During much of that time, he designed and taught courses in quantitative reasoning. In addition to this book, he has co-authored textbooks on statistical reasoning and calculus, as well as monographs in computational mathematics. He is also author of the book How America Got Its Guns (University of New Mexico Press).
Dr. Briggs is a University of Colorado President’s Teaching Scholar and the recipient of a Fulbright Fellowship to Ireland; he holds a BA degree from the University of Colorado and an MS and a PhD from Harvard University.