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Using & Understanding Mathematics: A Quantitative Reasoning Approach, 8th edition

Published by Pearson (January 26, 2022) © 2023

  • Jeffrey O. Bennett University of Colorado Boulder
  • William L. Briggs University of Colorado Denver

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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 will encounter in future courses, careers and daily life. Quantitative reasoning trailblazers Bennett and Briggs use a context-driven approach to motivate students and help them develop the skills needed to think critically about quantitative issues in contemporary society. The 8th Edition is revised extensively with updated applications, from the coronavirus pandemic to the latest presidential election and more.

Hallmark features of this title

  • The table of contents is organized by real-world context (not by mathematical content), with current applications throughout.
  • An Activity begins each chapter.
  • 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

  • New Learning Goals begin each unit, with a short box in the margin listing key learning goals for students.
  • New short-answer Chapter Review Questions review key content from the chapter, and are an ideal study tool before a quiz or test to help students gauge their understanding.
  • Extensive revisions pull in updated applications and examples from current events, ranging from federal taxes, NASA's Grace satellites, and global demographics to risk, life expectancy, the 2020 election, the 2020 census, and much more.
  • Updates related to the math of the pandemic offer many new, extremely relevant activities, examples, and exercises involving topics like vaccine effectiveness and the spread of COVID-19. New chapter-opening activities in Chapter 1 and Chapter 3 focus directly on pandemic mathematics, with more examples and exercises throughout the text.

Features of MyLab Math for the 8th Edition

  • New Learning Catalytics questions are available through MyLab Math and are referenced at point-of-use in the Annotated Instructor's Edition, making it easier to start using this bring-your-own-device student polling tool. All of the Quick Quiz exercises have been developed into Learning Catalytics to create a base of questions for instructor use.
  • Instructional videos are available for every example in the text and have been updated based on revisions made to the text. Corresponding video assessment questions make it easy to assign videos and check student understanding.
  • Interactive Concept Videos and Dynamic Lightboard Videos give students extra support on topics in an engaging way, while In Your World Videos use a "movie trailer" style to showcase a mathematical topic in a real-world context.
  • Integrated Review is updated in the 8th Edition MyLab course, providing comprehensive corequisite support regardless of the set-up of your corequisite course.
    • Integrated Review offers algorithmic exercises, instructional videos, and worksheets on prerequisite skills needed to be successful in this course.
    • Premade Skills Check and personalized homework assignments make it easy to begin using Integrated Review.

I. LOGIC AND PROBLEM SOLVING

  • GETTING STARTED: LITERACY FOR THE MODERN WORLD
  • Activity: 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
    • Activity: Pandemic Math
    • 1A. Living in the Media Age 
    • 1B. Propositions and Truth Values
    • 1C. Sets and Venn Diagrams
    • 1D. Analyzing Arguments
    • 1E. Critical Thinking in Everyday Life
    • Chapter 1 Summary
    • Chapter 1 Review Questions
  2. Approaches to Problem Solving
    • Activity: Global Melting
    • 2A. Understand, Solve, and Explain
    • Using Technology: Currency Exchange Rates
    • 2B. Extending Unit Analysis
    • Using Technology: Metric Conversions 
    • 2C. Problem-Solving Hints
    • Chapter 2 Summary
    • Chapter 2 Review Questions

II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE

  1. Numbers in the Real World
    • Activity: More Pandemic Math: Is 90% Good Enough?
    • 3A. Uses and Abuses of Percentages
    • 3B. Putting Numbers in Perspective 
    • Using Technology: Scientific Notation
    • 3C. Dealing with Uncertainty 
    • Using Technology: Rounding in Excel
    • 3D. Index Numbers: The CPI and Beyond  
    • 3E. Numerical Surprises: Polygraphs, Mammograms, and More
    • Chapter 3 Summary
    • Chapter 3 Review Questions
  2. Managing Money
    • Activity: Student Loans
    • 4A. Taking Control of Your Finances
    • 4B. The Power of Compounding
    • 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 
    • Using Technology: Powers of e 
    • 4C. Savings Plans and Investments
    • Using Technology: The Savings Plan Formula 
    • Using Technology: Fractional Powers (Roots) 
    • 4D. Loan Payments, Credit Cards, and Mortgages
    • Using Technology: The Loan Payment Formula (Installment Loans) 
    • Using Technology: Principal and Interest Portions of Loan Payments 
    • 4E. Income Taxes
    • 4F. Understanding the Federal Budget
    • Chapter 4 Summary
    • Chapter 4 Review Questions

III. STATISTICS AND PROBABILITY

  1. Statistical Reasoning
    • Activity: Cell Phones and Driving
    • 5A. Fundamentals of Statistics
    • Using Technology: Random Numbers
    • 5B. Should You Believe a Statistical Study?
    • 5C. Statistical Tables and Graphs
    • Using Technology: Frequency Tables in Spreadsheets
    • Using Technology: Bar Graphs and Pie Charts
    • Using Technology: Line Charts
    • 5D. Graphics in the Media
    • Using Technology: Graphs with Multiple Data Sets
    • 5E. Correlation and Causality
    • Using Technology: Scatterplots
    • Chapter 5 Summary
    • Chapter 5 Review Questions
  2. Putting Statistics to Work
    • Activity: Are We Smarter Than Our Parents?
    • 6A. Characterizing Data
    • Using Technology: Mean, Median, and Mode
    • 6B. Measures of Variation
    • Using Technology: Standard Deviation
    • 6C. The Normal Distribution
    • Using Technology: Standard Scores and Percentiles
    • 6D. Statistical Inference
    • Chapter 6 Summary
    • Chapter 6 Review Questions
  3. Probability: Living With The Odds
    • Activity: Lotteries
    • 7A. Fundamentals of Probability
    • 7B. Combining Probabilities
    • 7C. The Law of Large Numbers
    • 7D. Assessing Risk
    • 7E. Counting and Probability
    • Using Technology: Factorials 
    • Using Technology: Permutations 
    • Using Technology: Combinations
    • Chapter 7 Summary
    • Chapter 7 Review Questions

IV. MODELING

  1. Exponential Astonishment
    • Activity: Towers of Hanoi
    • 8A. Growth: Linear vs. Exponential
    • 8B. Doubling Time and Half-Life
    • Using Technology: Logarithms 
    • 8C. Real Population Growth
    • 8D. Logarithmic Scales: Earthquakes, Sounds, and Acids
    • Chapter 8 Summary
    • Chapter 8 Review Questions
  2. Modeling Our World
    • Activity: Climate Modeling
    • 9A. Functions: The Building Blocks of Mathematical Models
    • 9B. Linear Modeling
    • Using Technology: Graphing Functions 
    • 9C. Exponential Modeling
    • Chapter 9 Summary
    • Chapter 9 Review Questions
  3. Modeling With Geometry
    • Activity: Eyes in the Sky
    • 10A. Fundamentals of Geometry
    • 10B. Problem Solving with Geometry
    • 10C. Fractal Geometry
    • Chapter 10 Summary
    • Chapter 10 Review Questions

V. FURTHER APPLICATIONS

  1. Mathematics and The Arts
    • Activity: Digital Music Files
    • 11A. Mathematics and Music
    • 11B. Perspective and Symmetry
    • 11C. Proportion and the Golden Ratio
    • Chapter 11 Summary
    • Chapter 11 Review Questions
  2. Mathematics and Politics
    • Activity: Partisan Redistricting
    • 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 12 Summary
    • Chapter 12 Review Questions
  3. Mathematics and Business (online only)
    • 13A. Network Analysis
    • 13B. The Traveling Salesperson Problem
    • 13C. Scheduling Problems
    • Chapter 13 Summary

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. All 6 of his children's books have been selected for NASA's Story Time From Space. Among his other projects, Dr. Bennett proposed and co-led the development of the Voyage Scale Model Solar System in Washington, DC; created the free Totality app to help people learn about total solar eclipses; wrote an online primer on global warming; and developed a free, online curriculum for middle school Earth and Space Science. Learn more at Dr. Bennett's websites, Jeffrey Bennett: Astronomer, Teacher, & Writer, and Big Kid Science.

William L. 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 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.

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