Using & Understanding Mathematics: A Quantitative Reasoning Approach, 7th edition

Published by Pearson (July 14, 2021) © 2019

  • Jeffrey O. Bennett University of Colorado Boulder
  • William L. Briggs University of Colorado Denver
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Through their proven success as trailblazers in Quantitative Reasoning, Jeff Bennett and Bill Briggs' Using & Understanding Mathematics: A Quantitative Reasoning Approach prepares you for the mathematics you will encounter in college courses, your future career and life in general. Its quantitative reasoning approach helps you build the skills required to understand major issues in everyday life, and encourages you to develop the problem-solving tools needed to think critically about quantitative issues in contemporary society. The authors' unique learning aids and modular approach offer an interesting and flexible combination of technology and text. In the 7th Edition, updated data throughout reflects the most current information and events; an extensively revised chapter on managing money includes the most current financial information regarding loans, taxes and budgets; and much more.

I. LOGIC AND PROBLEM SOLVING

  • 1. Thinking Critically
    • Activity: Bursting Bubble
    • 1A. Living in the Media Age
    • In Your World: Fact Checking on the Web
    • 1B. Propositions and Truth Values
    • 1C. Sets and Venn Diagrams
    • Brief Review: Sets of Numbers
    • 1D. Analyzing Arguments
    • Mathematical Insight: Deductive Proof of the Pythagorean Theorem
    • 1E. Critical Thinking in Everyday Life
    • In Your World: Beware of “Up to” Deals
  • 2. Approaches to Problem Solving
    • Activity: Global Melting
    • 2A. Understand, Solve, and Explain
    • Brief Review: Common Fractions
    • Brief Review: Decimal Fractions
    • Using Technology: Currency Exchange Rates
    • In Your World: Changing Money in Foreign Countries
    • 2B. Extending Unit Analysis
    • In Your World: Gems and Gold Jewelry
    • Brief Review: Powers of 10
    • Using Technology: Metric Conversions
    • In Your World: Save Money and Save the Earth
    • 2C. Problem-Solving Hints
    • Mathematical Insight: Zeno’s Paradox

II. QUANTITATIVE INFORMATION IN EVERYDAY LIFE

  • 3. Numbers in the Real World
    • Activity: Big Numbers
    • 3A. Uses and Abuses of Percentages
    • Brief Review: Percentages
    • Brief Review: What Is a Ratio?
    • 3B. Putting Numbers in Perspective
    • Brief Review: Working with Scientific Notation
    • Using Technology: Scientific Notation
    • 3C. Dealing with Uncertainty
    • Brief Review: Rounding
    • Using Technology: Rounding in Excel
    • 3D. Index Numbers: The CPI and Beyond
    • Using Technology: The Inflation Calculator
    • In Your World: The Chained CPI and the Federal Budget
    • 3E. How Numbers Can Deceive: Polygraphs, Mammograms, and More
  • 4. Managing Money
    • Activity: Student Loans
    • 4A. Taking Control of Your Finances
    • 4B. 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
    • Using Technology: Powers of e
    • Brief Review: Four Basic Rules of Algebra
    • In Your World: Effects of Low Interest Rates
    • 4C. 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
    • 4D. 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
    • 4E. Income Taxes
    • 4F. Understanding the Federal Budget

    III. PROBABILITY AND STATISTICS

  • 5. Statistical Reasoning
    • Activity: Cell Phones and Driving
    • 5A. Fundamentals of Statistics
    • Using Technology: Random Numbers
    • 5B. Should You Believe a Statistical Study?
    • In Your World: The Gun Debate: Defensive Gun Use
    • 5C. Statistical Tables and Graphs
    • Using Technology: Frequency Tables in Excel
    • Using Technology: Bar Graphs and Pie Charts in Excel
    • Using Technology: Line Charts in Excel
    • 5D. Graphics in the Media
    • Using Technology: Graphs with Multiple Data Sets
    • 5E. Correlation and Causality
    • Using Technology: Scatterplots in Excel
  • 6. Putting Statistics to Work
    • Activity: Are We Smarter Than Our Parents?
    • 6A. Characterizing Data
    • Using Technology: Mean, Median, and Mode in Excel
    • 6B. Measures of Variation
    • Using Technology: Standard Deviation in Excel
    • 6C. The Normal Distribution
    • Using Technology: Standard Scores and Percentiles in Excel
    • 6D. Statistical Inference
    • In Your World: Is Polling Reliable?
  • 7. Probability: Living With The Odds
    • Activity: Lotteries
    • 7A. Fundamentals of Probability
    • Brief Review: The Multiplication Principle
    • 7B. Combining Probabilities
    • 7C. The Law of Large Numbers
    • 7D. Assessing Risk
    • In Your World: Terrorism, Risk, and Human Psychology
    • 7E. Counting and Probability
    • Using Technology: Factorials
    • Brief Review: Factorials
    • Using Technology: Permutations
    • Using Technology: Combinations

IV. MODELING

  • 8. Exponential Astonishment
    • Activity: Towers of Hanoi
    • 8A. Growth: Linear vs. Exponential
    • 8B. Doubling Time and Half-Life
    • Using Technology: Logarithms
    • Brief Review: Logarithms
    • 8C. Real Population Growth
    • In Your World: Choosing Our Fate
    • 8D. Logarithmic Scales: Earthquakes, Sounds, and Acids
    • In Your World: Ocean Acidification
  • 9. Modeling Our World
    • Activity: Climate Modeling
    • 9A. Functions: The Building Blocks of Mathematical Models
    • Brief Review: The Coordinate Plane
    • 9B. Linear Modeling
    • Using Technology: Graphing Functions
    • In Your World: Algebra’s Baghdad Connection
    • 9C. Exponential Modeling
    • Brief Review: Algebra with Logarithms
    • Mathematical Insight: Doubling Time and Half-Life Formulas
    • In Your World: Changing Rates of Change
  • 10. Modeling With Geometry
    • Activity: Eyes in the Sky
    • 10A. Fundamentals of Geometry
    • Mathematical Insight: Archimedes and Pi
    • In Your World: Plato, Geometry, and Atlantis
    • 10B. Problem Solving with Geometry
    • 10C. Fractal Geometry

V. FURTHER APPLICATIONS

  • 11. Mathematics and The Arts
    • Activity: Digital Music Files
    • 11A. Mathematics and Music
    • In Your World: Music Just for You
    • 11B. Perspective and Symmetry
    • 11C. Proportion and the Golden Ratio
  • 12. Mathematics and Politics
    • Activity: Partisan Redistricting
    • 12A. Voting: Does the Majority Always Rule?
    • In Your World: Counting Votes - Not as Easy as It Sounds
    • 12B. Theory of Voting
    • In Your World: The Electoral College and the Presidency
    • 12C. Apportionment: The House of Representatives and Beyond
    • 12D. Dividing the Political Pie

Credits

Answers to Quick Quizzes and Odd-Numbered Exercises

Index

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