Using & Understanding Mathematics

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 swimming as well as 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 & 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.

• I. LOGIC AND PROBLEM SOLVING 1. Thinking Critically Activity: Bursting Bubble1A. Living in the Media AgeIn Your World: Fact Checking on the Web1B. Propositions and Truth Values1C. Sets and Venn DiagramsBrief Review: Sets of Numbers1D. Analyzing ArgumentsMathematical Insight: Deductive Proof of the Pythagorean Theorem1E. Critical Thinking in Everyday LifeIn Your World: Beware of “Up to” Deals2. Approaches to Problem Solving Activity: Global Melting2A. Understand, Solve, and ExplainBrief Review: Common FractionsBrief Review: Decimal FractionsUsing Technology: Currency Exchange RatesIn Your World: Changing Money in Foreign Countries2B. Extending Unit AnalysisIn Your World: Gems and Gold JewelryBrief Review: Powers of 10Using Technology: Metric ConversionsIn Your World: Save Money and Save the Earth2C. Problem-Solving HintsMathematical Insight: Zeno’s ParadoxII. QUANTITATIVE INFORMATION IN EVERYDAY LIFE 3. Numbers in the Real World Activity: Big Numbers3A. Uses and Abuses of PercentagesBrief Review: PercentagesBrief Review: What Is a Ratio?3B. Putting Numbers in PerspectiveBrief Review: Working with Scientific NotationUsing Technology: Scientific Notation3C. Dealing with UncertaintyBrief Review: RoundingUsing Technology: Rounding in Excel3D. Index Numbers: The CPI and BeyondUsing Technology: The Inflation CalculatorIn Your World: The Chained CPI and the Federal Budget3E. How Numbers Can Deceive: Polygraphs, Mammograms, and More4. Managing Money Activity: Student Loans4A. Taking Control of Your Finances4B. The Power of CompoundingBrief Review: Powers and RootsUsing Technology: PowersUsing Technology: The Compound Interest FormulaUsing Technology: The Compound Interest Formula for Interest Paid More Than Once a YearUsing Technology: APY in ExcelUsing Technology: Powers of eBrief Review: Four Basic Rules of AlgebraIn Your World: Effects of Low Interest Rates4C. Savings Plans and InvestmentsMathematical Insight: Derivation of the Savings Plan FormulaUsing Technology: The Savings Plan FormulaUsing Technology: Fractional Powers (Roots)In Your World: Building a Portfolio4D. Loan Payments, Credit Cards, and MortgagesUsing Technology: The Loan Payment Formula (Installment Loans)Mathematical Insight: Derivation of the Loan Payment FormulaUsing Technology: Principal and Interest Portions of Loan PaymentsIn Your World: Avoiding Credit Card TroubleIn Your World: Choosing or Refinancing a Loan4E. Income Taxes4F. Understanding the Federal BudgetIII. PROBABILITY AND STATISTICS5. Statistical Reasoning Activity: Cell Phones and Driving5A. Fundamentals of StatisticsUsing Technology: Random Numbers5B. Should You Believe a Statistical Study?In Your World: The Gun Debate: Defensive Gun Use5C. Statistical Tables and GraphsUsing Technology: Frequency Tables in ExcelUsing Technology: Bar Graphs and Pie Charts in ExcelUsing Technology: Line Charts in Excel5D. Graphics in the MediaUsing Technology: Graphs with Multiple Data Sets5E. Correlation and CausalityUsing Technology: Scatterplots in Excel6. Putting Statistics to Work Activity: Are We Smarter Than Our Parents?6A. Characterizing DataUsing Technology: Mean, Median, and Mode in Excel6B. Measures of VariationUsing Technology: Standard Deviation in Excel6C. The Normal DistributionUsing Technology: Standard Scores and Percentiles in Excel6D. Statistical InferenceIn Your World: Is Polling Reliable?7. Probability: Living With The Odds Activity: Lotteries7A. Fundamentals of ProbabilityBrief Review: The Multiplication Principle7B. Combining Probabilities7C. The Law of Large Numbers7D. Assessing RiskIn Your World: Terrorism, Risk, and Human Psychology7E. Counting and ProbabilityUsing Technology: FactorialsBrief Review: FactorialsUsing Technology: PermutationsUsing Technology: CombinationsIV. MODELING 8. Exponential Astonishment Activity: Towers of Hanoi8A. Growth: Linear vs. Exponential8B. Doubling Time and Half-LifeUsing Technology: LogarithmsBrief Review: Logarithms8C. Real Population GrowthIn Your World: Choosing Our Fate8D. Logarithmic Scales: Earthquakes, Sounds, and AcidsIn Your World: Ocean Acidification9. Modeling Our World Activity: Climate Modeling9A. Functions: The Building Blocks of Mathematical ModelsBrief Review: The Coordinate Plane9B. Linear ModelingUsing Technology: Graphing FunctionsIn Your World: Algebra’s Baghdad Connection9C. Exponential ModelingBrief Review: Algebra with LogarithmsMathematical Insight: Doubling Time and Half-Life FormulasIn Your World: Changing Rates of Change10. Modeling With Geometry Activity: Eyes in the Sky10A. Fundamentals of GeometryMathematical Insight: Archimedes and PiIn Your World: Plato, Geometry, and Atlantis10B. Problem Solving with Geometry10C. Fractal GeometryV. FURTHER APPLICATIONS 11. Mathematics and The Arts Activity: Digital Music Files11A. Mathematics and MusicIn Your World: Music Just for You11B. Perspective and Symmetry11C. Proportion and the Golden Ratio12. Mathematics and Politics Activity: Partisan Redistricting12A. Voting: Does the Majority Always Rule?In Your World: Counting Votes - Not as Easy as It Sounds12B. Theory of VotingIn Your World: The Electoral College and the Presidency12C. Apportionment: The House of Representatives and Beyond12D. Dividing the Political PieCredits Answers to Quick Quizzes and Odd-Numbered Exercises Index