(eBook) (PDF) Using & Understanding Mathematics: A Quantitative Reasoning Approach, 7th edition

Description

Overview

With Using & Understanding Mathematics, see the relevance of mathematics in everyday life. From buying groceries to paying taxes, the text will help you develop your critical-thinking and quantitative reasoning skills — so you can master the math you’ll encounter in your college courses, future career, and daily life.

Published by Pearson (July 14th 2021) – Copyright © 2019
ISBN-13: 9780137553334
Subject: Liberal Arts Math
Category: Quantitative Reasoning

• Preface
• Acknowledgments
• Prologue: Literacy for the Modern World

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