Quantitative Reasoning and the Environment:
Mathematical Modeling in Context      

Table of Contents       

Part 1:   Essential Numeracy

 

Chapter 1:   Measurement and Units

• Mercury and the Inuit of Greenland
• Measuring
• Accuracy and Precision of Measurement
• Estimation and Approximation
• Units of Measurement
• Unit Conversion
• Compound Units
• Units in Equations and Formulas
• Unit Prefixes
• Scientific Notation and Order of Magnitude
• Powers of 10 and Logarithms
• Logarithmic Scales
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Global Warming
• Chapter Project:   Melting of the Ice Caps
   (to view projects, go to Chapter Projects )

 

Chapter 2:   Ratios and Percentages

• Ratios
• Normalization
• Percentage as a Type of Ratio
• Parts per Thousand
• Parts per Million and Parts per Billion
• Percentage as a Measure of Change
• Percentage Difference and Percentage Error
• Proportions
• Probability
• Recurrence Interval
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Sinkholes and Lakes
• Chapter Project:   Measuring Habitat of Florida Lakes
  

Chapter 3:   Charts and Graphs

• Pie Charts
• Bar Charts
• Frequency Histograms
• Using Technology:   Histograms
• Relative Frequency Histograms
• Scatterplots
• Using Technology:   Scatterplots
• Line Graphs
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth: Energy Demand and the Arctic National Wildlife Refuge
• Chapter Project:   U.S. Energy Flows  

 

Part 2:   Function Modeling

 

Chapter 4:   Linear Functions and Regression

• Modeling with Linear Functions
• Units of Measure in Linear Equations
• Dependent versus Independent Variables
• Graphing Linear Equations
• Using Technology: Graphs and Tables
• Approximating Almost-Linear Data Sets
  • straightedge method
  • least squares regression
• Using Technology: Linear Regression
• The Correlation Coefficient "r"
• Using Technology: The Correlation Coefficient
• Correlation Fallacies
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Population Growth
• Chapter Project: Fertility Rates in Developing Countries

 

Chapter 5:   Exponential Functions and Regression

• Exponential Rates and Multipliers
• The General Exponential Model
• Finding Exponential Functions—the More General Case
• Solving Exponential Equations
• Doubling Times and Half-Lives
• Approximating Almost-Exponential Data Sets
  • straightedge method
  • least squares regression
• Using Technology: Exponential Regression
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:  Chicken Nation
• Chapter Project: Broiler Chicken Production

 

Chapter 6:   Power Functions

• Basic Power Functions
• Solving Power Equations
• Approximating Almost-Power Law Data Sets
  • straightedge method
  • least squares regression
• Using Technology: Power Regression
• Power Law Frequency Distributions
• Power Law Distributions and Fractals
• Recurrence Intervals
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:    Earthquakes and Fractals
• Chapter Project: A New Model for Earthquakes

 

Part 3:   Difference Equation Modeling

 

Chapter 7:   Introduction to Difference Equations

• Sequences and Notation
• Modeling with Difference Equations
  • Linear Difference Equations
  • Exponential Difference Equations
• Why Use Difference Equations?
• Affine Difference Equations
• Using Technology: Difference Equations
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   The Politics of Immigration
• Chapter Project: Human Population and Migration

 

Chapter 8:   Affine Solution Equations and Equilibrium Values

• The Solution Equation to the Affine Model
• Equilibrium Values
• Classification of Equilibrium values
• Revisiting the Affine Solution Equation
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Get The Lead Out
• Chapter Project: Lead in the Body

 

Chapter 9: Logistic Growth, Harvesting and Chaos

• Modeling Logistic Growth with Difference Equations
• Logistic Equilibrium Values
• Harvest Models
• Periodic Behavior
• Chaotic Behavior
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Harvesting and Sustainable Forestry
• Chapter Project:   Tropical Forests Forever?

 

Chapter 10:   Systems of Difference Equations

• Systems Modeling
• Using Technology: Systems of Difference Equations
• Exponential Change and Stable Age Distributions
• What Else Besides Populations?
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   A River Runs Through Europe
• Chapter Project: Pollution in a Chain of Lakes

 

Part 4:   Elementary Statistics

 

Chapter 11:   Fundamentals of Statistics

• Measures of Center and Other Descriptive Statistics
• Weighted Means
• Quartiles and the 5 Number Summary
• Boxplots
• Using Technology: Finding Descriptive Statistics
• Shape of a Data Set
• Using Technology: Histograms
• A Skew Formula
• Comparing the Mean and Median
• Sampling
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Energy Makeover
• Chapter Projects:   Electric Bills and Super Bulbs

Chapter 12:   Standard Deviation

• Standard Deviation
• Calculating Position Using Z-scores
• Outliers
• Chebychev's Rule
• Normal Distributions
• The Empirical Rule
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Impermeable Surfaces and Urban Runoff
• Chapter Project: Urban Runoff Scorecard
  

Chapter 13:   Normal Distributions

• The Standard Normal Distribution
• Transformations to Normal
• Confidence Intervals
• Chapter Summary
• End-of-Chapter Exercises
• Science in Depth:   Hazardous Household Waste
• Chapter Project: Taxes on Toxics

 

Appendix:   Unit Conversions

Answers to Odd Exercises

Index