Viewing Life Mathematically
2.1 Set Notation
2.2 Subsets and Venn Diagrams
2.3 Operations with Sets
- Examples
- Example 1: Determining the Intersection of Sets
- Example 2: Using a Venn Diagram to Find the Intersection
- Example 3: Determining the Union of Sets
- Example 4: Combining Intersection and Union
- Example 5: Identifying Disjoint Sets
- Example 6: Using De Morgan's Laws
- Example 7: Determining the Cardinal Number of a Union
- Example 8: Applying the Inclusion-Exclusion Principle
2.4 Applications and Survey Analysis
3.1 Logic Statements and Their Negations
3.2 Truth Tables
3.3 Logical Equivalence and De Morgan's Laws
- Examples
- Example 1: Writing Variations of a Conditional Statement
- Example 2: Writing the Contrapositive of a Conditional Statement
- Example 3: Writing a Biconditional Statement
- Example 4: Applying De Morgan's Laws
- Example 5: Writing the Negation of a Conditional Statement
- Example 6: Writing the Negation of a Conditional Statement
3.4 Valid Arguments and Fallacies
5.1 The Language of Functions
5.2 Linear Growth
5.3 Discovering Quadratics
5.4 Exponential Growth
5.5 Logarithmic Growth
- Examples
- Example 1: Equivalent Logarithmic and Exponential Functions
- Example 2: Equivalent Logarithmic and Exponential Functions
- Example 3: Evaluating Logarithmic Functions
- Example 4: Application of Logarithmic Functions Involving Earthquakes
- Example 5: Application of Logarithmic Functions Involving Earthquakes
- Example 6: Application of Logarithmic Functions Involving Earthquakes
- Example 8: Human Memory Capacity and Logarithms
6.1 Everyday Geometry and Applications
- Examples
- Example 1: Determining the Length of a Line Segment
- Example 2: Complementary Angles
- Example 3: Supplementary Angles
- Example 4: Complementary and Supplementary Angles
- Example 5: Converting Decimal Degrees to Degrees, Minutes, and Seconds
- Example 6: Converting Degrees, Minutes, and Seconds to Decimal Degrees
- Example 8: Determining Location
- Example 9: Using GPS to Determine Location and Distance
6.2 Circles, Polygons, Perimeter, and Area
6.3 Volume and Surface Area
- Examples
- Example 1: Determining Volume
- Example 2: Using Volume to Meet Restrictions
- Example 4: Finding the Volume of a Right Circular Cylinder
- Example 5: Finding the Volume of a Right Circular Cone
- Example 6: Finding the Volume of a Square Pyramid
- Example 9: Finding the Surface Area of a Right Circular Cylinder
- Example 11: Using Surface Area
7.1 Introduction to Probability
7.2 Counting Our Way to Probabilities
7.3 Using Counting Methods to Find Probability
7.4 Addition and Multiplication Rules of Probability
- Examples
- Example 1: Applying the Addition Rule for Probability
- Example 2: Applying the Addition Rule for Probability
- Example 3: Applying the Addition Rule for Mutually Exclusive Events
- Example 4: Applying the Addition Rule for Mutually Exclusive Events
- Example 5: Independent vs. Dependent Events
- Example 6: Multiplication Rule for Independent Events
- Example 7: Multiplication Rule for Independent Events
- Example 8: Multiplication Rule for Dependent Events
7.5 Expected Value
8.1 Collecting Data
8.2 Displaying Data
- Examples
- Example 1: Interpreting a Frequency Distribution
- Example 2: Constructing a Frequency Distribution
- Example 3: Constructing a Grouped Frequency Distribution
- Example 4: Interpreting a Frequency Distribution
- Example 5: Interpreting Bar Graphs
- Example 6: Interpreting Bar Graphs with Multiple Populations
- Example 7: Interpreting a Histogram
- Example 8: Reading Graphs
8.3 Describing and Analyzing Data
8.4 The Normal Distribution
8.5 Linear Regression
9.1 Understanding Personal Finance
9.2 Understanding Interest
- Examples
- Example 1: Calculating Simple Interest
- Example 2: Calculating Simple Interest on Purchases
- Example 4: Comparing Compound Interest for Different Compounding Intervals
- Example 5: Calculating Continuous Compound Interest
- Example 6: Finding the Maximum Amount of Interest Possible in One Year
- Example 7: Annual Percentage Yield
- Example 9: Calculating Interest on Payday Loans
9.3 Saving Money
9.4 Borrowing Money
10.1 How to Determine a Winner
10.2 What's Fair?
10.3 Apportionment
- Examples
- Example 2: Distributing Money from the Super Bowl
- Example 3: Applying the Hamilton Method of Apportionment
- Example 4: Applying the Jefferson Method of Apportionment
- Example 5: Applying the Webster Method of Apportionment
- Example 6: Applying the Huntington-Hill Method of Apportionment
- Example 7: The Alabama Paradox
10.4 Weighted Voting Systems
13.1 Introduction to Graph Theory
- Examples
- Example 1: Identifying Parts of a Graph
- Example 2: Identifying Parts of a Graph
- Example 3: Identifying a Walk
- Example 4: Identifying a Path
- Example 5: Identifying Connected and Disconnected Graphs
- Example 6: Identifying Different Views of the Same Graph
- Example 7: Identifying Parts of a Graph
- Example 8: Drawing a Graph Given the Edges
13.2 Trees
13.3 Matchings
13.4 Planar Graphs
14.1 Prime Numbers
- Examples
- Example 1: Classifying a Number as Prime or Composite
- Example 2: Using a Factor Tree to Find a Prime Factorization
- Example 3: Classifying a Number as Prime or Composite
- Example 4: GCD Using Factor Trees
- Example 5: Using the GCD
- Example 6: Finding the GCD Using Euclid's Algorithm
- Example 7: Relatively Prime Numbers Using Euclid's Algorithm
14.2 Modular Arithmetic
14.3 Fermat's Little Theorem and Prime Testing
14.4 Fermat's Little Theorem and Public-Key Encryption
A.1 US Measurements
- Examples
- Example 1: Basic Conversions in the US Customary System
- Example 2: Converting US Units of Measure Using Multiplication/Division
- Example 3: Application: Converting US Units of Measure
- Example 4: Using Unit Fractions to Convert US Units of Measure
- Example 5: Application: Converting US Units of Measure
- Example 6: Application: Converting US Units of Measure
A.2 The Metric System: Length and Area
- Examples
- Example 1: Converting Metric Units of Length
- Example 2: Application: Converting Metric Units of Length
- Example 3: Converting Metric Units of Length
- Example 4: Converting Metric Units of Length
- Example 5: The Prefixes Mega-, Giga-, and Tera-
- Example 6: Converting Metric Units of Area
- Example 7: Converting Metric Units of Area
- Example 8: Converting Metric Units of Area
- Example 9: Converting Metric Units of Land Area
A.3 The Metric System: Capacity and Weight
- Examples
- Example 1: Common Metric Units of Capacity
- Example 2: Converting Metric Units of Capacity
- Example 3: Converting Metric Units of Capacity
- Example 4: Converting Metric Units of Capacity
- Example 5: Application: Converting Metric Units of Capacity
- Example 7: Converting Metric Units of Weight
- Example 8: Application: Converting Metric Units of Weight
A.4 US and Metric Equivalents
- Examples
- Example 1: Equivalent Measures of Temperature
- Example 2: Converting Units of Temperature
- Example 3: Converting Units of Temperature
- Example 4: Converting Units of Length
- Example 5: Converting Units of Area
- Example 6: Converting Units of Capacity (Liquid Volume)
- Example 7: Converting Units of Weight (Mass)