Viewing Life Mathematically

2.1 Set Notation

• Examples
• Example 1: Using the Roster Method to Represent a Set
• Example 2: Determining Equal and Equivalent Sets
• Example 3: Using Set-Builder Notation to Represent a Set
• Example 4: Determining Empty Sets
• Example 5: Determining the Complement of a Set

2.2 Subsets and Venn Diagrams

• Examples
• Example 1: Interpreting Venn Diagrams
• Example 2: Interpreting Venn Diagrams
• Example 3: Drawing a Venn Diagram with Subsets
• Example 4: Identifying Proper Subsets
• Example 5: Determining the Number of Subsets

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

• Examples
• Example 1: Interpreting a Venn Diagram of Three Sets
• Example 2: Constructing a Venn Diagram of Three Sets
• Example 3: Drawing a Venn Diagram for Survey Analysis
• Example 4: Drawing a Venn Diagram for Survey Analysis

3.1 Logic Statements and Their Negations

• Examples
• Example 1: Identifying Statements
• Example 2: Negating a Statement
• Example 3: Using Logic Symbols for Compound Statements Involving and
• Example 4: Using Logic Symbols for Compound Statements Involving or
• Example 5: Using Logic Symbols for Compound Statements Involving Implications

3.2 Truth Tables

• Examples
• Example 1: Constructing a Truth Table for a Conditional Statement
• Example 2: Constructing a Truth Table for a Disjunction
• Example 3: Constructing a Truth Table from Words
• Example 4: Constructing a Truth Table for a Tautology

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

• Examples
• Example 1: Determining the Validity of an Argument
• Example 2: Determining the Validity of an Argument
• Example 3: Determining Sound Arguments
• Example 4: Determining Sound Arguments
• Example 5: Identifying Fallacies

4.1 Rates and Unit Rates

• Examples
• Example 2: Identifying Rates
• Example 3: Working with Miles per Gallon
• Example 5: Finding Unit Rates

4.2 Ratios

• Examples
• Example 6: Using Multiple Ratios
• Example 7: Using Ratios to Find Quantities

4.3 Proportions and Percentages

• Examples
• Example 1: Changing Fractions to Percentages
• Example 2: Finding Proportions and Percentages
• Example 3: Using Proportions to Find Quantities
• Example 4: Working with Ratios and Proportions
• Example 6: Finding Proportions and Ratios
• Example 7: Using Percentages

4.4 Using Percentages

• Examples
• Example 1: Finding the Percentage Change
• Example 2: Shifting Reference Points

5.1 The Language of Functions

• Examples
• Example 1: Evaluating Functions
• Example 2: Exploring Mathematical Relationships

5.2 Linear Growth

• Examples
• Example 1: Using Direct Variation
• Example 2: Applying Linear Functions

5.3 Discovering Quadratics

• Examples
• Example 1: Graphing Quadratic Functions
• Example 2: Application of Quadratic Functions

5.4 Exponential Growth

• Examples
• Example 1: Introducing Exponential Growth
• Example 2: Application of Exponential Functions
• Example 4: Percent Increase

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

• Examples
• Example 1: Using Similar Triangles
• Example 2: Finding Perimeter
• Example 3: Finding Area
• Example 5: Finding the Area of a Parallelogram
• Example 6: Finding the Area of a Triangle
• Example 9: Using 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

• Examples
• Example 1: Determining Sample Spaces
• Example 3: Calculating Classical Probability
• Example 4: Empirical Probability with Multiple Trials
• Example 5: Classical vs. Empirical Probability

7.2 Counting Our Way to Probabilities

• Examples
• Example 1: Using the Fundamental Counting Principle with Replacement
• Example 3: Calculating Factorials
• Example 4: Using Combinations
• Example 5: Using Permutations
• Example 6: Using Permutations

7.3 Using Counting Methods to Find Probability

• Examples
• Example 1: Calculating Classical Probability Using Combinations
• Example 2: Calculating Classical Probability Using Permutations
• Example 3: Finding the Complement of an Event
• Example 4: Finding Probability Using Complements

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

• Examples
• Example 1: Identifying Parts of a Survey
• Example 2: Identifying Sampling Techniques

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

• Examples
• Example 1: Finding the Mean
• Example 2: Finding the Median
• Example 3: Finding the Mode
• Example 4: Finding the Mean, Median, and Mode
• Example 5: Finding the Range
• Example 6: Calculating Standard Deviation by Hand
• Example 9: Interpreting Percentiles

8.4 The Normal Distribution

8.5 Linear Regression

• Examples
• Example 1: Identifying Correlations

9.1 Understanding Personal Finance

• Examples
• Example 1: Determining Federal Income Tax
• Example 2: Determining Monthly Take Home Pay
• Example 3: Budgeting on a Given Income
• Example 5: Finding the Sale Price
• Example 6: Determining a Discount
• Example 7: Computing Percentage Decrease
• Example 8: Computing Percentage Increase

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

• Examples
• Example 1: Paying Off Credit Card Debt with a Fixed Payment
• Example 2: Purchasing a New Car
• Example 3: Determining Best New Car Incentive
• Example 4: Calculating Monthly Mortgage Payments

10.1 How to Determine a Winner

• Examples
• Example 2: Majority Rule Decision
• Example 3: Plurality Method
• Example 4: Borda Count Method
• Example 6: Pairwise Comparison Method

10.2 What's Fair?

• Examples
• Example 1: Condorcet Criterion and the Plurality Method
• Example 2: Majority Criterion and the Borda Count Method
• Example 3: Monotonicity Criterion and the Plurality with Elimination Method
• Example 4: Irrelevant Alternatives Criterion and the Pairwise Method of Comparison

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

• Examples
• Example 1: Weighted Voting System
• Example 2: Passing a Motion with a Coalition
• Example 4: Banzhaf Power Index
• Example 5: Determining a Pivotal Player
• Example 6: Number of Sequential Coalitions
• Example 7: Applying the SSPI

11.1 Applications of Geometry to the Arts

• Examples
• Example 1: The Fibonacci Sequence
• Example 2: More on the Fibonacci Sequence
• Example 4: Golden Rectangles
• Example 5: Golden Rectangles in Modern Architecture

11.2 Tiling and Tessellations

• Examples
• Example 1: Finding Triangular Numbers
• Example 2: Representing Square Numbers
• Example 4: Archimedean Tiling

11.3 Mathematics and Music

• Examples
• Example 1: Determining Half Steps, Whole Steps, and Octaves on a Keyboard
• Example 2: Determining Frequencies of Octaves
• Example 3: Musical Notes as Exponential Functions
• Example 4: Finding Major and Minor Chords on a Piano
• Example 5: Finding Frequency Ratios of Perfect Fifths

12.1 Baseball and Softball

12.2 Football

12.3 Basketball

12.4 Additional Sports: Tennis, Golf, and Track & Field

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

• Examples
• Example 1: Completing the Modular Congruence Table
• Example 2: Finding Modular Congruence

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)