- 1.1 Thinking Mathematically
- 1.2 Problem Solving: Processes and Techniques
- 1.3 Estimating and Evaluating

- 2.1 Set Notation
- 2.2 Subsets and Venn Diagrams
- 2.3 Operations with Sets
- 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
- Logic Statements and Their Negations
**Examples**- Example 1: Identifying Statements
- Example 2: Negating 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
- Truth Tables
**Examples**- Example 1: Constructing a Truth Table for a Conditional Statement
- Example 2: Constructing a Truth Table for a Disjuction
- Example 3: Constructing a Truth Table from Words
- Example 4: Constructing a Truth Table for a Tautolgy
- Example 5: Constructing a Truth Table for a Conditional Statement

- 3.3 Logical Equivalence and De Morgan's Laws
- 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 Negative of a Conditional Statement
- Example 6: Writing the Negative of a Conditional Statement

- 3.4 Valid Arguments and Fallacies

- 4.1 Rates and Unit Rates
- 4.2 Ratios
- 4.3 Proportions and Percentages
- 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 5: Using Proportions and Percentages
- Example 6: Finding Proportions and Ratios
- Example 7: Using Percentages

- 4.4 Using Percentages

- 5.1 The Language of Functions
- 5.2 Linear Growth
- 5.3 Discovering Quadratics
- 5.4 Exponential Growth
- 5.5 Logarithmic Growth
- 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 7: Application of Logarithmic Functions Involving Sound Intensity
- Example 8: Human Memory Capacity and Logarithms

- 6.1 Everyday Geometry and Applications
- 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 7: Application of Angles
- Example 8: Determining Location
- Example 9: Using GPS to Determine Location and Distance
- Example 10: Calculating Trigonometric Values
- Example 11: Using Trigonometric Functions
- Example 12: Using Trignometry

- 6.2 Circles, Polygons, Perimeter, and Area
- Circles, Polygons, Perimeter, and Area
**Examples**- Example 1: Using Similar Triangles
- Example 2: Finding Perimeter
- Example 3: Finding Area
- Example 4: Solving Problems Involving Area
- Example 5: Finding the Area of a Parallelogram
- Example 6: Finding the Area of a Triangle
- Example 7: Finding the Area of a Trapezoid
- Example 8: Area and Circumfrence of Circles
- Example 9: Using Area

- 6.3 Volume and Surface Area
- Volume and Surface Area
**Examples**- Example 1: Determinig Volume
- Example 2: Using Volume to Meet Restrictions
- Example 3: Finding the Volume of a Sphere
- 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 7: Finding the Surface Area of a Rectangular Solid
- Example 8: Calculating Surface Area
- Example 9: Finding the Surface Area of a Right Circular Cylinder
- Example 10: Using Volume
- Example 11: Using Surface Area
- Example 12: Using Volume

- 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
- 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

- 8.1 Collecting Data
- 8.2 Displaying Data
- 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
- 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 8: Using the Empirical Rule
- Example 9: Interpreting Percentiles
- Example 10: Interpreting Quartiles

- 8.4 The Normal Distribution
- 8.5 Linear Regression

- 9.1 Understanding Personal Finance
- 9.2 Understanding Interest
- Example 1: Calculating Simple Interest
- Example 2: Calculating Simple Interest on Purchases
- Example 3: Computing Compoand Interest
- 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 8: APR vs. APY
- Example 9: Calculating Interst on Payday Loans

- 9.3 Saving Money
- Example 1: Computing Principal Needed for Future Value
- Example 2: Calculating Future Value Using an Annuity Plan
- Example 3: Calculating Future Value for an Annuity
- Example 4: calculating Future Value of an IRA Using the Annuity Formula
- Example 5: Finding Monthly Payments in Order to Meet a Goal
- Example 6: Calculating Monthly Payments
- Example 7: Calculating Monthly Payments for a Retirement Fund

- 9.4 Borrowing Money

- 10.1 How to Determine a Winner
- 10.2 What's Fair?
- 10.3 Apportionment
- Example 1: Apportioning Money Based on Mumber of Institutions
- Example 2: Distributing Money from the Super Bowl
- Example 3: Applying the Hamilton Method of Apportionmen
- 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

- 11.1 Applications of Geometry to the Arts
- 11.2 Tiling and Tesseallations
- 11.3 Mathematics and Music

- 12.1 Baseball and Softball
- Example 1: Calculating Batting Average
- Example 2: Calculating Batting Average
- Example 3: Calculating On-Base Percentage
- Example 4: Calculating Slugging Percentage
- Example 5: Calculating OPS
- Example 6: Calculating Earned Run Average (ERA)
- Example 7: Calculating WHIP
- Example 8: Determining the Number of Combinations of Baseball Lineups

- 12.2 Footbal
- 12.3 Basketball
- 12.4 Additional Sports: Tennis, Golf, and Track & Field

- 13.1 Introduction to Graph Theory
- Example 1: Identifying Parts of a Graph
- Example 2: Indentifying Parts of a Graph
- Example 3: Identifying a Walk
- Example 4: Indentifying a Path
- Example 5: Identifying Connnected 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
- Example 9: Drawing a Graph without Edges Predetermined
- Example 10: Finding a Minimum Vertex Cover
- Example 11: Finding a Vertex Coloring
- Example 12: Identifying a Cycle in a Graph

- 13.2 Trees
- 13.3 Matchings
- 13.4 Planar Graphs
- Example 1: Determining the Number of Faces in a Planar Graph
- Example 2: Verifying Euler's Formula for a Graph
- Example 3: Applying Euler's Formula
- Example 4: Number of Edges in a Planar Graph
- Example 5: Establishing that a Graph is Not Planar Using Euler's Corollary
- Example 6: Classifying Graphs as Planar or Not
- Example 7: Establishing that a Graph is Not Planar Using Subgraphs
- Example 8: Classifying Graphs as Planar or Not

- 14.1 Prime Numbers
- 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