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Table of contents
  1. Preface
  2. 1 Sets
    1. Introduction
    2. 1.1 Basic Set Concepts
    3. 1.2 Subsets
    4. 1.3 Understanding Venn Diagrams
    5. 1.4 Set Operations with Two Sets
    6. 1.5 Set Operations with Three Sets
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  3. 2 Logic
    1. Introduction
    2. 2.1 Statements and Quantifiers
    3. 2.2 Compound Statements
    4. 2.3 Constructing Truth Tables
    5. 2.4 Truth Tables for the Conditional and Biconditional
    6. 2.5 Equivalent Statements
    7. 2.6 De Morgan’s Laws
    8. 2.7 Logical Arguments
    9. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  4. 3 Real Number Systems and Number Theory
    1. Introduction
    2. 3.1 Prime and Composite Numbers
    3. 3.2 The Integers
    4. 3.3 Order of Operations
    5. 3.4 Rational Numbers
    6. 3.5 Irrational Numbers
    7. 3.6 Real Numbers
    8. 3.7 Clock Arithmetic
    9. 3.8 Exponents
    10. 3.9 Scientific Notation
    11. 3.10 Arithmetic Sequences
    12. 3.11 Geometric Sequences
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  5. 4 Number Representation and Calculation
    1. Introduction
    2. 4.1 Hindu-Arabic Positional System
    3. 4.2 Early Numeration Systems
    4. 4.3 Converting with Base Systems
    5. 4.4 Addition and Subtraction in Base Systems
    6. 4.5 Multiplication and Division in Base Systems
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Projects
      5. Chapter Review
      6. Chapter Test
  6. 5 Algebra
    1. Introduction
    2. 5.1 Algebraic Expressions
    3. 5.2 Linear Equations in One Variable with Applications
    4. 5.3 Linear Inequalities in One Variable with Applications
    5. 5.4 Ratios and Proportions
    6. 5.5 Graphing Linear Equations and Inequalities
    7. 5.6 Quadratic Equations with Two Variables with Applications
    8. 5.7 Functions
    9. 5.8 Graphing Functions
    10. 5.9 Systems of Linear Equations in Two Variables
    11. 5.10 Systems of Linear Inequalities in Two Variables
    12. 5.11 Linear Programming
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  7. 6 Money Management
    1. Introduction
    2. 6.1 Understanding Percent
    3. 6.2 Discounts, Markups, and Sales Tax
    4. 6.3 Simple Interest
    5. 6.4 Compound Interest
    6. 6.5 Making a Personal Budget
    7. 6.6 Methods of Savings
    8. 6.7 Investments
    9. 6.8 The Basics of Loans
    10. 6.9 Understanding Student Loans
    11. 6.10 Credit Cards
    12. 6.11 Buying or Leasing a Car
    13. 6.12 Renting and Homeownership
    14. 6.13 Income Tax
    15. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  8. 7 Probability
    1. Introduction
    2. 7.1 The Multiplication Rule for Counting
    3. 7.2 Permutations
    4. 7.3 Combinations
    5. 7.4 Tree Diagrams, Tables, and Outcomes
    6. 7.5 Basic Concepts of Probability
    7. 7.6 Probability with Permutations and Combinations
    8. 7.7 What Are the Odds?
    9. 7.8 The Addition Rule for Probability
    10. 7.9 Conditional Probability and the Multiplication Rule
    11. 7.10 The Binomial Distribution
    12. 7.11 Expected Value
    13. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  9. 8 Statistics
    1. Introduction
    2. 8.1 Gathering and Organizing Data
    3. 8.2 Visualizing Data
    4. 8.3 Mean, Median and Mode
    5. 8.4 Range and Standard Deviation
    6. 8.5 Percentiles
    7. 8.6 The Normal Distribution
    8. 8.7 Applications of the Normal Distribution
    9. 8.8 Scatter Plots, Correlation, and Regression Lines
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  10. 9 Metric Measurement
    1. Introduction
    2. 9.1 The Metric System
    3. 9.2 Measuring Area
    4. 9.3 Measuring Volume
    5. 9.4 Measuring Weight
    6. 9.5 Measuring Temperature
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  11. 10 Geometry
    1. Introduction
    2. 10.1 Points, Lines, and Planes
    3. 10.2 Angles
    4. 10.3 Triangles
    5. 10.4 Polygons, Perimeter, and Circumference
    6. 10.5 Tessellations
    7. 10.6 Area
    8. 10.7 Volume and Surface Area
    9. 10.8 Right Triangle Trigonometry
    10. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  12. 11 Voting and Apportionment
    1. Introduction
    2. 11.1 Voting Methods
    3. 11.2 Fairness in Voting Methods
    4. 11.3 Standard Divisors, Standard Quotas, and the Apportionment Problem
    5. 11.4 Apportionment Methods
    6. 11.5 Fairness in Apportionment Methods
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  13. 12 Graph Theory
    1. Introduction
    2. 12.1 Graph Basics
    3. 12.2 Graph Structures
    4. 12.3 Comparing Graphs
    5. 12.4 Navigating Graphs
    6. 12.5 Euler Circuits
    7. 12.6 Euler Trails
    8. 12.7 Hamilton Cycles
    9. 12.8 Hamilton Paths
    10. 12.9 Traveling Salesperson Problem
    11. 12.10 Trees
    12. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Videos
      4. Formula Review
      5. Projects
      6. Chapter Review
      7. Chapter Test
  14. 13 Math and...
    1. Introduction
    2. 13.1 Math and Art
    3. 13.2 Math and the Environment
    4. 13.3 Math and Medicine
    5. 13.4 Math and Music
    6. 13.5 Math and Sports
    7. Chapter Summary
      1. Key Terms
      2. Key Concepts
      3. Formula Review
      4. Projects
      5. Chapter Review
      6. Chapter Test
  15. A | Co-Req Appendix: Integer Powers of 10
  16. Answer Key
    1. Chapter 1
    2. Chapter 2
    3. Chapter 3
    4. Chapter 4
    5. Chapter 5
    6. Chapter 6
    7. Chapter 7
    8. Chapter 8
    9. Chapter 9
    10. Chapter 10
    11. Chapter 11
    12. Chapter 12
    13. Chapter 13
  17. Index
Symbols
68-95-99.7 Rule 8.6 The Normal Distribution
A
a a is greater than b b 3.2 The Integers
absolute value of an integer 3.2 The Integers
acute angle 10.2 Angles
acyclic 12.10 Trees
additive system of numbers 4.2 Early Numeration Systems
adjusted gross income 6.13 Income Tax
Algebraic expressions 5.1 Algebraic Expressions
angle of depression 10.8 Right Triangle Trigonometry
annual percentage rate 6.3 Simple Interest
approval voting ballot 11.1 Voting Methods
approval voting system 11.1 Voting Methods
arithmetic sequence 3.10 Arithmetic Sequences
Arrow’s Impossibility Theorem 11.2 Fairness in Voting Methods
average (or mean) of a set of 3.2 The Integers
C
cardinal value 1.1 Basic Set Concepts
Cardinal voting systems 11.2 Fairness in Voting Methods
cardinality of the union of two sets 1.4 Set Operations with Two Sets
categorical frequency distribution 8.1 Gathering and Organizing Data
chain rule for conditional arguments 2.7 Logical Arguments
chromatic number 12.4 Navigating Graphs
clock arithmetic 3.7 Clock Arithmetic
combinations 7.3 Combinations
compound interest 6.4 Compound Interest
compound statement 2.2 Compound Statements
Condorcet criterion 11.2 Fairness in Voting Methods
constant difference 3.10 Arithmetic Sequences
constant of proportionality 5.4 Ratios and Proportions
constant sequence 3.11 Geometric Sequences
contrapositive 2.5 Equivalent Statements
countably infinite 1.1 Basic Set Concepts
credit limit 6.10 Credit Cards
cubic meter 9.1 The Metric System
cubic units 9.3 Measuring Volume
cumulative distribution function 7.10 The Binomial Distribution
G
geometric sequence 3.11 Geometric Sequences
geometric solids 10.7 Volume and Surface Area
glide reflection 10.5 Tessellations
golden ratio 13.1 Math and Art
golden rectangles 13.1 Math and Art
graph colorings 12.4 Navigating Graphs
greatest common divisor 3.1 Prime and Composite Numbers
gross income 6.13 Income Tax
H
Hamilton circuits 12.7 Hamilton Cycles
Hamilton cycles 12.7 Hamilton Cycles
Hamilton paths 12.8 Hamilton Paths
Hare Method 11.1 Voting Methods
Hindu-Arabic numeration system 4.1 Hindu-Arabic Positional System
K
Kruskal’s algorithm 12.10 Trees
O
obtuse angle 10.2 Angles
odds against 7.7 What Are the Odds?
odds in favor 7.7 What Are the Odds?
order of operations 3.3 Order of Operations
ordinary annuity 6.6 Methods of Savings
origination date 6.3 Simple Interest
P
percentiles 8.5 Percentiles
permutations 7.2 Permutations
perpendicular lines 10.1 Points, Lines, and Planes
positional system of numbers 4.2 Early Numeration Systems
preference ranking 11.1 Voting Methods
prime factorization 3.1 Prime and Composite Numbers
probability density function 7.10 The Binomial Distribution
proper subset 1.2 Subsets
properties of the real numbers 3.6 Real Numbers
Pythagorean Theorem 10.8 Right Triangle Trigonometry
S
savings account 6.6 Methods of Savings
scaling factor 10.3 Triangles
scientific notation 3.9 Scientific Notation
security deposit 6.11 Buying or Leasing a Car
Sequences 1.2 Subsets
series 1.2 Subsets
set builder notation 1.1 Basic Set Concepts
simple graph 12.1 Graph Basics
simple interest 6.3 Simple Interest
simple random sample 8.1 Gathering and Organizing Data
simplify an expression 5.1 Algebraic Expressions
solutions of a system of equations 5.9 Systems of Linear Equations in Two Variables
spanning trees 12.10 Trees
square meter 9.1 The Metric System
square units 9.2 Measuring Area
standardized score 8.6 The Normal Distribution
Stem-and-leaf plots 8.2 Visualizing Data
straight angle 10.2 Angles
subjective probability 7.5 Basic Concepts of Probability
subset 1.2 Subsets
systematic random sample 8.1 Gathering and Organizing Data
V
variable expenses 6.5 Making a Personal Budget
variable interest rate 6.8 The Basics of Loans
Venn diagram with three intersecting sets 1.5 Set Operations with Three Sets
vertex 10.2 Angles
vertical line test 5.7 Functions
W
weighted graph 12.7 Hamilton Cycles
well-defined sets 1.1 Basic Set Concepts
whole step 13.4 Math and Music
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