Algebra Know-It-ALL: Beginner to Advanced, and Everything in Between

Preface
 Acknowledgment
 Part 1 Numbers, Sets, and Operations
 1 Counting Methods
 Fingers and Sticks
 Roman Numerals
 Hindu-Arabic Numerals
 The Counting Base
 Practice Exercises
 2 The Language of Sets
 The Concept of a Set
 How Sets Relate
 Set Intersection
 Set Union
 Practice Exercises
 3 Natural Numbers and Integers
 How Natural Numbers are Made
 Special Natural Numbers
 Natural Number Nontrivia
 The Integers
 Practice Exercises
 4 Addition and Subtraction
 Moving Up and Down
 Identity, Grouping, and Signs
 The Commutative Law for Addition
 The Associative Law for Addition Practice Exercises5 Multiplication and Division
 Moving Out and In
 Identity, Grouping, and Signs
 The Commutative Law for Multiplication
 The Associative Law for Multiplication
 The Distributive Laws
 Practice Exercises
 6 Fractions Built of Integers
 \"Messy\" Quotients
 \"Reducing\" a Fraction or Ratio
 Multiplying and Dividing Fractions
 Adding and Subtracting Fractions
 Practice Exercises
 7 Decimal Fractions
 Powers of 10
 Terminating Decimals
 Endless Decimals
 Conversions
 Practice Exercises
 8 Powers and Roots
 Integer Powers
 Reciprocal-of-Integer Powers Multiplying and Dividing with ExponentsMultiple Powers
 Practice Exercises
 9 Irrational and Real Numbers
 The Number Hierarchy
 More About Irrationals and Reals
 How Real Variables Behave
 More Rules for Real Variables
 Practice Exercises
 10 Review Questions and Answers
 Part 2 Linear Equations and Relations
 11 Equations and Inequalities
 Equation Morphing Revisited
 Inequalities
 How Inequalities Behave
 Inequality Morphing
 Practice Exercises
 12 First-Degree Equations in One Variable
 Constants, Sums, and Differences
 Products and Ratios
 Combinations of Operations
 Word Problems Practice Exercises13 Mappings, Relations, and Functions
 Mapping \"Territories\"
 Types of Mappings
 Examples of Relations
 Examples of Functions
 Practice Exercises
 14 The Cartesian Plane
 Two Number Lines
 Three Relations
 Three Functions
 Practice Exercises
 15 Graphs of Linear Relations
 Slope-Intercept Form
 Point-Slope Form
 Equations from Graphs
 Practice Exercises
 16 Two-by-Two Linear Systems
 Morph and Mix
 Double Elimination
 Rename and Replace
 Practice Exercises
 17 Two-by-Two Linear Graphs
 We Morphed, We Mixed, We Can Graph
 We Added, We Eliminated, We Can Graph We Renamed, We Replaced, We Can GraphWe Couldn\'t Solve, but We Can Graph
 Practice Exercises
 18 Larger Linear Systems
 Eliminate One Variable
 Solve the Two-by-Two
 Substitute Back
 General Linear Systems
 Practice Exercises
 19 The Matrix Morphing Game
 How to Build a Matrix
 Matrix Operations
 A Sample Problem
 Practice Exercises
 20 Review Questions and Answers
 Part 3 Nonlinear Equations and Relations
 21 Imaginary and Complex Numbers
 The Square Root of -1
 The Imaginary Number Line
 Real + Imaginary = Complex
 Practice Exercises
 22 Quadratic Equations with Real Roots