Real‐World Algebra

by Kurt Verderber

Real‐World Algebra introduces algebraic concepts in a first-person conversational manner. It is written with students in mind and addresses them directly. The goal is to have students understand college algebra and introduce its connections to additional educational subjects, taking a cross-circular approach. Throughout the text, several examples include music, art, and other numerical applications and scenarios. This text provides a truly unique and understandable approach to functions and modeling.

Formats: Textbook

Product ISBN
Textbook 978‑1‑932628‑53‑1

Table of Contents

  1. Chapter 1: Real Numbers
    1. The Number Line
    2. Real Number Arithmetic
    3. Fractions, Decimals, and Percentages
    4. Changing Fractions to Decimals to Percentages and Back
    5. Prime Numbers and Perfect Numbers
  2. Chapter 2: Basics of the Math Language
    1. Exponents … Powers, and Roots
    2. Laws of Mathematics
    3. Prime Factorization
    4. The Order of Operations (Please Egg My Dad And Sister)
    5. Other Random Things You Should Know
    6. TI-83 Basics
  3. Chapter 3: Complex Numbers
    1. Anatomy of a Complex Number
    2. Magnitude (The Worm Hole)
    3. Complex Conjugates (The Doppelgänger)
    4. The Algebra of Complex Numbers
    5. Complex Numbers on the TI-83
  4. Chapter 4: Equations and Expressions
    1. The Vocabulary of Equations and Expressions
    2. Solving Simple Equations in One Variable
    3. Solving Equations with the TI-83 … The 6 Magic Buttons
    4. Combining Like Terms (CLT)
    5. Solving Literal Equations
    6. Problem Solving
  5. Chapter 5: The Function Concept
    1. What Is a Function?
    2. Function Notation
    3. What Do We Mean by “Families of Functions?”
    4. Transforming Functions
    5. Algebra of Functions (+, −, ×, but not /)
    6. Math Modeling with Functions
    7. Domain and Range of Functions
    8. Composition of Functions
    9. Inverse of a Function
  6. Chapter 6: The Linear Family of Functions
    1. Where Do Lines Live?
    2. Characteristics of Linear Functions (Slope and Intercept)
    3. Different types of Linear Functions
    4. f(x) = mx + b Does It All!
    5. Solving More Difficult Linear Equations
    6. Modeling Linear Functions on the TI-83
  7. Chapter 7: Several Linear Families (Systems)
    1. Substitution Method
    2. Different Types of Systems
    3. The 6 Magic Buttons (Revisited)
    4. Solving 3 Equations with 3 Unknowns
  8. Chapter 8: Exponential Functions
    1. Properties of the Exponential Family of Functions
    2. Population Growth and Decay
    3. Investments and Interest (A Second Derivation of e)
    4. Modeling Exponential Functions Using the TI-83
  9. Chapter 9: Logarithmic Functions
    1. Characteristics of the Logarithmic Family of Functions
    2. Logarithmic and Exponential Functions Are Inverses
    3. BEN Notation
    4. Properties of Logarithms
    5. Solving Exponential and Logarithmic Equations
    6. Modeling Logarithmic Functions (LnReg)
  10. Chapter 10: Quadratic Family of Functions
    1. Table of Polynomials
    2. The Parabola – Graph, Vertex, and Transformations
    3. The Trajectory Equation
    4. Solving Quadratic Equations
    5. Modeling Quadratic Functions (QuadReg)
    6. Domain and Range of Quadratics
  11. Chapter 11: Higher Order Polynomials
    1. What Is a Polynomial?
    2. Solving Higher Order Polynomial Equations
    3. Polynomial Long Division
    4. Modeling Higher Order Polynomial Functions
    5. Quadratic Forms
    6. Factors to Roots/Roots to Factors
    7. Pascal’s Triangle and the Binomial Expansion