Everyone's Algebra: A Principle-Based Approach

Abstract

Everyone's Algebra is a self-contained introductory algebra textbook designed to build genuine mathematical understanding from the ground up. Rather than cataloging procedures for rote memorization, it asks why each idea is true, what structure underlies each rule, and how one idea grows naturally into the next. The book spans thirty-one chapters organized in three arcs: Part I (Chapters 1–8) covers arithmetic foundations, from counting and place value through the four operations, fractions, exponentiation, and factorization; Part II (Chapters 9–24) develops core secondary-school algebra, including polynomials, systems of equations, quadratic equations (treated by three progressively deeper methods), complex numbers, the Fundamental Theorem of Algebra, and Vieta's formulas; Part III (Chapters 25–31) introduces sets and functions and surveys linear, quadratic, power, polynomial, rational, exponential, and logarithmic functions, concluding with real-world applications and a cumulative review. Solutions to all even-numbered exercises are provided, making the book fully accessible for independent study. The only prerequisites are the ability to count and knowledge of the multiplication table.