📄 Executive Summary
College Algebra 2e is an introductory college-level textbook designed for students preparing for advanced coursework in mathematics, science, business, and related disciplines. The text assumes a baseline familiarity with basic arithmetic and introductory algebra, beginning with a review of core prerequisites before advancing to college-level algebra. Its scope encompasses fundamental algebraic operations, the theory and application of functions, systems of equations, analytic geometry, and introductory discrete mathematics.
The curriculum progresses systematically from foundational concepts to advanced analytical methods. The opening chapters review real number properties, rules of exponents, radicals, polynomials, factoring techniques, and rational expressions. Building upon these basics, the book introduces the Cartesian coordinate plane, complex numbers, and systematic methods for solving linear, quadratic, polynomial, radical, rational, and absolute value equations and inequalities. It then establishes a comprehensive framework for functions, exploring notation, domain and range, rates of change, algebraic composition, geometric transformations, and inverse functions before examining specific function families—including linear, quadratic, general polynomial, rational, exponential, and logarithmic functions.
In its later chapters, the textbook covers advanced algebraic tools, analytic geometry, and discrete mathematics. Readers learn algebraic and matrix methods for solving linear and nonlinear systems of equations, including Gaussian elimination, matrix inverses, and Cramer's rule. The text also covers partial fraction decomposition, conic sections in Cartesian and polar forms, rotation of axes, arithmetic and geometric sequences, series and annuities, counting principles, the Binomial Theorem, and introductory probability. Throughout all units, the book highlights real-world modeling, demonstrating how mathematical formulas apply to financial calculations, population dynamics, radioactive decay, motion, and regression analysis with scatter plots.
After working through the textbook, a reader should be able to analyze, graph, and evaluate a wide variety of algebraic and transcendental functions, solve complex single-variable and multivariable systems, model practical scenarios with appropriate equations, and compute discrete probabilities and series sums. The book focuses strictly on algebraic methods; it leaves trigonometric functions and calculus-based techniques, such as the exact analytic determination of extrema for general polynomials, outside its scope.
