Algebra Index

Algebra Overview

Algebra studies mathematical relationships through symbols, variables, operations, expressions, equations, inequalities, and functions. It extends arithmetic by allowing quantities to be unknown, variable, or generalized, making it possible to describe patterns, solve problems, model relationships, and reason about entire classes of situations rather than single numerical examples. This discipline includes elementary algebra, intermediate algebra, polynomial theory, equations and inequalities, and functions, each of which builds the symbolic fluency needed for calculus, statistics, discrete mathematics, linear algebra, and applied mathematics. By studying algebra, learners develop the ability to translate problems into mathematical language, manipulate symbolic structures, identify relationships, and solve for unknown values in a precise and reusable way.

Categories

• Elementary Algebra

  Study basic algebraic expressions, variables, constants, operations, equations, graphing, simplification, substitution, and the symbolic rules used to represent unknown quantities.

• Equations and Inequalities

  Learn how to solve and interpret linear, quadratic, polynomial, rational, radical, exponential, and absolute value equations and inequalities across numerical and graphical contexts.

• Functions

  Explore mathematical relationships between inputs and outputs, including function notation, domain, range, graphs, transformations, composition, inverse functions, and common function families.

• Intermediate Algebra

  Examine more advanced algebraic techniques involving factoring, rational expressions, radicals, exponents, systems of equations, quadratic functions, and algebraic problem solving.

• Polynomial Theory

  Study polynomial expressions and functions, including degree, roots, factors, division, graph behavior, theorems about zeros, and structural properties of polynomial systems.