elementary algebra

Elementary algebra is the first floor of the algebra building: the part where letters first stand for numbers, and you learn to write, simplify, and solve with them. It is the algebra of high school — variables, expressions, equations, lines, factoring, and quadratics — all still firmly about ordinary numbers.

Its core skills form a ladder: representing quantities with variables, simplifying expressions by combining like terms, manipulating equations to isolate an unknown, and translating word problems into symbols and back. The numbers involved are the familiar ones — integers, fractions, decimals, and the real numbers — and the operations are the familiar four, plus powers and roots.

It is called “elementary” to contrast it with abstract (or “modern”) algebra, where the objects studied are no longer just numbers but whole structures — groups, rings, fields — with their own rules. The names are about altitude, not difficulty: elementary algebra is the indispensable groundwork that every later, more abstract layer is built upon.