School algebra is arithmetic with letters for unknowns
Elementary algebra keeps the usual number operations but lets symbols stand for unspecified values. That small move turns one numerical example into a general relationship—and still stays inside real and complex numbers, unlike abstract algebra's wilder structures.
Also called high school or college algebra, the subject is taught after arithmetic and before more abstract courses. Arithmetic manipulates particular numbers; algebra manipulates numbers, variables, and terms together. The point is not new algebraic structures beyond the reals and complexes, but fluent rewriting of expressions and equations. Variables let you state laws that hold for any values, describe problems before the data arrive, and encode quantitative science in compact equations.
Notation conventions pack a lot into little ink. Letters early in the alphabet often mark constants; letters near the end mark variables, usually printed in italics. A coefficient multiplies a variable; a term is a summand built from coefficients, variables, and exponents. Juxtaposition implies multiplication; a coefficient of one is omitted; higher powers are written to the left. Care is needed when a variable sits in an exponent, and a zero exponent yields one. When superscripts are unavailable, plain text and TeX use a caret, while languages such as Python write exponentiation with a double asterisk and insist on an explicit multiplication star.
The same arithmetic operations—addition, subtraction, multiplication, division, exponentiation—extend to these symbolic expressions. Solving an equation means transforming both sides by balanced steps until the unknown is isolated. Identities hold for all allowed values; conditional equations hold only for some. Graphs reinterpret solutions as points in a coordinate plane. Polynomials, factoring, and systems of equations sit at the center of the syllabus because they turn the general language of variables into concrete problem-solving tools used across science and further mathematics.
Source: Elementary algebra
