Algebra is a branch of mathematics that studies numbers, quantities, relationships, structures and algebraic equations. Elementary algebra is generally taught in middle schools, introducing the basic ideas of algebra: studying what happens when we add or multiply numbers, understanding the concept of variables and how to establish polynomials and find their roots.

The research object of algebra is not only numbers, but various abstract structures. For example, an integer set is an algebraic structure as a set with addition, multiplication and order relations. Among them, we only care about various relationships and their nature, but we don't care about the question "what is the number itself". The common types of algebraic structures are groups, rings, fields, modules, linear spaces and so on.

Extended data:

Algebra is the study of algebraic structure, which has two meanings:

The first meaning is to study all kinds of algebraic structures, so that not only the group ring domain, but also all kinds of substructures, weak structures and structures obtained by transforming the axioms of these structures; The second meaning is to study these algebraic structures through various ways and techniques, such as tuning, category theory, recent quantization and so on.

Algebra has both broad and narrow meanings. Generalized algebra refers to the sum of groups, rings, etc. , these structures and the methodology of studying them; Algebra in a narrow sense generally refers to the multiplication structure that satisfies some axiomatic conditions in metric space.

Composition:

Elementary algebra:

In ancient times, when arithmetic accumulated a large number of solutions to various quantitative problems, in order to find a systematic and more universal method to solve various quantitative relations, elementary algebra centered on the principle of solving algebraic equations was produced.

Elementary algebra is a branch of mathematics, which studies the theory and method of algebraic operation of numbers and words, more precisely, the theory and method of algebraic operation of real numbers and complex numbers, and the algebraic expressions of their coefficients.

Explain what elementary algebra is in common language, that is, if we define arithmetic as studying the characteristics of apples, pears, oranges and grapes respectively, then elementary algebra is studying the * * * properties of fruits.

The basic contents of elementary algebra are as follows:

Three kinds of numbers-rational number, irrational number and complex number;

Three types-algebraic, fractional and radical (collectively referred to as algebra);

Three kinds of equations-integral equation, fractional equation, irrational number equation (collectively referred to as algebraic equation), and algebraic equation composed of finite algebraic equations.