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Algebra studies addition, subtraction, multiplication, division and other operations and their general properties. There are many manifestations of operational properties, and algebraic structure is one of them. Typical algebraic objects include polynomials, algebraic expressions, algebraic equations, linear spaces, linear transformations, matrices, groups, rings, fields, modules and so on. Mathematical logic and combinatorial mathematics are also branches of mathematics with algebraic style.

Algebra studies addition, subtraction, multiplication, division and other operations and their general properties. There are many manifestations of operational properties, and algebraic structure is one of them. Typical algebraic objects include polynomials, algebraic expressions, algebraic equations, linear spaces, linear transformations, matrices, groups, rings, fields, modules and so on. Mathematical logic and combinatorial mathematics are also branches of mathematics with algebraic style.

When I was just learning algebra in junior high school, I first came into contact with monomials, polynomials, algebraic expressions (including fractions) and their operations and polynomial equations. Polynomials, fractions and solving equations can best embody the operational properties of addition, subtraction, multiplication and division, such as interchangeability, associative law and distributive law.

The solution of polynomial equation is an inexhaustible motive force for the development of mathematics. The solution of the equation has both practical needs and theoretical attraction, attracting mathematicians from generation to generation.

One-dimensional linear equation is simple and can be solved by primary school students now; Quadratic equation with one variable is not difficult. The Babylonians solved it more than 4000 years ago. This is the mathematics content that junior high school students should learn now. But the development of higher-order equations is very slow. It was not until the fifteenth and sixteenth centuries that people got the solutions of cubic and quartic equations in one yuan. This solution process is quite complicated and of little practical value.

After solving the cubic quartic equation of one yuan, people want to get the root solution of the higher-order equation, so mathematicians have been busy for a long time and spent a lot of effort, including many famous and great mathematicians, such as Lagrange, but all failed.