Traditional algebra uses expressions with characters (variables) to perform arithmetic operations, and characters represent unknowns or undetermined numbers. If division is not included (except integer division), then every expression is a rational coefficient polynomial. For example:1/2xy+1/4z-3x+2/3.
Algebraic equations represent conditions imposed on variables by making polynomials equal to zero. If there is only one variable, then what satisfies this equation will be a real number or a complex number-its root. Algebraic number is the root of the equation.
Algebraic synthesis
Elementary algebra is a branch of mathematics that studies the theory and method of algebraic operation of numbers and words, more precisely, it is a branch of mathematics that studies the theory and method of algebraic operation of real numbers and complex numbers and algebraic expressions with them as coefficients. In common language, if we define arithmetic as studying the characteristics of apples, pears, oranges and grapes respectively, then elementary algebra is studying the * * * properties of fruits.
Advanced algebra is the general term for the development of algebra to advanced stage. Higher algebra offered by universities generally includes linear algebra and polynomial algebra.
On the basis of elementary algebra, advanced algebra further expands the research object and introduces many new concepts and quantities which are completely different from usual ones, such as set, vector and vector space. These quantities have operational characteristics similar to numbers, but the research methods and operational methods are more complicated.