basic
basic content
Three Numbers-Rational Number, Irrational Number and Complex Number
Three forms-algebra, fraction and root.
The central content is equation-integral equation, fractional equation, radical equation and equation.
The content of elementary algebra is roughly equivalent to the content of algebra courses offered in modern middle schools, but it is not exactly the same. For example, strictly speaking, the concept, arrangement and combination of numbers should be classified as the content of arithmetic; Function is the content of analytical mathematics; The solution of inequality is a bit like the method of solving equations, but inequality, as a method of estimating values, essentially belongs to the category of analytical mathematics; Coordinate method is the study of analytic geometry. These are just a sorting method formed in history.
Elementary algebra is the continuation and expansion of arithmetic, and the research object of elementary algebra is algebraic operation and equation solving. Algebraic operations are characterized by a limited number of operations. All elementary algebra has ten rules. This is the key point to understand and master when learning elementary algebra.
rule
Five basic algorithms: additive commutative law, additive associative law, multiplicative commutative law, multiplicative associative law and distributive law;
The basic properties of the two equations: adding a number on both sides of the equation at the same time, the equation remains unchanged; Both sides of the equation are multiplied by a non-zero number at the same time, and the equation remains unchanged;
Three exponential laws: power with the same base and exponential addition with the same base; Exponential power, constant basis, exponential multiplication; The power of the product is equal to the product of power.
Elementary algebra has been further developed in two aspects: on the one hand, it studies linear equations with many unknowns; On the other hand, it is to study higher-order equations with higher unknowns. At this time, algebra has developed from elementary algebra to advanced algebra.
( 1)a-b=0，a=b
(2)a+b=0，a=-b，b=-a
(3)a*b=0, a=0 or b=0.
(4)a-b) (a-b)=0，a=b
high
research objects
Advanced algebra is a general term for the development of algebra to an advanced stage, including many branches. 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. A set is the sum of things with certain attributes; Vector is a quantity with both direction and value; Vector space, also called linear space, is a collection of many vectors, which conforms to the rules of some specific operations. The object of operation in vector space is not just a number, but a vector, and its operation properties are also very different.
Differences and relations between linear algebra and linear algebra
Many people confuse advanced algebra with linear algebra and don't understand the difference.
Advanced algebra is a specialized course for college mathematics majors, while linear algebra is a course for science, engineering and some medical majors besides college mathematics majors.