Geometry is the whole content of mathematics. Algebra not only appears in the form of geometry, but also often relies on geometric methods to solve and demonstrate. It was not until the establishment of analytic geometry that the trend of algebra appeared, and geometric problems often relied on algebraic methods to solve and demonstrate.
Algebra began to be independent from geometry and became a new branch of mathematics. At that time, the achievements were: the formula solution of quadratic equation in one variable, the binomial theorem with natural number as index; The emergence of trigonometry and so on.
The simplest mathematical programming problem is linear programming, and its constraints and objective functions are linear. The solution of linear programming problems will be transformed into the solution of linear equations through the knowledge of linear algebra such as determinant and matrix. The emergence of linear programming and its simplex method has greatly promoted the development of operational research. A large number of practical problems are transformed into linear programming, and it becomes a reality to solve some large and complex practical problems with the help of computers.
In the infinite dimensional space, in order to meet the development requirements of modern mathematics, the concept of function has also been given a more general meaning: different from the concept of function in mathematical analysis, it refers to a corresponding relationship between two data sets; The functional relationship considered is to establish a corresponding relationship between any two sets, in which the transformation from infinite dimensional space to infinite dimensional space is called operator. Different types of functions can be regarded as points or vectors of "function space", thus obtaining the general concept of "abstract space".
In the study of probability statistics, the statistical inference method of "inferring the whole from the local" is used. Because of the wide range of random phenomena, it is impossible and unnecessary to observe and experiment all of them. The conclusions drawn from some data should be inferred from the whole range.