It's all elementary number theory, elementary mathematics knowledge, that is, elementary mathematics you learned from teachers in normal schools, and these knowledge are the basis of mathematics that you should learn in a real university. The key point is to cultivate the idea of combining numbers with shapes, the idea of inequality and the idea of classified discussion. From algebra to you, an important prerequisite for the development of algebraic thought is the arithmetic in your primary school and kindergarten, and then it develops into the unknown equation and equation thought in junior high school. These ideas in elementary school and junior high school are not mathematics, but counting methods. High school algebra is the real elementary algebra. In college, you can learn matrix theory and so on, all of which are advanced algebra. Algebra learning system originated from the algebra classes taught by Professor Nott and Professor Anting in two European universities in the 1920s. In 1930s, Vander Waals Deng (inventor of Vandermonde determinant in linear algebra) thought that the algebra part of modern mathematics had reached a complete foundation. However, due to the unsolved Goldbach conjecture, the paving work for the establishment of algebra was too messy and the method was still thin. Algebra has existed since biological counting, but it is not complete. The completeness of algebra is embodied in the richness of operation rules in group ring field and the expansion of number system. From the second half of the16th century, some people have been exploring the completeness theory of algebra, and by the19th century, some talents began to improve it. These people have the concept of Gaussian cyclotomic domain, Abel's algebraic function, Galois's group theory and algebraic equations, and Kumor and Dai Dejin's ideal wheel. Kroneck's number field, Jordan's group theory, Hilbert's number field and invariant theory are the basis of completeness of algebra. With the integrity foundation, exploring methodology is equivalent to finding existing building materials and building a building with architects. Then let's talk about what algebra has, such as solving quadratic equations in one variable, permutation and combination, Newton's binomial theorem. These are the basic algebraic parts of algebra. In ancient Europe (West (Egyptian, Greek)) and ancient China (East), the arithmetic thoughts of primary school and junior high school could not be generalized, but they appeared at the same time. Then there is analysis, and high school is not deeply involved. The emphasis of high school is calculus (your function thought, vector thought and limit, derivative thought, analytic geometry thought including complex variable function theory, which you should associate with physics, such as the relationship between speed and distance, speed and acceleration). The analysis is huge, with series theory, in which Fourier and Taylor are the key figures, as well as ordinary differential equations, partial differential equations and variational methods. The inventor of analytical science is Newton, which is used to solve the problems of speed and acceleration and the orbit of planets. This is the most basic analysis basis, which originated in Newton's period, that is, in the middle of the seventeenth century. Among them, Leibniz, who accompanied Newton, perfectly summarized the completeness and methodology of analytical science. The focus of your high school is to learn analytic geometry well and understand the essential relationship and difference between curve equation and function in analytic geometry. Analytical science exudes the philosophical aura of dialectics everywhere, which is very interesting. Geometry, which is the oldest and most active part. Its founder is Euclid. The reason why it is ancient is that both the ancient East and the ancient West have their own geometric theory systems. It is active because algebra, statistics and analytic geometry can be integrated into it, providing you with unique ideas. Geometry lies in "cleverness". There were jigsaw puzzles in the ancient East. The Pythagorean Theorem in the ancient East is neck and neck with the Pythagorean Theorem in the ancient West. Geometry in senior high school is still limited, and the analysis method shines with the aura of geometry, but geometry in junior high school is the most difficult, but you don't involve some difficulties. There is a competition for real geometry, and junior high school geometry is all European geometry. This is an orthodox theory, but non-Euclidean geometry is more useful in solving some multi-dimensional space of distorted space, just like Newton's classical mechanics theory and Einstein's relative theory solve problems from different angles but they are all geometry. Non-Euclidean geometry originated from Klein, who put forward the "He Rungen Program" in the 1970s of 19. This program uses algebra to describe geometry, so geometry becomes active in algebra. There are trigonometry, projective theory, algebraic geometry and analytic geometry in high school, and the geometry in university is more cruel and gorgeous. Geometry is a developing discipline, because its completeness and methodology are not as deep as the needs of the universe. Then there is mathematical linguistics, which is a part of logic, emphasizing set theory and propositions (that is, negative propositions in your high school, etc.). ). I think it's Hilbert, the founder of set science. He put forward the idea of generalized space and space transformation, which was almost ignored in very abstract high schools. The problem of this mathematical language is ignored by many people because it is too abstract. In short, this part of the theory is everywhere, but it is very philosophical. You need to study the philosophical system to understand this part. Generally speaking, I think the mathematical language in mathematics is relatively strict and mechanical (and you should know Marx's dialectical materialism very well). This part is the beauty that has not been uncovered. After studying it, I studied it. It doesn't matter if you don't study, unless you really do math in the future. Among them, I want to focus on the philosopher Aristotle, who put forward law of excluded middle and the law of contradiction. This is an important way to judge the proposition. It is ok for you to understand the relationship between the four propositions in high school. His successor was Leibniz, who invented a set of languages for sorting out calculus. I think Leibniz is one of the stewards of modern mathematics. Another part of mathematics is optimization theory, which involves some approximation principles. High school is rare, so you should learn linear optimization, which is the most concrete and simple part. As for its wide application, there are optimization problems everywhere in physical chemistry and biology, among which Euler and Bernoulli are the founders of this part, as well as Lagrange and so on. This part appeared in17th century. I won't say more, this is a big professional problem. Then there is statistics, that is, the probability problem you study, but the probability problem you design is the most common and intuitive, and the real statistician is from concrete to abstract. Some European philosophers and writers have expounded this issue profoundly, such as Huygens (who put forward the term game of chance). In fact, in the15th century, the game of chance was widely circulated in Italy, which was equivalent to a game. Bernoulli created the rules of probability theory (Bernoulli appeared for the second time). This man regards random phenomena as a model and concludes that the classical axiomatic theorem of probability is the essence of probability you are learning now. The modern axiomatic theorem was put forward by Kemo Gerloff, a mathematician in the former Soviet Union. Some of them opened up the field of physical statistics, including Maxwell (whose contribution lies in electromagnetic field) and Boltzmann (whose contribution lies in quantum mechanics). Laplace started analytic probability as early as the beginning of19th century, which is the focus of college probability. Your probability is the most basic concept put forward by Bernoulli, probably in1early 8th century (17 13). Scientific Algorithm This is a subject that is accompanied by the rise of the computer industry, but it involved algebra, analysis and geometry before, and there is no way to make statistics. It can only be said that the key point is that von Neumann invented the computer in 1946. We can't let the computer do stupid calculations, which requires skills and scientific algorithms, so this subject was summarized and produced, specializing in algorithms. Among them, the key tasks are gauss elimination (this elimination method is not as simple as the concept in junior high school, so let's learn it in universities), Newton interpolation method (binomial theorem), iterative method, some approximate algorithms and partial differential equation solutions. To sum up, high school mathematics can be summarized by several people, Gauss, Veda, Newton, Bernoulli and Euclid. These people are all figures before19th century. It can be seen that high school mathematics mainly studies people before19th century, laying the foundation for our modern mathematics. It's not that it's not worth mentioning, but there are some things to mention at all costs. Since the continuous development of the computer industry, mathematics has also developed at an alarming rate. /kloc-Mathematics before 0/9th century is so simple and romantic. When you set foot in college mathematics, you will find it so unpredictable. I think it is very important to study mathematics by innuendo. The essence of learning mathematics is to play and observe, which is limited to your high school textbooks. Read more math books outside high school, and you will gain more, not only math knowledge, but also the sublimation of life. Many mathematicians are famous. Look at the story behind the theorem that made them famous. Mathematics is a subject full of love and deception.