Mathematics is a subject to develop thinking, and it is also the basis of learning technology, such as physics, chemistry, machinery, computer, photoelectric technology and so on. If you can't learn math well, these things will be difficult to learn. So, you must learn math well.

In the process of learning, we must: listen more (attend lectures), remember more (remember the structure of important questions, remember concepts, remember formulas), read more (read books), do more (do homework), ask more questions (ask questions if you don't understand), do more experiments, review more and summarize more. Concentrate on class by taking notes.

We should arrange a simple and feasible plan to improve our learning methods. At the same time, we should properly participate in school activities and develop in an all-round way.

At other times, we should ensure the study time and the quality of all subjects.

Get enough sleep (8 hours) every day to ensure learning efficiency.

Arrange appropriate free time to communicate with family and friends.

Through unremitting efforts, the results will be improved and stabilized step by step. Try your best in the exam, be careful in the exam, and be calm in the final sprint. After the exam, you should sum up carefully so that you can study better in the future.

Now: let go of the burden, usually: study hard. Before the exam: prepare carefully. During the exam: don't give up. After the exam: be normal. Remember!

Success always comes from unremitting efforts, and success always belongs to diligent people. I wish you success!

What are the nature, types and characteristics of mathematical knowledge?

Mathematics, as an expression of human thinking, embodies people's aggressive will, meticulous logical reasoning and pursuit of perfection. Its basic elements are: logic and intuition, analysis and reasoning, individuality and individuality. Although different traditional schools can emphasize different aspects, it is the interaction of these opposing forces and their comprehensive efforts that constitute the vitality, availability and lofty value of mathematical science.

Nature is a description of quantitative relations and spatial forms.

It belongs to the category of natural science and consists of concepts, axioms, theorems, inferences and propositions.

It is characterized by abstraction and strictness.

What is mathematical knowledge?

Mathematics, whose English is Mathematics, is a plural noun. "Mathematics used to be arithmetic, geometry, astronomy and music, which was higher than grammar, rhetoric and dialectics."

Since ancient times, most people regard mathematics as a kind of knowledge system, which is the systematic summation of theoretical knowledge formed through strict logical reasoning. It not only reflects people's understanding of "Engels' spatial form and quantitative relationship in the real world", but also reflects people's understanding of "possible quantitative relationship and form" Mathematics can not only come from the direct abstraction of the real world, but also from the labor creation of human thinking.

Judging from the development history of human society, people's understanding of the essential characteristics of mathematics is constantly changing and deepening. "The root of mathematics lies in common sense, and the most obvious example is non-negative integers." Euclid's arithmetic comes from non-negative integers in common sense. Until the middle of19th century, the scientific exploration of numbers remained in common sense. "Another example is the similarity in geometry." In individual development, geometry even precedes arithmetic. "One of its earliest signs is the understanding of similarity. "Similar knowledge is discovered so early", just like being born. "Therefore, before the19th century, it was generally believed that mathematics was a natural science and an empirical science, because mathematics was closely related to reality at that time. With the deepening of mathematical research, the view that mathematics is a deductive science gradually occupied a dominant position after the middle of19th century, which was developed in the research of Bourbaki school. They think that mathematics is a science of studying structure, and all mathematics is based on algebraic structure. Corresponding to this view, from Plato in ancient Greece, many people think that mathematics is the knowledge of research mode. Mathematician A.N. Whiiehead (186- 1947) said in Mathematics and Goodness, "The essential feature of mathematics is to study patterns in the process of abstracting from patterned individuals. 193 1 year, the proof of Godel's incompleteness theorem (k, G0de 1, 1978) declared the deficiency in the deductive system of axiomatic logic, so people thought that mathematics is an empirical science, and the famous mathematician von Neumann thought that mathematics has both deductive science and empirical science.

For the above viewpoints about the essential characteristics of mathematics, we should analyze them from a historical perspective. In fact, the understanding of logarithmic essential characteristics develops with the development of mathematics. Because mathematics comes from the practice of distributing goods, calculating time and measuring land and volume, the mathematical object at this time (as the product of abstract thinking) is very close to objective reality, and it is easy for people to find the realistic prototype of mathematical concepts, so people naturally think that mathematics is an empirical science; With the deepening of mathematical research, non-Euclidean geometry, abstract algebra and * * * theory have emerged, especially modern mathematics is developing towards abstraction, pluralism and high dimension. People's attention is focused on these abstract objects, and the distance between mathematics and reality is getting farther and farther. Moreover, mathematical proof (as deductive reasoning) plays an important role in mathematical research. Therefore, mathematics has emerged as the free creation of human thinking and the science of studying the relationship between quantity and quantity. These understandings not only reflect the deepening of people's understanding of mathematics, but also are the result of people's understanding of mathematics from different aspects. As someone said, "Engels thought that mathematics is the study of quantitative relations and spatial forms in the real world, which is not contradictory to bourbaki's structural view. The former reflects the origin of mathematics, while the latter reflects the level of modern mathematics. It is a building built by a series of abstract structures. "Mathematics is the knowledge of research methods, which explains the essential characteristics of mathematics from the perspective of abstract process and level of mathematics. In addition, from the ideological source, people regard mathematics as a science of deduction and research structure, which is based on human innate belief in the inevitability and accuracy of mathematical reasoning and a concentrated expression of self-confidence in their own rational ability, roots and strength. Therefore, people think that this method of developing mathematical theory, that is, deductive reasoning from axioms that are self-evident, is absolutely reliable, that is, if axioms are true, then the conclusions deduced from axioms must also be true. Applying these seemingly clear, correct and perfect logics, the conclusions drawn by mathematicians are obviously beyond doubt and irrefutable.

What are the advantages of learning mathematics?

1, to meet the needs of people's daily life, work, counting, calculation and reasoning. In people's daily life and work, it is essential to count things, calculate various quantities and compare related quantities. Mathematical knowledge and thinking methods are needed here.

2. Exercise people's thinking level and thinking quality, such as calculation ability, logical thinking ability and spatial imagination ability. Mathematical science is a rigorous and meticulous science, so people's thinking has been exercised while learning mathematical science knowledge.

3. Mathematics learning can provide necessary technical support for further study of natural science and social science. Mathematics, as a basic subject to understand the world, can support the in-depth development of different applied sciences ideologically and technically like a computer system.

4. Learning mathematics can help us understand and learn the scientific and rigorous scientific attitude and style embodied in mathematicians, and improve our scientific literacy.

5. Mathematics is the basic science for human beings to know the world, especially in modern times where high technologies emerge one after another and competition is increasingly fierce. Everyone should master some mathematical knowledge to improve their competitiveness in society.

reference data

Baidu encyclopedia-mathematics

What are the characteristics of mathematics?

Mathematics is a subject to develop thinking, and it is also the basis of learning technology, such as physics, chemistry, machinery, computer, photoelectric technology and so on. If you can't learn math well, it will be difficult to learn it. So, you must learn math well. In the process of learning, we must: listen more (attend lectures), remember more (remember important problem structures, remember concepts, remember formulas), and read more (. Review more and summarize more. Concentrate by taking class notes. Make a simple and feasible plan to improve learning methods. At the same time, participate in school activities appropriately and develop in an all-round way. At other times, we should ensure the study time and the study quality of all subjects, and we should not be partial to subjects. We must ensure adequate sleep (8 hours) every day. Ensure learning efficiency. Arrange appropriate free time to communicate with family and friends. Make unremitting efforts to improve and stabilize your grades step by step. Try your best in the exam, be careful in the exam, and be calm in the final sprint. Summarize it carefully after the exam to facilitate better study in the future. Now: let go of the burden, usually: study hard. Before the exam: prepare carefully, during the exam: don't say anything. Success always comes from unremitting efforts, and success always belongs to diligent people. I wish you success!

. .

What are the advantages of learning mathematics?

1, to meet the needs of people's daily life, work, counting, calculation and reasoning.

In people's daily life and work, it is essential to count things, calculate various quantities and compare related quantities. Mathematical knowledge and thinking methods are needed here. 2. Exercise people's thinking level and thinking quality, such as calculation ability, logical thinking ability and spatial imagination ability.

Mathematical science is a rigorous and meticulous science, so people's thinking has been exercised while learning mathematical science knowledge. 3. Mathematics learning can provide necessary technical support for further study of natural science and social science.

Mathematics, as a basic subject to understand the world, can support the in-depth development of different applied sciences ideologically and technically like a computer system. 4. Learning mathematics can help us understand and learn the scientific and rigorous scientific attitude and style embodied in mathematicians, and improve our scientific literacy.