One of the most fundamental similarities between mathematical papers and other scientific papers is the unity of scientific content, scientific language and writing form. Its particularity is reflected in the formatting of structure, the rigor of logic, the simplicity of language and the universality of symbols.
Formatting of 1 structure
The structure of mathematical papers is not much different from the common format of general scientific papers, but there are different layouts in some specific links, which are arranged according to the content of scientific research results. The preface of mathematics should generally include the background and motivation of the subject, the subject to which it belongs, the evaluation of the existing achievements, the position of the subject in the field, the scope of the subject and the goals achieved.
The body part is the core of a mathematical paper. As for the writing layout, there are some differences in the expression of the results because of the mathematical disciplines, topics and research methods involved in the research work, so it is impossible to make a unified regulation. For pure mathematical theory, this part should include theorems and proofs of theorems, lemmas used to prove theorems and inferences drawn from theorems, and examples given to prove or verify a problem. For the problems in applied mathematics, this part should generally include the description of practical problems, the establishment of mathematical models, the methods to solve problems, its theoretical basis and concrete examples.
2 the rigor of logic
As a published achievement, a mathematical paper should be written according to the requirements of logical rigor, otherwise it is not a mathematical paper. Math papers should be impeccable and stand scrutiny. When describing theorem proving, we should examine whether each step has a basis, and what its basis, definition, axiom and theorem are. We must never be vague, let alone take it for granted. When you use the word "obvious", you should carefully consider whether it is really "obvious". In the process of reasoning with intuitive natural language, we should pay special attention to whether there are any situations that have not been considered and whether strict reasoning can be used instead. It must be carefully scrutinized here, and some irreparable mistakes often appear here.
Writing mathematical papers according to deductive logic system is a traditional way to publish results. The mathematical paper written in this form has a compact structure, which makes the whole paper form a strict logical structure and can accommodate more information in a smaller space. But this traditional writing method hides the thinking process of mathematicians. It is of course important for us to write a paper and publish the results, but it is not enough to do so alone, and it should also give people more enlightenment. To tell readers how this theorem was put forward and how to think of this proof, it is necessary to write it in the thinking process of mathematicians. Of course it will increase the length of the paper. However, we don't need to write the thinking process in every paper, just choose those typical inspiring mathematical achievements to write their thinking process. Reading such papers can inspire people to discover and invent mathematics, thus better cultivating people's mathematical creativity. The reason why Euler's works can be the source of enlightening people's wisdom is that he also wrote some loose guessing processes in his works, so that readers can easily see how Euler thinks. Therefore, when writing a thesis, we need the proof process of the theorem to be strict, and some ideas of the proposition and proof of the theorem do not have to be based on strict logical reasoning. In fact, it is also impossible. Therefore, strict and not strict are relative.
Concise name of 3 languages
Mathematical thesis requires concise language, accurate expression of mathematical concepts and logical reasoning with just the right language, so that between the lines, too many words are added and less words are subtracted. It can express the most exquisite mathematical results with the least language and embody the richest mathematical content.
In the process of mathematical reasoning, it is not necessary to write a theoretical basis for each step. Mathematics thesis is not a textbook, it is aimed at professionals. Therefore, the reasoning process is based on the principle that peer experts can understand, and the proof steps do not need to be written in such detail, allowing greater jumps. Especially those common reasoning steps, obvious reasoning process and obvious theoretical basis can be brushed aside without pen and ink. This paper needs the least space and the most information. Mathematical concepts and theorems commonly used in this paper need no explanation. The source of the new concept rent theorem in mathematical application should be noted so that readers can check it correctly. If papers with sources are not suitable for searching, they can be explained for readers' convenience. Although some new concepts and theorems have the same name, they have different meanings in different papers, so the source is indicated to avoid ambiguity for readers.
Mathematical terminology is a special term used in the field of mathematical science. With the development of mathematical science, people's understanding of mathematics is deepening day by day, and new concepts that reflect the essence and express the content of mathematics are constantly emerging. These new concepts are fixed in the special Mongolian language and form mathematical terms. Do these new concepts need to be given in the form of definitions and with what?
What kind of words to use to repair it needs serious consideration. In order to define the concept of irrigation, it is necessary to consider the importance of its function and the universality of its application. To give a new concept a proper name, we need to consider the relationship between the meaning of this concept and the names of some existing concepts. In the long history of mathematical development, every mathematical term has been used for a long time with its precise and fixed meaning. Some names don't need to be changed, although they don't match the meaning. Such as irrational numbers, imaginary numbers.
Proper use of some classical Chinese words in axioms, definitions and theorems can make mathematical papers more refined, concise and accurate. For example, if and only if four words are used in the theorem, the relationship between conditions and conclusions in the theorem is clearly expressed. When defining mathematical concepts and describing theorems, the sentence structure is rigorous and standardized, relatively fixed and single. When writing, you should imitate these existing standard sentence patterns and use common fixed formats in your own writing, so that the paper will be clean, concise, powerful, accurate and reliable, giving people a pleasing feeling.
The universality of symbols.
Mathematical symbols and formulas composed of symbols are widely used in mathematical papers, forming a set of mathematical language symbol system, which, like natural language, undertakes the function of storing and transmitting mathematical information. The use of mathematical symbols and formulas can concisely reflect accurate and profound mathematical knowledge, intensively express mathematical content, make people clear at a glance, facilitate memory, calculation and reasoning, and facilitate international communication. This can reduce the length of the paper and make the handwriting clear and delicate. For example, it is much easier to remember that the formula on the right side of the equation appears many times in the paper, so it is recorded as the symbol IR dish on the right side of the equation. Symbolic use; Expressing the mathematical concepts and theorems to be expounded and using mathematical symbols appropriately and coherently can make a paper easy to read and make people enjoy beauty. Every paper will use a lot of symbols, so when writing a math paper, we should first consider the symbol system, which symbols should be capitalized in English, which should be lowercase, which should be bold, which should be French, which should be Greek and so on. Only in this way can the whole article be coordinated, neat and beautiful.
Pay attention to coordination when using symbols. For example, a ternary linear function is generally expressed as ax+b+z or a: two: ten a: two:+:inferior:, if it is expressed as "'inferior: +by:+. X: This seems incongruous. And if the given two sets are represented as A and B, it is not good. Traditionally, they are represented as A and B. The equation is better to change Z into Y, and the expression is as follows.
Because two variables are considered, they are usually represented by 2 and y, which is a customary representation. Some customary laws in mathematics should be preserved when writing papers. When natural language and mathematical symbol language are used together, they should conform to the Chinese language norms. Sometimes, although there are some anomalies, it does not affect the expression of meaning. For example, two must be greater than zero, which can be expressed as less than >: 0.
Although it is not in the Chinese word order, this kind of metamorphosis is allowed and reasonable. Repetition of natural language and mathematical symbols (such as natural numbers) is also allowed. This repetition makes the expression clear and coherent, not redundant.