First, the grammatical structure.
In mathematics, grammatical structure is relatively standard, and it is generally expressed in concise, clear, accurate and complete language. Grammatical correctness is very important for understanding and deducing mathematical problems.
Different from the general language, ambiguity and ambiguity should be avoided as much as possible in mathematics, and some words or phrases in the language can be ignored to express complex concepts and ideas in a concise way.
For mathematics writing, we need to pay attention to the correctness of grammar and the clarity of expression, and use grammatical structures such as sentence components, subject-predicate object structures and modifiers to emphasize the essence and avoid the problem of unclear or inconsistent components.
Second, logical reasoning.
Mathematical knowledge is reasoned in logical order, so logical reasoning must be done well in mathematical writing. In other words, some seemingly unrelated propositions and mathematical formulas in mathematical articles must be linked through logical relations, so that readers can understand and accept the ideas and viewpoints in the articles.
Therefore, mathematical writing usually has the characteristics of rigor, accuracy, correctness, logic and coherence. At the same time, we should pay attention to some classical language rules in mathematical writing, such as the structure of proof, which should be based on premise, with intermediate deduction as the main body, and finally draw a conclusion. In addition, for the common "sufficient and necessary" proof method, two directions need to be clearly stated.
Third, the use of symbols.
In mathematics, symbol is a very important expression tool, which runs through the whole mathematical knowledge system. Therefore, mathematics writing needs to pay attention to the accuracy and consistency of symbol use. We should not only master the meanings and application rules of various symbols, but also follow the unified symbol convention.
For example, for the set of natural numbers, some people are used to using the capital letter n, while others like to use the symbol Z+ or positive integer symbols, but these are all symbolic habits, so when writing, they should be consistent with the readers and try to avoid ambiguity.
In addition, mathematical symbols are sometimes mixed with words, so it is necessary to pay attention to the consistency of typesetting and style, especially in formula derivation and interpretation, so that readers can better understand and accept the content of the article.
Expand knowledge:
In addition to the above three aspects, mathematics writing needs to pay attention to practicality and inspiration, not only to have theoretical analysis, but also to illustrate the essence of the problem through examples and applications.
In addition, for those difficult or abstract concepts or definitions, readers can deepen their understanding and understanding of these concepts through metaphor, analogy, contrast and intuitive feeling. In actual writing, we should also pay attention to the beauty of writing and language, so that readers can better accept and understand the ideas and information of the article.
The above is the difference between mathematics writing and reading, mainly including grammatical structure, logical reasoning and symbol use. In mathematics writing, we need to pay attention to accuracy, clarity, coherence and practicality, follow unified language rules and symbolic conventions, and at the same time, we can strengthen readers' understanding and understanding of concepts through metaphor, analogy and comparison.