1. Determine the research topic: First of all, you need to determine a specific research topic, which is usually an unsolved problem or an incomplete problem. Choose a subject that you are interested in and has certain research value.

2. Consult literature: Before writing, you need to consult relevant mathematical literature to understand the existing research results, common methods and skills in this field. This is helpful to better understand the problem and provide background and reference for your own research.

3. Formulation of research methods: According to literature review, select one or more suitable research methods and explain in detail how to implement these methods. This includes defining variables, establishing models, and choosing appropriate statistical or mathematical tools.

4. Data collection and analysis: according to the selected research methods, collect relevant data and make necessary analysis. This may involve actual data collection, data preprocessing, statistical analysis and other steps.

5. Writing a thesis: After completing data analysis and research, start writing a thesis. The paper should include the following parts: Abstract: Briefly summarize the main contents, research methods and conclusions of the paper. Introduction: Introduce the research background, research purpose and significance, and the structure of the paper. Literature review: Review the existing literature related to this study, and expound the research status and existing problems.

Methods: The research methods were described in detail, including data source, processing and analysis process. Results and discussion: state the research results, and make necessary explanations and discussions on the results. Conclusion: Summarize the research results and point out the limitations of the research and the future research direction. References: list all references cited in the paper to enhance the credibility and readability of the paper.

Revision and improvement: after the first draft is completed, it needs to be revised and improved many times. Check grammar and spelling mistakes to ensure that the content of the paper is coherent and logical. You can also ask peers or tutors to review the papers and put forward valuable opinions and suggestions. Submission and publication: submit the completed papers to academic journals or conferences for review. According to the feedback from the reviewers, necessary modifications and adjustments are made to finally meet the publishing requirements.

Writing a mathematical paper needs to go through sufficient preparation and research process, and pay attention to the rationality of the method and the reliability of the data. After repeated revisions and improvements, a paper with academic value was finally presented.