How to Write a Winning Math Modeling Competition Paper: Structure & Tips

1 Competition Paper Structure

Mathematical modeling papers follow a fixed format. A complete competition paper usually includes seven parts:

(1) Abstract: overview of modeling ideas, model type, algorithm, model features, main results, and keywords for indexing.

(2) Problem Restatement: restate the background and requirements, and provide overall analysis and modeling approach.

(3) Model Assumptions and Symbol Explanation: list reasonable assumptions and explain symbols and variables, often in a table.

(4) Model Building and Solution: core content; organize by problem order, present analysis, derivations, basic and final models, solution algorithms, implementation steps, software used, and result analysis, error analysis, and model verification.

(5) Model Evaluation: discuss model characteristics, advantages, disadvantages, improvement methods, and potential extensions.

(6) References: list cited literature.

(7) Appendix: include detailed flowcharts, program code, tables, and data results that are inconvenient to place in the main text.

Four reviewing principles: reasonableness of assumptions, creativity of modeling, correctness of results, and clarity of presentation.

2 Writing the Abstract

The abstract is crucial; reviewers first screen papers based on it. Teams should spend over three hours drafting and revising the abstract, using exemplary past abstracts for imitation. Write the abstract after the main paper is formed to ensure a macro view of structure, ideas, and results. Team members may draft independently and then merge and edit.

An abstract is a concise, unannotated statement of the paper’s content, covering the real problem, modeling approach, built model, solution method, main results, and model validation and promotion. It should be succinct, highlight model, algorithm, innovations, and results, avoid empty language, and be 500–1000 Chinese characters (about one page). Finally, list 3–5 keywords describing the problem features.

Typical abstract format: [Abstract] For the problem ..., using ... method, we built ... model, solved it with ... method, obtaining ... results. ... [Keywords] ...

Overall, the first paragraph summarizes the whole paper, then each question is addressed with modeling ideas, model, algorithm, results, and analysis. Specific formulas are usually omitted, but model type and main outcomes are presented.

3 Writing the Main Text

3.1 Problem Restatement and Analysis

Problem restatement expresses the contestant’s understanding in their own words, clarifying the problem without copying the original statement.

Problem analysis may follow the restatement or be a separate section, describing background, research status, objectives, and overall solution ideas. It helps organize modeling progress, akin to a construction blueprint.

3.2 Model Assumptions and Symbol Explanation

Assumptions must be reasonable and directly needed for modeling; avoid unnecessary or irrelevant assumptions. Record assumptions as they arise during modeling.

Symbols should be listed in a table with symbol, meaning, unit, and simple relationships, using consistent notation (e.g., uppercase for constants, lowercase for variables). Consistency prevents confusion.

3.3 Model Building and Solution

This section is the core. Model building translates assumptions into mathematical expressions, forming a solvable structure.

Model building should prioritize practicality and simplicity; use elementary methods when sufficient, and avoid overly complex techniques. Clearly explain principles, provide complete and concise model statements, and note any simplifications.

Model solution involves applying mathematical methods, algorithms, or software. Include derivations, algorithm steps, flowcharts, and results. Mention software names; detailed code can be placed in the appendix. Analyze results with error analysis, stability, sensitivity, and compare alternative solutions when applicable.

3.4 Model Evaluation and Promotion

Discuss the model’s strengths and weaknesses, possible improvements, and how it can be extended or generalized.

3.5 References

Cite all sources used in the text, following the competition’s specified format. Use bracketed numbers like [1] in the text and list full bibliographic details in the reference section.

[Number] Author. Book Title. Publication place: Publisher, Year.

[Number] Author. Paper Title. Journal, Volume(Issue): pages, Year.

[Number] Author. Resource Title. URL, Access date.

3.6 Appendix

The appendix contains supplementary material such as program code, detailed flowcharts, and extensive data tables. Ensure consistency with the main text, avoid contradictory data, and provide explanations for any included programs.

Reference

Yang Huiyue, Wu Songlin. Mathematical Modeling Competition Practice Guide and Paper Analysis . Beijing: Tsinghua University Press, 2021.