math-modeling-paper

Mathematical modeling competition paper writing

Usage process

After receiving a writing task, operate according to the following steps:

Step 0: Check the modeling source

First determine whether the user has already completed modeling:

The user has already used math-modeling-solver to complete modeling and has paper draft fragments → identify [PAPER_READY] signal or the user says "modeling is done/preparing to write the paper", directly load the draft fragments, and start writing from the corresponding chapter
The user has not modeled and directly wants to write the paper → suggest first using math-modeling-solver to complete modeling, or directly proceed to Step 1 to determine the writing stage
The user already has their own modeling plan → directly proceed to Step 1

Step 1: Identify the competition type and writing stage

Confirm with the user (if the information is incomplete):

Competition type: National competition (CUMCM) or American competition (MCM/ICM)? This determines the structure template, language, and review focus.
Current stage：
- Planning: Have not started writing yet, need to determine the paper structure and key points of each part
- Writing: Currently writing a specific chapter, need guidance
- Polishing: Already have a first draft, need to optimize expression and check logic
- Checking: The full text is complete, need to do final format and standards checking

Step 2: Load the corresponding reference files

Load detailed guides according to the competition type:

National competition → read references/cumcm-guide.md
American competition → read references/mcm-icm-guide.md

Required reading:

Literature review/summary writing → read references/literature-review.md(model selection rationale, parameter traceability, and citation format must be supported by literature)

Load as needed according to the current stage:

Abstract-related → read references/abstract-writing.md
Model validation-related → read references/model-validation.md
Need sentence pattern references → read references/common-phrases.md
Determine problem type strategy → read references/problem-type-strategies.md
Figures/tables/code standards → read references/figure-and-code-guide.md
American competition Memo/Letter → read references/memo-writing.md

Step 3: Guide or check section by section

Following the order of the paper structure, execute four-step guidance for each chapter: "purpose → structure → what to write → red lines". See the sections below for specific rules.

Step 4: Self-review before delivery (mandatory)

After the full paper is completed,mustperform four rounds of systematic self-review. Load the following two files:

references/self-review-framework.md — Four-round self-review framework: argument logic → chapter structure → expression quality → format standards
references/de-ai-writing.md — De-AI writing guide: identification and removal of eight types of AI traces + injecting authenticity

Self-review process:

First round(argument logic): Check whether each claim is supported by evidence; unsupported claims/logical leaps/circular reasoning must be fixed
Second round(Chapter structure): Check whether the six elements of the abstract and the seven elements of modeling and solving are complete
Round 3(Presentation quality): Compare against de-ai-writing.md Scan AI traces item by item, and check data accuracy
Round 4(Formatting standards): Consistency of figure and table numbering, references, page numbers, and other formatting
Give a self-review conclusion: ✅ Pass / ⚠️ Conditional pass / ❌ Fail
If ❌, redo the self-review after fixing

Only after passing each round may you proceed to the next round. If time is tight, complete at least Round 1 (argumentation logic)—this is the key gap that distinguishes third prize from first prize.

Paper structure template

CUMCM standard structure

Chapter	Suggested length	Core points
Abstract	1 page (500-800 words)	Each question must have quantitative results
Problem restatement	0.5-1 page	Break down the problem in your own words, not by copying
Problem analysis	1-2 pages	Why this model was chosen, not "what method will be used"; recommend including an overall modeling flowchart
Model assumptions and notation	1 page	Every assumption serves the modeling; reject filler
Data processing	2-4 pages	Explain why it is handled this way (if there is little content, it may be embedded in the first sub-problem)
Modeling and solving for Problem 1	4-6 pages	Objective → rationale → formulas → solving → results → analysis → validation
Modeling and solving for Problem 2	5-7 pages	Same as above (embed sensitivity/error analysis at the end of each sub-problem)
Modeling and solving for Problem 3	5-7 pages	Same as above
Model evaluation and improvement	1-2 pages	Summary of strengths and weaknesses + validation conclusions; evaluate this model, not the algorithm
References	0.5-1 page	≥6 entries, including journal papers and English-language literature
Appendix	As needed	Complete code + list of supporting materials

Total main text length: 20-28 pages (excluding appendix)

On the placement of model validation: In actual award-winning papers, sensitivity analysis/error analysis is usually embedded at the end of each sub-problem solution (e.g., 5.1.6 Sensitivity Analysis), rather than as a separate chapter. If the validation content is substantial (2 pages or more), a separate "Model Validation" chapter may be set up; if the validation content for each sub-problem is relatively short, it is sufficient to summarize the validation conclusions in the "Model Evaluation and Improvement" chapter.

MCM/ICM standard structure

Chapter	Suggested length	Core points
Summary Sheet	1 page	English, hook sentence + full coverage of quantitative results
Table of Contents	0.5 page	Automatically generated
Introduction	2-3 pages	Background + Restatement + Literature Review + Our Work flowchart
Assumptions & Notations	1-2 pages	5-6 entries, each with Justification
Data Processing	1-2 pages	Standalone section, methods + rationale
Model 1-3 (per task)	4-6 pages per model	Each model gets a name + abbreviation, including algorithm pseudocode
Sensitivity Analysis	1-3 pages	Multi-method validation, either standalone or embedded
Strengths & Weaknesses	1 page	Specific evaluation of this model
References	1 page	≥5 items, primarily journal sources
AI Usage Report	1 page	Declare use of AI tools
Appendix	As needed	Code

Total main body length: 25-26 pages

Section-by-section writing rules

1. Title

National competition: state the research object + core method clearly. E.g., "An XX Scheduling Model Based on Multi-Objective Optimization and Sensitivity Analysis"

MCM/ICM: create a memorable title + model name. E.g., "Golden Dynamics: Bayesian-AI Olympic Forecasting"

Avoid: directly copying the competition problem, overly vague titles

2. Abstract (the most critical 1 page)

This is the basis for the first round of review screening. Golden rules that must be followed in both competitions:

Red line 1: Every question must have a number. Every sub-problem in the abstract must include at least one specific quantitative result. Writing only methods without results is prohibited. Comparison:

Incorrect writing	Correct writing
Established a multiple linear regression model to analyze the influencing factors	During co-pyrolysis, tar yield showed a significant negative correlation with INS content (R²=0.873, p<0.01)
Used a genetic algorithm to obtain the optimal solution	The optimal planting scheme's total profit is 40.2448 million yuan, a 23.7% increase over the baseline scheme

Red line 2: Results must be precise. Do not give only ranges or omit data. MCM/ICM papers should further provide error metrics such as confidence intervals, NRMSE, and coverage rates.

National competition abstract structure: Problem background (1 sentence) → Overall approach (1 sentence) → Problem 1 method + results → Problem 2 method + results → Problem 3 method + results → Model validation/strengths (1-2 sentences) → Keywords (3-5)

MCM/ICM abstract structure: Hook sentence (1 sentence) → Problem statement (1-2 sentences) → Each Task's model name + brief method description + quantitative results → Key conclusions → Keywords (6-8)

For detailed templates and sentence patterns, see references/abstract-writing.md。

3. Problem restatement

Re-decompose the problem in your own words; do not copy and paste the original problem text.

Good practice: First summarize the problem background, then break the tasks into sub-problems, and finally explain the solution objective of each problem.

Length control: National competition 0.5-1 page, MCM/ICM 2-3 pages (including background and literature review).

4. Problem analysis

This is the key section that distinguishes "applying a model" from "understanding the problem."Award-winning papers invest 1-2 pages here for in-depth analysis, rather than simply listing methods.

Red line: Do not write "we will use method A to do X." That is a list of methods, not analysis.

The correct writing follows the "why" logic:

What is the mathematical essence of this problem? (Prediction/evaluation/classification/optimization/mechanism?)
What are the input variables and output results respectively?
Why choose this model instead of others? (MustCompare at least one alternative and cite literature evidence to support the choice rationale)
What is the progressive relationship among the questions?
What are the difficulties? How to address them?

Format: Write separately by sub-question, with each sub-question receiving a paragraph of independent analysis (e.g., 2.1 Analysis of Problem One, 2.2 Analysis of Problem Two).

Strongly recommended: At the end of the problem analysis, place aoverall modeling flowchart(block diagram/arrow diagram), showing the model corresponding to each sub-question and the data flow among them. About 70% of award-winning papers include this diagram.

Example writing (good)：

Problem One requires evaluating the comprehensive benefits of different schemes. This is a typical multi-indicator comprehensive evaluation problem. Commonly used methods for evaluation problems include the Analytic Hierarchy Process (AHP), TOPSIS, and fuzzy comprehensive evaluation. Considering that this problem has a large number of indicators and some indicators have a certain degree of fuzziness, this paper selects the fuzzy comprehensive evaluation method, which can handle both quantitative indicators and experts' fuzzy judgments on qualitative indicators. The determination of indicator weights adopts the entropy weight method to reduce subjectivity. The evaluation results of Problem One will serve as input constraints for the optimization model in Problem Two.

Example writing (poor)：

For Problem One, we first perform data processing, then use the fuzzy comprehensive evaluation method for evaluation, and finally obtain the evaluation results.

5. Model Assumptions

Red line 1: Do not write useless assumptions. The following types of assumptions must be deleted:

"Assume the data are authentic and reliable" ← The problem has already provided the data
"Assume random factors are ignored" ← Too general
"Assume emergencies are not considered" ← Does not serve the modeling

Red line 2: Every assumption must be used later in the text. When writing assumptions, you must think clearly about how they are reflected in the model.

Correct approach: Assumptions should serve the modeling, in the format "assumption content + why this assumption is reasonable." List them by category (e.g., physical simplification type, data type, parameter type).

6. Symbol Description

Only include core variables, do not pile in all variables. Each symbol includes: symbol, meaning, unit (required).

7. Data Processing

Red line: Do not only write the method; explain why.

Content coverage: data sources → missing value handling → outlier handling → standardization/normalization → feature extraction → quantifiable analysis

Each type of processing must explain the reason. For example: "Because the units of different crop yields differ greatly, Z-score standardization is used to eliminate the influence of units."

MCM/ICM papers treat data processing as an independent chapter, and this is a bonus point.

8. Model Establishment and Solution

This is the core of the main text; each sub-question is developed according to the following structure:

Standard six-step structure：

Problem objective (what this section is to solve)
Reason for model selection (why this model, not another)
Model formulas (derived from the problem, not copied from a textbook)
Parameter explanation (the meaning of each parameter and the basis for its value)
Solution steps (algorithm pseudocode + flowchart may be used)
Result presentation (tables + figures)
Result analysis (what this result shows)

Red line 1: Formulas must be targeted to the problem. Do not copy generic formulas from textbooks without adapting them to the problem. Derive from first principles, and the symbols in the formulas must correspond to the specific variables of this problem.

Red line 2: Results must be accompanied by explanations. After each table/figure, there must be 1-3 sentences explaining "what this result shows" and "why this result occurs"; do not merely describe "the figure shows...".

Red line 3: Code and paper must be consistent. The methods claimed in the paper must be implemented in the code. If you claim to use XGBoost, then write XGBoost; the code cannot be running linear regression.

Additional MCM/ICM requirements: Give each model a creative name + abbreviation (e.g., HARMONIE, CHAMPS), and provide an algorithm pseudocode box (Input / Output / Steps).

9. Model validation (the core of pushing for a higher award)

This is the key gap from third prize to first prize. In actual award-winning papers, sensitivity analysis/error analysis is usually embedded at the end of each sub-problem solution (e.g., 5.1.6 Sensitivity Analysis), with a length of 0.5-1 page per sub-problem.

Required items：

Sensitivity analysis: Change key parameters (recommended ±10%, ±20%) and observe changes in results. Draw a tornado diagram or sensitivity curve.
Error analysis: Report MSE/MAE/R², and discuss sources of error and acceptability.

Bonus items：

Stability/robustness testing: Monte Carlo random perturbation, report reliability curves
Assumption validation: Go back and check whether key assumptions hold in the model
Comparative experiments: Use another method to solve the same problem and compare differences in results
Cross-validation: K-fold or hold-out validation

Organization：

Approach 1 (recommended): Embed at the end of each sub-problem chapter (e.g., 5.1.6 Sensitivity Analysis), and finally summarize the key validation conclusions in the model evaluation chapter
Approach 2: Consolidate all validation content into an independent chapter (suitable when the validation content exceeds 2 pages or multiple validation methods are used)

For detailed methods, see references/model-validation.md。

10. Results analysis and interpretation

Red line: Do not just include figures and tables without explanation. After each figure or table, there must be an analysis paragraph.

Three-part analysis:

What is this result? (Summarize in one sentence)
Why is this the result? (Connect to the model mechanism or data characteristics)
What significance does this result have for the problem background? (Return to the actual problem)

11. Strengths, weaknesses, and improvements

Red line: Evaluate "this model," not "the algorithm used."

Incorrect wording (evaluating the algorithm)	Correct wording (evaluating this model)
Linear regression is simple and intuitive, and easy to implement	This model assumes crop yield is a linear function of sunshine-rainfall factors; the structure is clear but does not consider interaction effects
Genetic algorithms easily fall into local optima	The AGA used in this model effectively improves convergence for the XX problem through adaptive crossover and mutation probabilities

Write 3-5 weaknesses, and each one should acknowledge the limitations brought by the specific modeling choices of this model. Do not write universally applicable statements like "strong data dependence."

12. References

Red Line 1: It is prohibited to cite non-academic sources such as CSDN blogs, Zhihu, Baidu Baike, and AI tools (e.g., DeepSeek/ChatGPT).

Red Line 2: If it is cited in the main text, it must be listed; if it is listed, it must appear in the main text.

Quantity requirements: National competition ≥6 entries, MCM/ICM ≥5 entries. Being able to cite English journal papers is a bonus, but not mandatory. For MCM/ICM, citing more than 8 entries is recommended to demonstrate the depth of literature research.

Correct sources：

Journal papers (Chinese: CNKI core journals; English: IEEE/Elsevier/Springer, etc.)
Textbooks (e.g., Jiang Qiyuan, Mathematical Models; Si Shoukui, Mathematical Modeling Algorithms and Applications)
Dissertations
National standards (e.g., GB 12327-1998)
Official data sources (e.g., National Bureau of Statistics, World Bank)

13. Appendix

Must include:

Complete runnable source code(do not include only fragments). The 2026 national competition rules clearly state: if necessary source programs are missing or the programs cannot run, award eligibility may be revoked.
List of supporting material files
Longer intermediate result tables (optional)

Code standards：

The code should have clear section comments indicating which sub-problem it corresponds to
Method names/variable names in the code should be consistent with the notation in the paper
MATLAB/Python/C++ are all acceptable; the choice depends on the problem type (see references/problem-type-strategies.md）
The code does not need to be explained line by line in the main text, but the methods claimed in the paper must be implemented in the code

For detailed figures, tables, and code standards, see references/figure-and-code-guide.md。

Quick reference of key differences between the two competitions

Dimension	National competition CUMCM	MCM/ICM
Language	Chinese	English
Most valued	Quantified results in the abstract, model validation	Model innovation, multi-model fusion, original derivations
Model naming	Not required; algorithms may be referred to directly by name	Must have a creative name + abbreviation
Sensitivity analysis	Embedded in sub-problems or as an independent chapter	Required (1-3 pages, either independent or embedded)
References	≥6 entries	≥5 entries
Literature review	Required (may be incorporated into the problem analysis)	Almost required (the Introduction must include a Literature Review); the rationale for model selection must be supported by literature
AI usage report	Recommended since 2024	~37% of papers include it (1 page), listing tools + queries
Flowchart	Recommended (place an overall framework diagram in the problem analysis)	Almost required (Our Work figure, a signature feature)
Memo/Letter	Not involved	Common in Problems B/D/E/F, see memo-writing.md
Abstract page	On the first page of the main text	Separate Summary Sheet (~400-550 words)
Review focus	Method correctness, result reasonableness, model validation	Innovation in modeling approach, writing and presentation ability

LaTeX / Word formatting checklist

After completing the paper, check item by item:

General checks

All formulas are numbered, and the numbering format is consistent
All figures and tables have captions; table captions are above, figure captions are below
Figure and table captions are sufficiently descriptive (not "Figure 1: Results figure")
All symbols appear in the symbol description table
All cited references are marked in the main text
The main text word count is within the required range (National Competition <30 pages, MCM/ICM <25 pages)

Additional checks for MCM/ICM

English spelling and grammar (can be checked with Grammarly)
Summary Sheet is on a separate page
AI Usage Report is on a separate page
Figure and table captions are in English
Algorithm pseudocode format is standardized (Algorithm 1, 2, 3...)

Reference resources

references/cumcm-guide.md — Detailed writing approach for each chapter of the National Competition
references/mcm-icm-guide.md — Detailed writing approach for each chapter of MCM/ICM
references/abstract-writing.md — Abstract templates and sentence patterns (bilingual Chinese-English)
references/model-validation.md — Comprehensive collection of model validation methods
references/literature-review.md — Literature search strategies, review writing, citation formats, parameter traceability
references/common-phrases.md — Common academic sentence patterns (bilingual Chinese-English)
references/problem-type-strategies.md — Differentiated strategies for Problems A/B/C
references/figure-and-code-guide.md — Figure and table standards and code appendix requirements
references/memo-writing.md — Writing guidance for MCM/ICM Memo/Letter
references/de-ai-writing.md — Guide to removing AI flavor in writing (identification of eight types of AI traces + injecting authenticity + mathematical modeling-specific standards)
references/self-review-framework.md — Four-round self-review framework (argumentation logic → chapter structure → expression quality → formatting standards)