Complete Guide to the National Mathematical Modeling Contest: Modeling, Topic Selection, and Award-Winning Strategies in the AI Era

The National Mathematical Modeling Contest is one of the most influential academic competitions in China. Founded in 1992, it has been running for over three decades. The China Undergraduate Mathematical Contest in Modeling (CUMCM) is jointly organized by the Department of Higher Education of the Ministry of Education and the China Society for Industrial and Applied Mathematics. The scale of participation has grown from just 74 universities at its inception to over 1,600 universities and tens of thousands of teams annually today, making it one of the largest extracurricular science and technology activities nationwide, as well as an important indicator of the level of applied mathematics education at universities. With the widespread adoption of AI tools, the logic of contest preparation is undergoing profound changes. Based on the national contest insight livestream lecture by Teacher Yang from the Bilibili channel "Math Modeling Fueling Station," this article systematically outlines the essential principles of the mathematical modeling contest, the judging criteria, and the new paradigm of contest preparation in the AI era.

The Essence of Mathematical Modeling: Solving Real-World Problems with Mathematical Methods

The core of mathematical modeling is the complete process of transforming real-world problems into mathematical problems and then solving and verifying them. Teacher Yang illustrated this intuitively with a classic example: a cafeteria has five windows—how many should be open at lunchtime? Opening too many raises costs, while opening too few fails to meet dining demand. Essentially, this is an optimization problem balancing cost against demand—keeping queue times under 5 minutes while minimizing operating costs.

Behind this example lies the classic combination of Queueing Theory and operations optimization. Queueing theory was founded by Danish engineer Erlang in 1909 to study the stochastic processes of waiting phenomena in service systems. Such problems are typically abstracted into the M/M/c model (Poisson arrivals, exponential service time, c servers), with core parameters including arrival rate λ, service rate μ, and number of servers c. The optimization objective is quantified through an objective function—for example, minimizing total cost = operating cost + waiting time loss cost, subject to the constraint of average waiting time ≤ 5 minutes. This modeling framework is widely applied in scenarios such as hospital registration, bank counters, and customer service centers, making it a recurring classic problem type in modeling contests.

This example reveals the core logical chain of modeling: first analyze the real situation → abstract into key points → define mathematical variables and objectives → build a mathematical model and solve → return to real-world validation.

What you may not have noticed is that the datasets used in national contest problems all come from real data generated in real life, rather than fabricated numbers. Therefore, the entire modeling process must rely on mathematical methods and cannot depend solely on textual logical reasoning. This logic runs through the entire modeling process and does not change with the chosen topic.

Paper Structure: Consistent Logic Throughout

Examining the abstracts of excellent national contest papers reveals that they all follow the same three-part logic: what problem (phenomenon) is being addressed → what model (mathematical method) is established → what results are obtained and verified (result validation). Take an award-winning paper as an example: its abstract opens by describing the phenomenon, then abstracts it into mathematical models such as the logit transformation, and finally presents the results along with error analysis.

It is worth mentioning that the logit transformation is a core technique in the Generalized Linear Model (GLM) for handling binary dependent variables. The logit function is defined as log(p/(1-p)), mapping probability values from [0,1] to (-∞,+∞), enabling the linear regression framework to apply to classification problems—namely, Logistic Regression. In modeling contests, the logit model is often used to predict the probability of an event occurring, such as predicting user churn, disease incidence, or policy implementation effects. Its coefficients have clear statistical interpretability (log odds ratio), balancing prediction accuracy and interpretability, and are viewed by judges as highly academically rigorous.

The standard paper template includes: abstract, problem restatement, problem analysis, model assumptions (3-8 items), symbol descriptions, model establishment and solution (the core review section), sensitivity and robustness analysis, model evaluation and extension, references, and appendices. Among these, references and appendices are recommended to be retained to reflect the completeness of the paper.

National Contest Judging Rules and Award Thresholds

The national contest adopts a three-person team system, divided into the undergraduate division (choosing one of problems A/B/C) and the junior college division (choosing one of problems D/E). The judging criteria center on four core dimensions: reasonableness of assumptions, creativity of modeling, correctness of results, and clarity of written expression.

According to Teacher Yang, national contest scoring is extremely strict—his supervising teacher, with over a decade of teaching experience, has seen a maximum score of only 78. The correspondence between scores and award tiers is roughly as follows:

• Above 60 points qualifies for national-level recommendation; above 70 points fairly securely earns a National First Prize
• 45-60 points corresponds to Provincial First Prize
• 30-45 points corresponds to Provincial Second/Third Prize
• Below 30 points usually receives no award

Judges first look at the abstract to decide whether the paper advances to the next round, with an average review time of about 15 minutes per paper. This means the quality of the abstract directly determines whether a paper is taken seriously.

Topic Selection Strategy: Balancing Difficulty and Competition

The three undergraduate division problems each have their own characteristics:

• Problem A: Engineering and physics background, with differential equations and physical models as core tools. It is the most difficult and least chosen. Its advantage is that students from liberal arts colleges who choose Problem A can more easily win a National Second Prize; its disadvantage is that if you fail to earn a National Second, you are very likely to end up with a Provincial Third or no award
• Problem B: Social hot topics or interdisciplinary problems, of medium difficulty, sometimes swapped with Problem A as an "anti-prediction" measure
• Problem C: Leaning toward economics, management, and data analysis; the easiest and most popular, with the fiercest competition. In recent years, data processing requirements have been added for the first time

Teacher Yang's personal experience is quite instructive: he majored in finance as an undergraduate, chose Problem C the first time and won Provincial First, chose Problem A the second time and won National First, and chose Problem A in the American contest and won an F Award. This shows that topic selection should be based on "which problem you can do best," rather than your academic background. Moreover, the national contest is essentially intramural competition—each school can only recommend two National First and two National Second candidates per problem.

Three Core Competencies for Contest Preparation in the AI Era

Contest preparation requires working on three major areas: modeling ability, programming ability, and writing ability.

Before AI, coding ability was the key factor in winning awards. After the widespread adoption of AI, since most code can now be completed with AI assistance, modeling ability has become the decisive factor, because it concentrates the two core elements of problem comprehension and innovation.

Modeling: Comprehension First, Innovation Foremost

The importance of problem comprehension cannot be overstated. Teacher Yang gives an example: if a 25-point optimization problem is misinterpreted as a statistics problem, it can earn at most 1-2 points. Therefore, mastering the application scenarios of various models is crucial—optimization types (integer/linear/dynamic programming), prediction types (regression, time series, differential equations), evaluation types, and network types all require a clear understanding of where they apply.

For beginners, Teacher Yang offers three practical paths to innovation:

1. Integration innovation: such as "prediction + optimization" (predict parameters first, then optimize), or converting a network-type problem into an optimization problem
2. Comparison innovation: using both principal component analysis and cluster analysis to solve the same problem and comparing their performance
3. Corrective innovation: using the analytic hierarchy process to adjust the detailed parameters of regression analysis

But innovation must be built on accurate problem comprehension. If an optimization-type problem is "innovated" off-track into a statistical model, judges will deem it off-topic.

Programming: Prefer Python

In the AI era, Python holds advantages over MATLAB: it is open-source, has a rich ecosystem and abundant libraries, and many AI Agents can generate and run Python code on their own, which is harder for MATLAB. In addition, Python's plotting output is also more visually appealing.

From a technical ecosystem perspective, MATLAB is developed by MathWorks and has a powerful matrix computation kernel and mature toolboxes (such as Simulink and the Optimization Toolbox), remaining mainstream in the engineering simulation field. However, Python—leveraging open-source libraries such as NumPy, SciPy, Pandas, and Scikit-learn—has built a complete ecosystem covering data processing, machine learning, and deep learning. The output quality of visualization libraries such as Matplotlib, Seaborn, and Plotly has also comprehensively surpassed MATLAB's default graphics. More importantly, current mainstream AI coding assistants (such as GPT-4o and GitHub Copilot) have far superior code generation capabilities for Python than for MATLAB, and can achieve a complete closed loop of code generation → running → debugging within the Jupyter Notebook environment—this is precisely the technical foundation for AI Agents running code on their own.

A team needs at least two members with a programming foundation, and the software versions used by all three members should be internally standardized to avoid version incompatibility issues during the contest.

Writing: Let the Paper Faithfully Present the Modeling Approach

No matter how good the modeling approach is, it still needs to be presented through clear writing. The abstract must reflect four elements: "what was done, how it was done, what results were obtained, and whether the results are reliable." Place at least one figure or table per page to avoid visual fatigue, and figure and table labels should be complete and standardized.

AI Usage Guidelines: Allowed but with Clear Boundaries

The national contest organizing committee has published regulations on the use of artificial intelligence, with the core principle being openness and transparency: AI may be used but must comply with the regulations, and core modeling and analysis must be completed independently by the participating team.

Teacher Yang offers highly actionable advice:

• Code may be written with AI assistance, because there is little difference in the AI-detection rate between AI-generated and human-written code during originality checks
• The main body of the paper must be written by yourself—AI-generated text is overly ornate, fond of bullet-point lists, and prone to leaving behind prompt fragments, which judges can spot at a glance
• AI-generated content must be annotated in the main text, and an AI usage report PDF must be attached in the supporting materials
• References must be verified to actually exist—AI sometimes "fabricates" references that don't exist at all

For Problem A, the organizing committee has also added review guidelines to "ensure code is verifiable," and increased the data volume to prevent contestants from relying solely on AI to solve problems—ultra-large datasets are prone to errors when computed by AI, so contestants must rely on their own programming.

The Red Line of Academic Integrity

Never upload your paper to internet-connected AI such as DeepSeek or Kimi, or to originality-check platforms such as CNKI or Dayacn. These platforms retain backups on the backend, and once the organizing committee's originality check matches such a backup, it may be judged as 100% duplication, leading to disqualification from awards or even public censure.

Two different technical levels are involved here: traditional text plagiarism detection (such as CNKI) is based on text similarity algorithms (cosine similarity, longest common subsequence, etc.), calculating the duplication rate by comparing against literature already indexed in the database; while AI-Generated Content detection (AIGC Detection) is an emerging technology in recent years that identifies machine-generated text by analyzing the distribution of perplexity and burstiness features in the text—human writing typically exhibits high perplexity and high burstiness, whereas AI-generated text tends to be smooth and uniform. Having the main body written by humans is precisely a practical strategy for avoiding the risks of both types of detection.

Originality-check standards: over 20% disqualifies you from Provincial First/National First; over 40% earns no award; over 60% results in public censure. As long as you write it yourself, the duplication rate usually will not exceed 20%, and it is recommended to submit directly without checking.

Team Collaboration and the Four-Day Schedule

The team should clearly divide roles into modeler, programmer, and writer:

• The modeler is responsible for model selection, writing mathematical formulas, and writing the abstract (these three best reflect innovation and logic, and must be done by the person with the clearest thinking)
• The programmer is responsible for code implementation, data processing, and visualization, with the key being to ensure the code runs
• The writer is responsible for the problem restatement, problem analysis, and other sections, as well as creating figures and tables

Special reminder: when using AI, there must be no "disconnect" between the modeler and the programmer—the model built and the code written must be one and the same, otherwise there is a risk of being judged as fraudulent.

The Four-Day Rhythm and Key Milestones

The national contest runs from 6 PM on September 10, when problems are released, to 8 PM on September 13, when submissions are due:

• Day 1: Carefully read all three problems, discuss within the team to determine the topic preference, and search literature to draw the logical chain
• Before 2 PM on Day 2: The topic must be finalized; in the evening, strive to obtain final usable results
• Day 3: Refine the model and innovation, and be sure to write the abstract and produce a draft while your mind is clear
• Day 4: Wrap up and finalize, polish the abstract repeatedly 2-3 times, pay attention to the MD5 code, and never submit at the last minute

Regarding the MD5 code, this is the basic principle of digital file integrity verification: MD5 (Message Digest Algorithm 5) is a hash function that maps a file of arbitrary length into a fixed 128-bit digest value. The national contest organizing committee requires participating teams to record the MD5 value after submitting the paper PDF, in order to prevent tampering after submission—any modification to the file (even a single space) will completely change the MD5 value, thereby leaving a verifiable trace of tampering. Therefore, the essence of the reminder to "pay attention to the MD5 code" is: ensure the final submitted version is completely finalized, and do not modify it in any way after submission.

Teacher Yang particularly emphasizes sensitivity analysis, an easily overlooked scoring point: for Problem C, failing to perform sensitivity analysis on questions 2, 3, and 4 deducts 5 points each, totaling 15 points—exactly equal to the difference between the national contest line and the provincial first prize line. Even if the problem does not explicitly require it, be sure to complete it.

Sensitivity Analysis is a core method for testing the robustness of a mathematical model, essentially studying the degree to which the model's output responds to perturbations in input parameters. Common methods include: one-at-a-time (OAT) sensitivity analysis, i.e., changing a single parameter by ±10%~20% and observing the change in results; and global sensitivity analysis (such as the Sobol index method), which perturbs multiple parameters simultaneously to assess interaction effects. From the reviewer's perspective, sensitivity analysis not only verifies the model's resistance to noise but also reflects the modeler's clear awareness of the model's limitations—this is precisely the key to high scores in the "model evaluation" section, and it explains why the organizing committee lists it as a completeness requirement of equal importance to the modeling itself.

In addition, the naming of the submitted supporting materials folder must not reveal school or personal information—even a school abbreviation may be traced and lead to disqualification.

Final Thoughts

AI has not lowered the difficulty of the national modeling contest; instead, it has prompted the organizing committee to make scoring standards increasingly refined and problem difficulty continuously higher. What truly determines success or failure remains solid problem-comprehension ability, deep innovative thinking, and standardized paper expression. AI is an auxiliary tool for improving efficiency, but it cannot replace independent thinking.

As Teacher Yang put it: "Complete first, then perfect"—write what you can first, then pursue innovation and logical coherence. This is the steady path to winning awards.

Key Takeaways