When preparing for mathematical modeling competitions such as CUMCM (China Undergraduate Mathematical Contest in Modeling), MCM/ICM (Mathematical Contest in Modeling), or HiMCM, most students encounter key bottlenecks:
| Dimension | Traditional Static GitHub Repos | Generic LLMs (ChatGPT / DeepSeek) | 🌟 Math Modeling Trainer (This Project) |
|---|---|---|---|
| Problem Diversity | Limited to historical contest problems | Always repeats the same drone/SEIR problem prompts | 🛡️ 5-Round Cross-Disciplinary Cooldown: strictly rotates across 8 diverse industrial/scientific scenarios |
| Interaction Mode | Passive reading of static solution PDFs | Dumps 3000-word full answers and code immediately | 🎯 Socratic Step-by-Step Mentoring: problem understanding -> qualitative framing -> top-level skeleton -> algorithm intuition |
| Algorithm Rigor | Blindly copying packages without boundary knowledge | Suggests fragile models with zero consideration of contest grading criteria | 🧠 Dual-Direction Algorithm Defense: explains why this method works AND why alternative candidates fail |
| Review & Archiving | Fragmented notes lost after sessions | Dialogues disappear without reusable outputs | 📋 5D High-Score Review Cards: formatted code block ready for 1-click export to Obsidian / LaTeX |
graph TD
Start([User Invocation: Start Contest Practice / Review]) --> CheckCooldown[1. Read Cooldown Board in 历史记录.md]
CheckCooldown --> FilterPool[2. Filter Out Scenarios & Models in 5-Round Cooldown]
FilterPool --> PickScenario[3. Select Fresh Cross-Disciplinary Scenario from Pool]
subgraph Socratic_Coaching [Contest-Grade Q1~Q4 Step-by-Step Guidance]
Present[Present Complete Problem Background, Parameters & Q1~Q4] --> Q1[Start Guidance for Q1]
Q1 --> S1[① Qualitative Framing: Optimization / Prediction / Evaluation]
S1 --> S2[② Top-Level Skeleton: Decision Variables, Physical Bounds, Objectives]
S2 --> S3[③ Algorithm Intuition: Guide user to formulate the computer search logic]
S3 --> S4[④ Academic Naming & Dual-Defense: Why this works vs failure modes of others]
S4 --> Card1[⑤ Generate 5D High-Score Review Summary Card]
Card1 --> Q2[Proceed to Next Sub-Question...]
end
PickScenario --> Present
Card1 -. Automatic Archival .-> UpdateLog[4. Automatically Append to 历史记录.md Log]
Clone this repository into your workspace, or copy .cursor/skills/math-modeling-daily-review/ directly:
# In your workspace root
mkdir -p .cursor/skills
git clone https://github.com/Dunphil692/math-modeling-trainer.git temp-repo
cp -r temp-repo/.cursor/skills/math-modeling-daily-review .cursor/skills/
cp temp-repo/templates/历史记录.md ./历史记录.md
rm -rf temp-repoSymlink into your global skills directory:
ln -s /path/to/math-modeling-trainer/skills/math-modeling-daily-review ~/.gemini/config/skills/Place SKILL.md and 历史记录.md in your workspace, then ask in your conversation:
"Start mathematical modeling contest practice mode, generate a full contest-grade problem for today"
This Skill covers the complete lifecycle of math modeling competitions from daily algorithm training
| Mode | Trigger Phrases | Core Value Delivered |
|---|---|---|
| Mode A: Deep Algorithm Review | "Review ARIMA", "Explain TOPSIS" | Problem intuition, formal formulation, hyper-parameter physics, pros/cons. |
| Mode B: Interactive Drill & Quiz | "Quiz me", "Test my understanding" | Concept discrimination questions on edge cases and algorithm pitfalls. |
| Mode C: 5-Round Cooldown Contest Drill | "Generate contest problem", "Mock CUMCM" | 8-scenario cooldown rotation, Q1~Q4 step-by-step guidance, 5D review cards. |
| Mode D: 72h In-Contest War-Room | "War room mode", "Problem selection & plan" | 3D feasibility scoring, 3-member 72h Gantt scheduling, 300-word abstract formula. |
| Mode E: Contest Judge Paper Review | "Review my paper draft", "Judge paper defense" | 100-point deduction audit: abstract numbers, invalid assumptions, dual defenses. |
The repository includes ready-to-run Python scripts featuring Nature / Science / IEEE palettes:
visualization/ (Plotting Toolkit)
├── plot_style.py # 1-click Nature/Science styling & font management
├── pareto_front_3d.py # 3D Multi-Objective Pareto front surface & projections
├── convergence_comparison.py # Multi-algorithm convergence plot with ±1σ shadow bands
├── sensitivity_heatmap.py # 2D Parameter cross-perturbation sensitivity heatmap
└── network_spatial_trajectory.py # Vehicle / drone spatial routing & network topology
solvers/ (Optimization Scaffolds)
├── pulp_mixed_integer.py # Mixed Integer Linear Programming (MILP) scaffold
├── scipy_sqp_optimization.py # Constrained Non-linear Programming (SLSQP) scaffold
└── monte_carlo_sensitivity.py # Monte Carlo parameter uncertainty robustness framework
After finishing each sub-question, the AI coach automatically produces a self-contained 5D review summary card in a clean monospace block:
================================================================================
【Sub-Question Q1: Semiconductor Multi-Stage Sampling & Decision】5D Review Card
================================================================================
[Problem & Parameters]
- Nominal defect rate p0 = 10%, confidence level 1-alpha = 95%, consumer tolerance beta = 10%
- Determine optimal sample size n and threshold k balancing producer & consumer risks.
--------------------------------------------------------------------------------
① 📌 Model Architecture
- Model Type: Statistical Quality Control (SQC) / Hypothesis Testing & Sampling Design
- Decision Variables: Sample size n in Z+, Rejection threshold k in Z+
- Constraint Bounds: P(X > k | p <= p0) <= alpha, P(X <= k | p >= p1) <= beta
- Objective: min n (Minimize testing cost while satisfying dual risk boundaries)
② 🧠 Algorithm & Rationale
- Search Intuition: Binomial OC (Operating Characteristic) Curve Grid Search
- Solver Engine: Discrete bisection scan using scipy.stats.binom.cdf.
③ 🛡️ Dual Defense & Pitfall Warning
- Why this algorithm: Fully compliant with international inspection standards (ISO 2859-1).
- Why NOT Gaussian approximation: When n*p < 5, normal approximation introduces severe truncation errors, leading to high false-positive rates (major grading deduction point).
④ 📊 Qualitative Insights
- Sample size n scales super-linearly with confidence requirements; inspection strictness trades off with unit testing cost.
⑤ 🔗 Next Step Bridge
- Expected residual defect rate from Q1 directly serves as the prior input probability for Q2 assembly stages!
================================================================================
Includes ready-to-use cheat sheets and mathematical formulation templates:
- 📊 Evaluation Models: AHP, TOPSIS, Entropy Weight Method, Fuzzy Comprehensive Evaluation, Grey Relational Analysis, DEA, CRITIC.
- 📈 Forecasting Models: Multivariate Linear/Logistic Regression, Time Series (ARIMA/SARIMA), Grey Model GM(1,1), SVR, LSTM, Epidemiological SIR dynamics.
- ⚙️ Optimization Models: Linear/Integer Programming (MIP), Non-linear Programming (NLP), Multi-Objective Pareto Optimization, Dynamic Programming, Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Shortest Path (Dijkstra/Floyd).
- 🤖 Statistics & Machine Learning: K-Means/DBSCAN, PCA, Random Forest/GBDT/XGBoost/LightGBM, SVM, Cellular Automata, Monte Carlo Simulation.
- ⏱️
references/contest-72h-playbook.md: 72-Hour contest war-room playbook and 3-role Gantt schedule. - 🔍
references/contest-paper-reviewer-guide.md: 5D Judge defense and paper deduction checklist. - 📖
references/algorithm-selection-guide.md: Complete algorithm selection tree and dual defense lexicon. - 🎨
visualization/: Academic publication-grade visualization suite. - ⚙️
solvers/: Optimization and statistical simulation solver templates. - 📝
templates/历史记录.md: 5-Round cooldown board and training archive template. - 💡
examples/: Full walkthroughs of semiconductor QC, fresh supply dynamic pricing, and mock judge paper review.
Contributions are warmly welcome!
- Add new cross-disciplinary scenarios to
templates/历史记录.md. - Enrich algorithm defenses & counter-examples in
references/algorithm-selection-guide.md. - Contribute new publication-grade plots to
visualization/. - Submit full problem walk-through examples to
examples/.
Please review our Contributing Guide (CONTRIBUTING.md).
This project is licensed under the MIT License.
If you use this project in your academic training or research, please consider citing it using CITATION.cff.