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@harrisonqian / Young Builder Resources / wiki/math-modeling.md
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--- visibility: public-edit --- # math modeling math modeling competitions are the most underrated competitions for builders. unlike contest math (AMC/AIME/USAMO), math modeling gives you a real-world problem and asks you to build a mathematical model to solve it. no memorization, no tricks — just applied thinking. the skills transfer directly to [[publishing-research|research]], [[shipping-products|product building]], and [[work-experience|engineering work]]. if you like building things and you like math, this is your competition. ## why math modeling is special contest math asks: "solve this problem that has a known elegant solution." math modeling asks: "here's a messy real-world situation. build a model. make predictions. justify your approach." the second one is closer to what engineers and researchers actually do. the skills you develop — framing problems, choosing assumptions, validating models, writing technical reports — are the same skills you use in [[publishing-research|research papers]], [[shipping-products|product analytics]], and [[work-experience|engineering internships]]. also: math modeling competitions are team-based (usually 3-4 people), which means you're developing collaboration skills. and the results are strong on a resume — a top-10% finish in MCM/ICM as a high schooler is a real accomplishment. ## the competitions ### HiMCM (High School Mathematical Contest in Modeling) - **format:** 36 hours, teams of up to 4, November - **organizer:** COMAP - **what we did:** fire/evacuation scenario with Monte Carlo simulation and spectral bisection - **team:** three teammates and me - **my take:** this is the entry point. massively underrated. 36 hours is enough time to build a real model without the sleep-deprivation of a hackathon. the problems are genuinely interesting — real-world scenarios with no single right answer. ### MCM/ICM (Mathematical Contest in Modeling / Interdisciplinary Contest in Modeling) - **format:** 4 days (Jan/Feb), teams of up to 3 - **organizer:** COMAP - **result:** Meritorious (top 10%) - **what we did:** spectral bisection, cellular automata, graph traversal - **my take:** this is the college version, but high schoolers can compete. placing Meritorious (top 10%) as high schoolers competing against college teams was a genuine accomplishment. 4 days is enough time to go deep — our paper was substantial. - **2026 dates:** January 29 - February 2 ### M3 Challenge (MathWorks Math Modeling Challenge) - **format:** 14 hours, one weekend (Feb/Mar) - **organizer:** SIAM (Society for Industrial and Applied Mathematics) - **result:** 143/770 (top 19.8%), qualified for second round - **my take:** free to enter, $100,000+ in total prizes. the 14-hour constraint is brutal but teaches you to scope aggressively — the same skill you need for [[competitions-hackathons|hackathons]]. high school juniors and seniors eligible. ### MTFC (Modeling the Future Challenge) - **result:** semifinalist (2025-26) - **what we did:** equitable bus routing - **my take:** the problems have a social-impact angle, which makes the modeling more interesting. "optimize bus routing for equity" is the kind of problem that doesn't have a clean mathematical answer — you have to make value judgments and defend them. ### IMMC (International Mathematical Modeling Challenge) - **format:** 6-day sprint (March) - international pool of competitors - similar flavor to HiMCM/MCM but with more time and an international dimension ## techniques worth learning these come up repeatedly across modeling competitions: - **Monte Carlo simulation** — randomly sample scenarios to estimate probabilities and outcomes. we used this for the fire evacuation model. versatile, intuitive, and works when analytical solutions are intractable. - **spectral methods** — eigenvalue-based approaches for graph problems. spectral bisection was key in both our HiMCM and MCM papers. - **cellular automata** — grid-based simulations where each cell follows local rules. emergent behavior from simple rules. great for modeling physical processes (fire spread, traffic, epidemics). - **graph traversal and network analysis** — most real-world problems can be modeled as graphs. shortest paths, flow optimization, community detection. - **optimization** — linear programming, integer programming, gradient descent. the core of most modeling problems is "maximize/minimize something subject to constraints." - **sensitivity analysis** — how does your answer change when you change your assumptions? judges care about this a lot. it shows you understand the limitations of your model. - **FEM simulation** — finite element methods for physics-based modeling. more advanced, but powerful for structural/thermal/fluid problems. ## related modeling work outside competitions the modeling mindset extends beyond competitions. problems I've worked on: - elevator scheduling optimization - drone routing for delivery - disease testing strategies - Olympics scoring system analysis - irrigation optimization - sheep population dynamics - trading algorithm design - firefighter sweeping route optimization each of these is a self-contained modeling exercise that could become a [[publishing-research|research paper]], a section of a [[competitions-hackathons|competition submission]], or a portfolio piece for [[work-experience|job applications]]. ## practical advice 1. **practice with past problems.** COMAP archives past MCM/ICM and HiMCM problems. SIAM archives past M3 Challenge problems. work through them under time constraints. 2. **learn LaTeX.** your submission is a technical paper. LaTeX (via Overleaf) is the standard for mathematical typesetting. judges notice well-formatted papers. 3. **master one simulation tool.** Python with NumPy/SciPy/matplotlib is the default. MATLAB works too (and MathWorks sponsors M3 Challenge). the tool doesn't matter — fluency does. 4. **write clearly.** the paper matters as much as the model. judges read dozens of papers in a day. clear writing with good figures stands out. explain your assumptions, justify your choices, acknowledge limitations. 5. **build your team deliberately.** you want: someone strong at mathematical formulation, someone strong at coding/simulation, and someone strong at writing/visualization. overlap is fine but coverage matters. 6. **start with HiMCM.** it's the most accessible, the time pressure is manageable, and it teaches you the modeling-paper workflow. then move to MCM/ICM. math modeling is where [[learning-paths|mathematical thinking]] meets [[shipping-products|building things]]. the competitions are the structured version, but the modeling mindset applies everywhere — any time you're trying to understand a system, make predictions, or optimize something, you're modeling. see [[competitions-hackathons]] for the full competition landscape and [[publishing-research]] for turning modeling work into papers.
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