H HiMCM Prep

Resources & glossary

Official COMAP material

Books that pay off

  • A First Course in Mathematical Modeling — Giordano, Fox, Horton. The HiMCM/MCM canonical textbook. Every chapter maps to a problem type you'll see.
  • Mathematical Modeling: Models, Analysis and Applications — Banerjee. Strong on ODEs and population models.
  • Operations Research: An Introduction — Taha. For the optimization side (LP, IP, networks, queueing).
  • The Elements of Statistical Learning — Hastie, Tibshirani, Friedman (free PDF online). Reference for regression, classification, sensitivity. Read selectively.
  • How to Write Mathematics — Halmos / Steenrod (the AMS book). Tiny, classic, makes your writing better in an afternoon.

Free courses & tutorials

Datasets & data tools

Writing & typesetting

Communities (during prep — not during the contest!)

  • Art of Problem Solving forums (search "HiMCM").
  • r/HighSchoolMath on Reddit — occasional HiMCM discussion.
  • School math/CS clubs — find a former team member at your school.
During the contest window, all outside-team discussion is banned. Don't post on Discord, Reddit, Stack Exchange, or anywhere else. COMAP monitors the web and has disqualified teams for this.

Glossary

AHP
Analytic Hierarchy Process. Method for deriving criterion weights from pairwise comparisons.
ARIMA
AutoRegressive Integrated Moving Average. A flexible time-series forecasting model.
Carrying capacity ($K$)
The maximum sustainable size of a population given its environment. Appears in logistic growth.
Compartmental model
A model where the system is divided into discrete states (compartments) with flows between them (e.g., SIR).
CWM
Combined Weight Model. Common HiMCM approach: average AHP weights (subjective) with EWM weights (data-driven).
EWM
Entropy Weight Method. Computes weights based on the variation each criterion shows across alternatives.
Finalist
HiMCM award level. Papers that reach final judging (~5%). Above Meritorious, below Outstanding.
Hectare
10,000 m². A 20-acre area is about 8.1 hectares.
HiMCM
High School Mathematical Contest in Modeling. The contest this whole site is for.
IM²C
International Mathematical Modeling Challenge. The international round held in spring; US teams qualify via Meritorious+ at HiMCM.
IP / MIP
Integer Programming / Mixed-Integer Programming. Optimization with discrete-valued variables.
LP
Linear Programming. Optimization with a linear objective and linear constraints.
Markov chain
A discrete-state stochastic process where the future depends only on the current state.
Meritorious
HiMCM award level. Excellent across modeling, analysis, and communication. Roughly the top 20% (Meritorious + Finalist + Outstanding).
Monte Carlo
Simulation method that draws random samples to estimate distributions of outputs.
NCTM
National Council of Teachers of Mathematics. Co-sponsors the NCTM Award given to selected HiMCM Outstanding teams.
NPV
Net Present Value. Sum of discounted future cash flows; central to financial models.
ODE / PDE
Ordinary / Partial Differential Equation. ODE = single independent variable (usually time); PDE = multiple (e.g., time and space).
Outstanding
The top HiMCM award (~1% of submissions).
SDE
In the 2024 problem, "Sport, Discipline, or Event" — not stochastic differential equation.
Sensitivity analysis
The process of measuring how a model's outputs depend on its inputs/parameters.
TOPSIS
Technique for Order of Preference by Similarity to Ideal Solution. Multi-criteria ranking method based on distance to ideal best/worst.
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