Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hamzabellouch/agent-skills --skill mathematical-modeling-and-applied-mathgit clone --depth 1 https://github.com/hamzabellouch/agent-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hamzabellouch/agent-skills/mathematical-modeling-and-applied-math)<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/mathematical-modeling-and-applied-math"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/mathematical-modeling-and-applied-math/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hamzabellouch/agent-skills/mathematical-modeling-and-applied-math"><img src="https://agentmods.dev/badge/skills/hamzabellouch/agent-skills/mathematical-modeling-and-applied-math.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00059 | $0.00476 |
| Opus 5.5 | $0.00024 | $0.00190 |
| Sonnet 5.5 | $0.00012 | $0.00095 |
| Haiku 4.5 | $0.00006 | $0.00048 |
Grade A, and why
mathematical-modeling-and-applied-math scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured today.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
Mathematical Modeling & Applied Mathematics
Modeling cycle
- Define the question and the quantity of interest. 2. Identify variables, parameters, assumptions. 3. Choose the framework (ODE, PDE, stochastic, discrete, network, agent-based, optimization). 4. Non-dimensionalize. 5. Solve/simulate. 6. Validate with data; check sensitivity. 7. Interpret, state limits of validity, iterate.
Classic models
- Population: exponential, logistic r N (1 - N/K), Lotka-Volterra predator-prey, age-structured Leslie matrices, Allee effect.
- Epidemics: SIR dS/dt = -beta S I/N, dI/dt = beta S I/N - gamma I; R0 = beta/gamma; herd immunity threshold 1 - 1/R0; SEIR; network and stochastic versions.
- Finance: compound interest A = P e^{rt}; present value; Black-Scholes PDE, geometric Brownian motion; portfolio theory (mean-variance); Value-at-Risk.
- Economics: supply-demand equilibria, game theory, Solow growth, input-output matrices (Leontief).
- Engineering: RC/RLC circuits, spring-mass-damper, heat conduction, beams, control systems (PID, transfer functions, stability by poles), Kalman filter.
- Social/networks: PageRank (dominant eigenvector of Google matrix), diffusion on graphs, opinion dynamics, traffic flow (LWR conservation law).
- Chemistry/biology: mass-action kinetics, Michaelis-Menten, Turing patterns, Hodgkin-Huxley.
Analysis tools
Dimensional analysis, scaling, perturbation methods (regular/singular), multiple scales, sensitivity (partial derivatives, Sobol indices), parameter estimation (least squares, MLE, Bayesian), identifiability, uncertainty quantification, cross-validation.
Communication
State assumptions explicitly, show equations, graph results with units, give a plain-language conclusion and caveats.
What ships with it
1 file beside SKILL.md in the same directory: the scripts, references and assets a skill reads on demand. Not counted in the per-session cost; read them before you install if any of them is executable.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- today First seen · 25 lines · 59 tokens per session scan A 6c6c897bd4a6
mathematical-modeling-and-applied-math is a skill published in the GitHub repository hamzabellouch/agent-skills (8 stars, last pushed today), licensed MIT. It adds 59 tokens to every session and 476 once invoked, about $0.0002 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-10-17.
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