Method
Method
How this portal is organised, what the levels and stars mean, and the rules its content follows.
Every topic answers the same questions
A formula alone is not understanding. Each topic page is built around eight questions, in this order, so that pages can be compared and nothing essential is skipped:
- What is it?
- Why does it exist?
- What problem does it solve?
- How is it interpreted geometrically?
- How is it computed?
- Where does it show up in computing?
- Where does it show up in AI?
- What depends on it?
The thesis
- Calculus
- describes change and accumulation
- lets us model systems
- lets us optimize
- lets us approximate
- lets us simulate
- and is a core piece of AI, graphics, physics, robotics and scientific computing
Levels
Each topic has one of four levels — how far into a typical university curriculum it sits:
Connections and how strong they are
The map has 640 edges. "Builds on" edges join mathematical topics; "applied in" edges go from mathematics to computing, and each one is rated and explained in a note. No connection is added just to fill the map.
- fundamental
- The computing topic cannot be stated or computed without it.
- frequent
- Used routinely in practice.
- advanced
- Appears in deeper treatments, proofs or state-of-the-art methods.
- indirect
- Real but tangential; worth knowing, not essential.
- historical
- Mattered for how the field developed, less for how it works today.
Stars (1–5) say how much the computing topic really depends on the mathematical one. Example:
Strongest connection between each area and each domain
Computed from the data: each cell is the strongest single "applied in" edge from a topic of the row to a topic of the column.
| λ | ℒ | 3D | ⚙ | ⚛ | ∿ | ⇄ | ⊕ | ψ | |
|---|---|---|---|---|---|---|---|---|---|
| Foundations | 5 | 5 | 5 | 4 | 5 | 5 | 2 | 5 | |
| Linear algebra (bridge) | 5 | 5 | 4 | 5 | 4 | ||||
| Sequences and limits | 5 | 4 | |||||||
| Continuity | 5 | 4 | 1 | 3 | 4 | 2 | |||
| Derivatives | 5 | 5 | 4 | 5 | 5 | 4 | 2 | ||
| Fundamental theorems | 4 | 3 | 4 | ||||||
| Extrema and optimization | 5 | 5 | 5 | ||||||
| Numerical methods | 5 | 5 | 4 | 4 | 5 | 5 | |||
| Taylor series | 5 | 5 | 4 | 3 | |||||
| Integrals | 5 | 4 | 5 | 4 | 5 | 4 | |||
| Series | 5 | 5 | 3 | ||||||
| Multivariable calculus | 5 | 5 | 5 | 5 | 5 | 5 | |||
| Vector calculus | 3 | 5 | 5 | 4 | 5 | ||||
| Differential equations | 5 | 5 | 5 | 5 | 3 | ||||
| Dynamical systems and chaos | 3 | 4 | 4 | 5 | 5 | 1 | |||
| Transforms | 5 | 5 | 5 | 5 | 5 | ||||
| Probability and calculus | 5 | 5 | 5 | 5 |
λ = Scientific computing and algorithmsℒ = AI and machine learning3D = Computer graphics⚙ = Robotics and control⚛ = Physics and simulation∿ = Signals, media and vision⇄ = Optimization and systems⊕ = Cryptography and securityψ = Quantum computing and physics
How it is built
- All content lives in data files (one YAML file per area), not in components; every user-facing text exists in English and Spanish, and the build fails if a translation, a reference or a formula is broken.
- Formulas are written in TeX and rendered to MathML at build time. There is no backend, no tracking and a strict Content Security Policy.
- The prerequisite graph is checked to be acyclic, which is what lets every topic page compute "the full path to this topic" and "where is it used" automatically.