Maths MOC
Maths is the language layer for the rest of the vault: it gives precise objects, transformations, measurement, approximation, and proof. Use this map when a physics or computing idea needs a cleaner mathematical base.
Core foundations
- MATHS index — top-level orientation for the maths folder.
- Fundamental index — notation, functions, constants, and algebraic habits.
- Set theory index — sets, relations, mappings, intervals, and Number sets.
- Function — inputs, outputs, Domain, Codomain and range, and composition.
- Inverse functions — reversing a function when the relevant mapping is bijective.
Main subject maps
- Calculus MOC — limits, derivatives, integrals, change, and accumulation.
- Linear Algebra MOC — vector spaces, operators, eigenvectors, and quantum-mechanics structure.
- Geometry MOC — points, lines, Area, shapes, and spaces.
- Vector Calculus index — gradients, divergence, curl, and Del operator ∇.
- Stats index — variation, uncertainty, Normal distribution, and inference.
- ML index — optimisation and statistical learning.
- Exponents, Logarithms, and Roots — powers, roots, logarithms, and Euler’s number.
Natural bridges to physics
- Derivative underpins Velocity, acceleration, rates of change, and field gradients.
- Integral underpins work/energy accumulation, continuous charge distributions, action integrals, and totals from densities.
- Vector space, Hilbert space, and linear operators underpin Susskind-style quantum mechanics.
- Number sets, SI units, and dimensions keep formulas physically meaningful.
- Euclidean spaces and Vector Calculus index are the default setting for mechanics and electromagnetism.