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.