Fundamental Key concepts

Fundamental maths is the grammar layer: it tells you what the symbols mean before any advanced technique begins.

Core concepts

• A Set is a collection of objects. Most definitions start by saying which set an object belongs to.
• A Function maps each input in its Domain to exactly one output.
• The codomain is the declared target set; the range/image is what the function actually hits.
• A Relation is more general than a function: one input can relate to zero, one, or many outputs.
• A Mapping is a function-like assignment between sets; in most elementary contexts it is just another word for function.
• Inverse functions reverse a function only when the relevant domain/codomain choices make the function bijective.
• Euler’s number is the natural base for continuous growth and decay.

Learning habit

When you meet a formula, ask four questions: What are the allowed inputs? What kind of outputs are produced? Are there hidden restrictions such as division by zero or square roots of negatives? Does the formula represent a mathematical object or a physical quantity with units?

This habit pays off in Calculus MOC, Stats index, and physics notes like Velocity and Work.