Mathematics

Checkpoints

• Linear Elementry A short introduction to what it means for a mathematical operation to be linear, covering the two defining rules and the idea of a linear combination.
• Metric Space Elementry A gentle introduction to metric spaces — the mathematical framework for talking about distance in any setting — and the four simple rules that make a distance function well-behaved.
• Peano Axioms Elementry A beginner-friendly introduction to the five Peano axioms — the simple rules that define the natural numbers from the ground up.
• Rational Numbers Elementry A beginner-friendly introduction to rational numbers — the fractions that fill the gaps between whole numbers — covering what they are, why division demands them, and how to combine them.
• Semigroup & Monoid Elementry A beginner-friendly introduction to semigroups and monoids — two of the simplest algebraic structures — and how they appear in everyday programming through string concatenation, natural number addition, and more.
• Finite-dimensional Vector Space Elementry An introduction to vector spaces — the algebraic structures built around addition and scaling — with a focus on finite-dimensional spaces, bases, and dimension.