Chapter · Math
Number Systems
Follow the extension chain ℕ → ℤ → ℚ → ℝ → ℂ, where each step is forced by an equation the previous system couldn't solve. Then step sideways into modular arithmetic, which wraps the integers into a finite cyclic structure — your first taste of a ring.
Topics
Topic 1
Classification of Numbers
The chain ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ. What each extension gains, what it costs, and where transcendentals live.
Topic 2
Positional Numeration & Bases
How positional notation encodes numbers as sums of powers of a base. Binary, octal, hex; conversions both ways; arithmetic and fractions in any base.
Topic 3
Complex Numbers
From i² = −1 to Euler's formula. Rectangular and polar form, the Argand diagram, De Moivre, and the roots of unity.
Topic 4
Modular Arithmetic
Clock arithmetic, congruence, residue classes, Fermat's little theorem, the Chinese Remainder Theorem, and the math behind RSA.