Algoramic

Entry point

  • Overview
    • Big-O Notation
    • Divide and Conquer
    • The n log n Speed Limit
    • Stable vs Unstable Sorting
    • From Coin Flips to the Bell Curve
    • What Is a Vector?
    • A Matrix Is a Transformation

Subjects

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Foundations

Short building-block explainers to read before (or alongside) the topic articles.

Articles

Big-O Notation

How an algorithm’s cost grows with input size — the common complexity classes on one set of axes, from O(1) to O(2ⁿ).

Divide and Conquer

Break a problem into smaller copies of itself, solve those, and combine — the recurrence behind merge sort, quicksort and binary search, and why it costs O(n log n).

The n log n Speed Limit

Why no comparison sort can beat O(n log n): a sort is a tree of yes/no questions, and telling n! orderings apart needs at least log₂(n!) of them.

Stable vs Unstable Sorting

A sort is “stable” when items with equal keys keep their original order. See the difference on a tie, and why it matters for sorting by more than one key.

From Coin Flips to the Bell Curve

Count the heads in n coin flips and the binomial distribution emerges — then fills into the normal bell curve. A hands-on look at the Central Limit Theorem.

What Is a Vector?

A vector is an arrow with direction and magnitude. See its components, its length, and how two vectors add tip-to-tail — the foundation of vector math.

A Matrix Is a Transformation

A 2×2 matrix transforms all of space at once. Watch the grid and basis vectors morph, see its columns as their landing spots, and the determinant as area scaling.

Related categories

Algorithmic ComplexitySorting AlgorithmsProbability & DistributionsVector MathMatrix Math