Short building-block explainers to read before (or alongside) the topic articles.
How an algorithm’s cost grows with input size — the common complexity classes on one set of axes, from O(1) to O(2ⁿ).
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).
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.
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.
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.
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 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.