How to turn 'a hundred million users' into requests per second, storage, bandwidth and cache size in a few lines of arithmetic. The handful of numbers worth memorising, a worked URL-shortener example, and how each estimate should change the design.

Why inheritance hierarchies explode when behaviours combine, how composing small objects avoids it, and when inheritance is still the right tool. With the arithmetic, the fragile base class problem, and decorators in TypeScript.

Keyword search finds exact terms; vector search finds meaning; each misses what the other catches. How BM25 scores documents, why you can't just add the two scores, how reciprocal rank fusion merges rankings using positions alone, and where a reranker fits.

How a subject notifies a list of observers through a small interface, so new reactions can be added without editing the code that triggers them. Implementing it in TypeScript, its pitfalls — ordering, errors, leaks, re-entrancy — and how it relates to event emitters, pub/sub and the DOM.