Quantitative finance is the mathematics of markets — probability, statistics, options pricing, risk and trading. It is what "quant" is short for, and it has nothing to do with quantum physics.
Every quant course you can buy hands you the same pile: a stochastic-calculus formula, a table of Greeks, a Sharpe ratio, and no idea why any of them exist. This one is built the other way round. It starts from one sentence — put a number on an uncertain future, using only finite noisy data, then size your bet against the risk of being wrong — and that sentence has exactly four verbs, which turn out to be the whole subject: you model the uncertainty, estimate it from data you don't fully trust, price a claim on it, and then act under it. Underneath sits the mathematics every other course assumes you already have and never teaches — so we teach it, from sets and counting up, with no gaps. This is not interview prep and it is not a formula sheet. It is for the pleasure of understanding the thing properly: you'll leave able to re-derive any result and reason about a case you have never seen. Every idea opens with a hook and lands on something you can drag, break, or predict.
The maths every quant course assumes and never teaches — sets, series, calculus, logs, linear algebra.
Start hereProbability from the axioms up: random variables, the distribution family tree, Markov chains, paradoxes.
OpenEvery statistic is itself random. Sampling, p-values done honestly, regression, and the one sin: in-sample.
OpenThe bias–variance dial, regularization, trees and boosting, and scoring a classifier honestly.
OpenNo-arbitrage, Brownian motion and Itô, the one pricing engine, the Greeks, and the volatility smile.
OpenSizing the bet: Sharpe and Kelly, VaR and the tail, factors, pairs, carry — and the spread that eats it.
OpenBig-O, the core data structures, dynamic programming and the order book, then a real vectorized stack.
OpenReason from nothing, build all ten projects — theory you can run is theory you own — and see the field.
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