Quant Finance Math

The linear algebra a working quant actually uses — vectors and matrices as the language of portfolios, covariance, factor models, and regression. Twelve modules from vector geometry to SVD and PCA, with every theorem grounded in a finance use case: portfolio risk, factor extraction, yield-curve decomposition, Cholesky simulation, and the numerical traps that bite production code.

The probability and statistics a quant or risk analyst must own — distributions, MLE, hypothesis testing, Bayesian updating, multivariate normality, copulas, and extreme-value theory. Twelve modules taught from the standpoint of a working desk: why log returns are nearly normal until they aren't, why correlation collapses in a crisis, and the small set of distributions that cover 95% of real return modelling.

The time-series machinery a quant uses every day — ARMA, GARCH, cointegration, VAR, and state-space models — taught with the financial intuition that makes the algebra stick. Eleven modules from stationarity to Kalman filtering, building toward a volatility model on NSE returns and a pairs-trading cointegration test you can defend.

The optimisation toolbox behind every portfolio, hedging, and risk-budget problem in modern finance — convex programming, KKT, duality, quadratic programming, conic and stochastic optimisation. Ten modules taught practically: every theorem is followed by the finance problem it solves and the solver call (cvxpy, scipy, MOSEK) that produces the answer.

From Markowitz to risk parity and Black-Litterman — the modern portfolio-theory canon as it is actually used at Morgan Stanley, Bridgewater, and AQR. Twelve modules covering mean-variance, CAPM, APT, factor models (Fama-French, momentum, quality), Bayesian portfolio construction, alternative risk measures (VaR/CVaR/drawdown), and the real-world frictions that separate the optimisation output from the position you put on.

The continuous-time mathematics behind Black-Scholes, interest-rate models, and modern derivatives pricing. Ten modules from Brownian motion to Girsanov, taught the way Steven Shreve teaches it — but with the African and emerging-market context where these models behave differently in practice.

Where the maths meets the computer. The numerical-analysis toolbox a working quant uses to actually compute a price or a risk number — floating point, root-finding, interpolation, quadrature, finite differences for PDEs, Monte Carlo with variance reduction, and the LSM algorithm for American options. Ten modules pairing the algorithm with the production caveats.