Number theory, linear algebra, sequences, and mental math — the mathematical toolkit for quant interviews.
Modular arithmetic, divisibility, and number properties
Fast computation tricks and numerical estimation
Geometric series, harmonic numbers, Fibonacci, and convergence
Matrices, determinants, eigenvalues, and matrix exponentiation
Chain rule, partial derivatives, gradients, Taylor series, and key integrals for quant finance
Lagrange multipliers, KKT conditions, convexity, and gradient descent for portfolio optimization
First-order ODEs, second-order linear ODEs, PDE classification, and connections to stochastic calculus
Cholesky decomposition, SVD, condition numbers, and positive definiteness for covariance matrices