About MTB Quant Library

What this is

A structured set of written lessons covering the mathematics used in quantitative finance and applied math — from foundational topics (vectors, limits, basic probability) through advanced material (SVD, stochastic differential equations, GARCH models). Each subject is organized into chapters ordered by learning progression and labeled by difficulty (Easy, Medium, Hard, Rigorous).

Content is written for self-directed learners at any level — undergraduate, graduate, PhD, or anyone reviewing or branching into a new topic. No prior enrollment or course sequence is assumed within each subject; each is self-contained.

This site exists to help learners study these subjects for free. Access requires no account, login, or payment.

What this is not

• Not a bootcamp, certification program, paid course, or trading course
• Not financial, investment, or trading advice
• Not a general K-12 or introductory homework-help site
• Not a blog, news site, or community/discussion platform
• Not affiliated with any university course or accredited program

Subjects covered

• Linear Algebra — vectors, matrix operations, eigenvalues, decompositions (LU, QR, SVD), and related topics
• Calculus — limits, derivatives, integrals, series, multivariable calculus, differential equations
• Probability & Statistics — distributions, inference, hypothesis testing, regression
• Stochastic Calculus — Brownian motion, Itô's lemma, stochastic differential equations, risk-neutral pricing
• Numerical Methods — root-finding, numerical integration, Monte Carlo methods, optimization
• Time Series — stationarity, ARMA/GARCH models, cointegration

Each subject is written to be studied independently, using only material introduced within that subject.