About MTB Quant Library
MTB Quant Library is a free, self-study reference for quantitative mathematics — covering Linear Algebra, Calculus, Probability & Statistics, Stochastic Calculus, Numerical Methods, and Time Series.
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.
Terms & Legal
Educational purpose only
MTB Quant Library provides free educational reference material on quantitative mathematics. The content is for learning and self-study. It is not a substitute for formal coursework, professional training, supervised research, or licensed advice in any jurisdiction.
Not verified or certified
Chapters are written as a structured study aid. They are not peer-reviewed academic publications, not certified by any university or regulator, and not guaranteed to be complete, current, or free of error. Formulas, proofs, numerical examples, and explanations may contain mistakes or omissions. Always cross-check critical results against primary textbooks, papers, or a qualified instructor before relying on them for graded work, research, production systems, or exams.
No investment or professional advice
Nothing on this site is financial, investment, trading, tax, legal, accounting, or other professional advice. Mentions of markets, instruments, risk, pricing models, or portfolios are pedagogical examples only. They do not recommend buying, selling, or holding any security or product, and they do not constitute an offer or solicitation. You are solely responsible for any decisions you make.
No warranty; limitation of liability
The site and all content are provided "as is" and "as available," without warranties of any kind, express or implied, including merchantability, fitness for a particular purpose, and non-infringement. To the fullest extent permitted by law, NinetySevenGroup Co., Ltd., MT Blue, and their affiliates, officers, and contributors are not liable for any direct, indirect, incidental, special, consequential, or exemplary damages arising from use of — or inability to use — this site or its content, including reliance on any formula, model, or explanation published here.
Commercial product; free access
MTB Quant Library is a commercial product of NinetySevenGroup Co., Ltd. Access to the published lessons is currently free and does not require an account. Free access does not waive intellectual-property rights, create a warranty, or imply endorsement by any third party. Features, availability, packaging, or pricing may change.
Intellectual property
Unless otherwise noted, chapter text, explanations, diagrams, branding, and site design are owned by NinetySevenGroup Co., Ltd. You may use the material for personal study. You may not copy, scrape, redistribute, republish, sell, or train commercial models on the content without prior written permission, except where applicable law expressly allows limited quotation with attribution.
Third-party links and brands
Links to ninetysevengroup.net, mtblue-nsg.com, or other external sites are for convenience. Those sites have their own terms. MT Blue is a brand operated under NinetySevenGroup Co., Ltd.; naming a brand is not a representation about any particular legal entity structure beyond what is stated here.
Your responsibility
By using MTB Quant Library you agree to use it only for lawful educational purposes, to verify material that matters for your work or studies, and not to treat the site as advice, certification, or a guarantee of correctness.