M.T Blue

MTB Quant Library

M.T Blue is a software and data development team at mtblue-nsg.com. MTB Quant Library is one of its projects: a free self-study reference shown here.

A structured reference for rigorous study

MTB Quant Library is a free, self-study collection of written lessons in mathematics, organized into chapters, ordered by progression, and labeled by difficulty. Each subject stands alone: no account, no enrollment, and no assumed course sequence beyond what that subject introduces.

The library spans five tracks. Further Mathematics covers core calculus. Pure Mathematics covers structures such as linear and abstract algebra. Applied Mathematics covers models and computation. Probability & Statistics covers probability, stochastic calculus through SDEs, and time series. Quantitative Finance covers derivatives pricing and portfolio choice. Choose a track below to browse its subjects.

Further Mathematics

Core analysis beyond a first pass: calculus from limits through multivariable methods.

IncludesCalculus.

Enter Further Mathematics →

Pure Mathematics

Structures that stand on their own: linear algebra, abstract algebra, and related theory.

IncludesLinear Algebra, Abstract Algebra, Topology, and Discrete Mathematics.

Enter Pure Mathematics →

Applied Mathematics

Models and computations: differential equations, approximation, matrix factorizations, Markov chains, and numerical schemes.

IncludesDifferential Equations, Approximation, Numerical Linear Algebra, Markov Chains, and Numerical Methods.

Enter Applied Mathematics →

Probability & Statistics

Probability, stochastic calculus through SDEs, and time-series methods: the shared toolkit behind models and markets.

IncludesProbability & Statistics, Stochastic Calculus, and Time Series.

Enter Probability & Statistics →

Quantitative Finance

Portfolio choice and derivatives pricing written for markets, risk, and quantitative decision-making.

IncludesDerivatives Pricing and Portfolio Theory & Asset Pricing.

Enter Quantitative Finance →

Roadmap

Chapters that can be started in either order share a card. An arrow is a true prerequisite: the lower card needs the upper one. Drag to pan, scroll to zoom, or use reset to fit the whole tree. On touch devices, tap a card to see prerequisites, then tap the title again to open.

EasyMediumHardRigorous
Further MathematicsCalculus
Limits and Continuity
Further MathematicsCalculus
Derivatives: Definition and Rules
Further MathematicsCalculus
Chain Rule, Implicit Differentiation
Further MathematicsCalculus
Applications of Derivatives: Core
Further MathematicsCalculus
Applications of Derivatives: Optimization
Further MathematicsCalculus
Integrals: Definition and FTC
Further MathematicsCalculus
Techniques of Integration
Further MathematicsCalculus
Improper Integrals
Further MathematicsCalculus
Sequences and Series
Further MathematicsCalculus
Convergence Tests
Further MathematicsCalculus
Power Series and Taylor Series
Further MathematicsCalculus
Taylor Series Advanced
Applied MathematicsApproximation
Taylor Expansions and Approximation in Applied Contexts
Further MathematicsCalculus
Parametric Equations and Polar Coordinates
Further MathematicsCalculus
Vectors in 2D/3D
Further MathematicsCalculus
Partial Derivatives
Further MathematicsCalculus
Multiple Integrals
Further MathematicsCalculus
Vector Calculus: Gradient, Divergence, Curl
Applied MathematicsDifferential Equations
Differential Equations: First Order
Applied MathematicsDifferential Equations
Differential Equations: Second Order and Systems
Pure MathematicsLinear Algebra
Vectors & Vector Spaces
Pure MathematicsLinear Algebra
Matrix Operations
Pure MathematicsLinear Algebra
Systems of Linear Equations
Pure MathematicsLinear Algebra
Gaussian Elimination & Row Reduction
Pure MathematicsLinear Algebra
Determinants
Pure MathematicsLinear Algebra
Linear Transformations
Pure MathematicsLinear Algebra
Eigenvalues & Eigenvectors
Pure MathematicsLinear Algebra
Diagonalization
Pure MathematicsLinear Algebra
Change of Basis
Pure MathematicsLinear Algebra
Norms & Distance Metrics
Inner Products & Orthogonality
Pure MathematicsLinear Algebra
Gram-Schmidt Process
Pure MathematicsLinear Algebra
Projections & Least Squares
Pure MathematicsLinear Algebra
Positive Definite Matrices
Pure MathematicsLinear Algebra
Covariance Matrices & Quadratic Forms
Applied MathematicsNumerical Linear Algebra
Matrix Decompositions: LU
Applied MathematicsNumerical Linear Algebra
Matrix Decompositions: QR
Applied MathematicsNumerical Linear Algebra
Matrix Decompositions: SVD
Applied MathematicsMarkov Chains
Markov Chains & Steady States
Applied MathematicsNumerical Linear Algebra
Numerical Stability & Conditioning
Pure MathematicsAbstract Algebra
Algebraic Structures & Axioms
Pure MathematicsAbstract Algebra
Groups: Definition and Examples
Pure MathematicsAbstract Algebra
Subgroups & Cyclic Groups
Pure MathematicsAbstract Algebra
Cosets & Lagrange's Theorem
Pure MathematicsAbstract Algebra
Normal Subgroups & Quotient Groups
Pure MathematicsAbstract Algebra
Group Homomorphisms & Isomorphism Theorems
Pure MathematicsAbstract Algebra
Direct Products & Direct Sums
Group Actions
Pure MathematicsAbstract Algebra
Sylow Theorems
Free Groups & Presentations
Pure MathematicsAbstract Algebra
Rings: Definition and Examples
Pure MathematicsAbstract Algebra
Ideals & Quotient Rings
Pure MathematicsAbstract Algebra
Ring Homomorphisms
Pure MathematicsAbstract Algebra
Polynomial Rings
Pure MathematicsAbstract Algebra
Euclidean Domains & Principal Ideal Domains
Pure MathematicsAbstract Algebra
Chinese Remainder Theorem
Pure MathematicsAbstract Algebra
Fields: Definition and Basic Properties
Pure MathematicsAbstract Algebra
Field Extensions
Pure MathematicsAbstract Algebra
Splitting Fields & Algebraic Closures
Pure MathematicsAbstract Algebra
Galois Theory: Fundamentals
Pure MathematicsAbstract Algebra
Galois Theory: Solvability by Radicals
Pure MathematicsAbstract Algebra
Modules over Rings & Structure Theorems
Probability & StatisticsProbability & Statistics
Sample Spaces & Events
Probability & StatisticsProbability & Statistics
Probability Axioms
Probability & StatisticsProbability & Statistics
Conditional Probability & Bayes
Probability & StatisticsProbability & Statistics
Independence of Events
Probability & StatisticsProbability & Statistics
Discrete Random Variables
Probability & StatisticsTime Series
Discrete Time and White Noise
Probability & StatisticsTime Series
Stationarity, ACF, and PACF
Probability & StatisticsTime Series
Linear Processes and ARMA Models
Probability & StatisticsTime Series
Unit Roots, Differencing, and ARIMA
Probability & StatisticsTime Series
Forecasting, Information Criteria, and Diagnostics
Probability & StatisticsTime Series
Volatility Clustering and GARCH
Probability & StatisticsTime Series
Vector Autoregressions and Granger Causality
Probability & StatisticsTime Series
Cointegration and Error Correction
Probability & StatisticsTime Series
Spectral Analysis and Linear Filters
Probability & StatisticsTime Series
State-Space Models and the Kalman Filter
Probability & StatisticsStochastic Calculus
Random Walks and the Continuous-Time Limit
Probability & StatisticsStochastic Calculus
Brownian Motion: Definition and Path Properties
Probability & StatisticsStochastic Calculus
Quadratic Variation and Why Calculus Breaks
Probability & StatisticsStochastic Calculus
Filtrations, Adapted Processes, and Martingales
Probability & StatisticsStochastic Calculus
The Itô Integral
Probability & StatisticsStochastic Calculus
Itô's Lemma
Probability & StatisticsStochastic Calculus
Stochastic Differential Equations
Probability & StatisticsStochastic Calculus
Geometric Brownian Motion
Probability & StatisticsStochastic Calculus
Mean-Reverting SDEs: The Ornstein–Uhlenbeck Process
Quantitative FinanceDerivatives Pricing
Girsanov's Theorem and Change of Measure
Quantitative FinanceDerivatives Pricing
Feynman–Kac and the Black-Scholes PDE
Quantitative FinanceDerivatives Pricing
The Black-Scholes Formula, Greeks, and Put-Call Parity
Quantitative FinanceDerivatives Pricing
Martingale Pricing, Risk-Neutral Valuation, and Completeness
Quantitative FinancePortfolio Theory & Asset Pricing
Returns, Risk, and the Opportunity Set
Quantitative FinancePortfolio Theory & Asset Pricing
Diversification and Covariance
Quantitative FinancePortfolio Theory & Asset Pricing
Mean-Variance Optimization
Quantitative FinancePortfolio Theory & Asset Pricing
The Minimum-Variance Frontier
Applied MathematicsNumerical Methods
Floating-Point Arithmetic and Rounding Error
Applied MathematicsNumerical Methods
Root-Finding Algorithms
Applied MathematicsNumerical Methods
Polynomial Interpolation
Applied MathematicsNumerical Methods
Piecewise Polynomials and Splines