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The Quantt Syllabus

Everything inside Quantt, laid out module by module. 201 lessons across 3 streams — a free, browseable map of what we cover.

New lessons ship every week and we are growing this syllabus all the time — treat the counts and structure as a living snapshot, not a fixed contract.

This page is a rough indication and high-level overview only. For the complete picture of what is in the product today (including exercises, notebooks, and pacing), get full access.

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Stream

Mathematics

From rusty school maths to quant fluency — with an optional pricing-theory deep dive.

12 modules · 74 lessons

Stream

Technology

The software-engineering and ML foundation that turns ideas into shipped systems.

14 modules · 74 lessons

Stream

Finance

How modern markets work, and the models we use to price and risk-manage them.

11 modules · 53 lessons

Mathematics

74 lessons

The quantitative backbone that underpins every pricing model, risk system, and trading strategy. Calculus, linear algebra, probability, statistics, and stochastic processes, taught in the order you need them — with a research track that reaches time series before optional measure theory and Ito calculus.

M01

Foundations

8 lessons

Start with everyday finance vocabulary, then build fluent algebra, functions, exponentials and logs, sequences for cash-flow maths, and enough trigonometry to read complex numbers without panic. Desk jargon is introduced only after the words are defined.

  1. 01
    Finance Concepts for Maths

    Includes: Why this matters · Assets vs Portfolios · What a Return Is (vs Price) · The Risk-Free Rate: "Safe Interest" · Volatility: How Bouncy Is It? · Bonds and Coupons · Options: A Right, Not an Obligation · Portfolio Weights vs Quantities · Basis Points · Summary

  2. 02
    Algebra & Equations

    Includes: Why this matters · Rearranging Equations: The Balance Principle · Linear Equations in One Unknown · Simultaneous Equations: Solving Two Equations Together · Working with Formulas: Isolating a Variable · Percentages, Proportions and Rates · Inequalities: Reasoning with Ranges · Absolute Value: Distance and Tolerance · Summary

  3. 03
    Functions & Notation

    Includes: Why This Module Matters · What Is a Function? · Domain and Range · Common Function Types · Composition of Functions · Inverse Functions · Sigma Notation (Summation) · Product Notation · Mathematical Reasoning (Intuition Level) · Common Notation Reference · Summary

  4. 04
    Powers, Roots & Polynomials

    Includes: Why this matters · Integer Powers and the Laws of Exponents · Negative and Zero Exponents · Roots and Fractional Powers · Scientific Notation and Orders of Magnitude · Polynomials: Degree, Evaluation, and Light Expansion · Factorisation Intuition · Common Pitfalls · Summary

  5. 05
    Exponentials & Logarithms

    Includes: Why This Module Matters · Laws of Exponents: The Ground Rules · The Number $e$ — The Most Important Constant in Finance · The Exponential Function $e^x$ · Natural Logarithms · Continuous Compounding: The Standard in Quantitative Finance · Log Returns: The Quant's Preferred Measure · Log Transformations: A Powerful Tool · Exponential Growth in the Real World · Common Pitfalls · Summary

  6. 06
    Sequences & Series

    Includes: Why this matters · Sequences: patterns in numbers · Series: adding up the terms · Annuities and bond cash flows · Worked example: mortgage amortisation · Convergence and infinite series · Perpetuities and the Gordon Growth Model · Putting it together: from patterns to present values · Summary

  7. 07
    Trigonometry Essentials

    Includes: Why this matters · Radians vs Degrees · The Unit Circle · Sine, Cosine, and Tangent: Definitions · Key Identities · Periodicity · Converting Between Polar and Cartesian Coordinates · Common Pitfalls · Summary

  8. 08
    Complex Numbers & Euler's Formula

    Includes: Why this matters · The imaginary unit and complex arithmetic · The complex plane and modulus · Polar form · Euler's formula · De Moivre and roots of unity · Where this shows up later (optional) · Practice drills (mental checklist) · Summary

M02

Calculus

10 lessons

Pricing and risk live in rates of change and totals. This module builds limits through multivariable calculus, with root-finding and quadrature while the ideas are fresh. Ordinary and partial differential equations, plus Fourier tools, sit in a later Advanced Calculus module so the core path stays climbable.

  1. 01
    Limits & Continuity

    Includes: Why This Module Matters · What Is a Limit? · Limit Laws: Breaking Complex Limits into Pieces · One-Sided Limits · Continuity: The "No Surprises" Property · Limits at Infinity: Long-Run Behaviour · Important Theorems About Continuous Functions · Where Continuity Breaks Down in Finance · From Limits to Derivatives: A Preview · Summary

  2. 02
    Differentiation

    Includes: Why This Module Matters · The Derivative: What It Really Means · The Basic Derivative Rules · Combining Derivatives: Product, Quotient, and Chain Rules · Higher-Order Derivatives · The Greeks: Derivatives of Option Prices · Economic Interpretation: Marginal Analysis · Numerical Differentiation: When There's No Formula · Common Mistakes to Avoid · Summary

  3. 03
    Taylor Expansions

    Includes: Why this matters · The core idea · First- and second-order approximations · Deriving the classic expansions from first principles · Duration and convexity as Taylor terms · The Greeks as a multivariable Taylor expansion · Small-$x$ approximations every quant should know · When the approximation fails · Summary

  4. 04
    Optimisation

    Includes: Why This Module Matters · Finding Critical Points · The First Derivative Test · The Second Derivative Test · Convexity and Concavity: Why They Matter Enormously · Financial Optimisation Examples · Numerical Optimisation: When Calculus Isn't Enough · Summary

  5. 05
    Integration

    Includes: Why This Module Matters · Antiderivatives (The Reverse of Differentiation) · Definite Integrals: Area Under a Curve · The Fundamental Theorem of Calculus · Substitution (u-Substitution) · Integration by Parts · Numerical Integration · Financial Applications of Integration · Improper Integrals · Summary

  6. 06
    Root Finding & Interpolation

    Includes: Why this matters · Bisection · Fixed-point iteration and convergence order · Newton–Raphson and the secant method · Convergence and failure modes · Implied volatility as a root-finding problem · Linear and cubic-spline interpolation · Preview: building curves · Summary

  7. 07
    Numerical Integration (Quadrature)

    Includes: Why this matters · The trapezoidal rule · Simpson's rule · Error analysis · Adaptive quadrature · Gaussian quadrature · Integrating densities and expectations · When quadrature beats Monte Carlo · Summary

  8. 08
    Vectors

    Includes: Why This Module Matters · What Is a Vector? · Vector Operations · Norms: Measuring the "Size" of a Vector · The Dot Product (Inner Product) · Orthogonality: The Mathematics of Diversification · Linear Combinations and Span · Projection: Decomposing Risk · Higher Dimensions: From 2D/3D to Finance · Vectors in Python (Preview) · Summary

  9. 09
    Partial Derivatives & Gradients

    Includes: Why this matters · Functions of Two Variables · Partial Derivatives: One Variable at a Time · Higher-Order Partials: A Light Preview of the Hessian · The Gradient: Combining Partials into a Vector · Directional Derivatives: Steepest Ascent Is Not the Only Direction · Putting It Together: A Worked Multivariable Example · Summary

  10. 10
    Multivariable Calculus

    Includes: Why This Module Matters · Functions of Several Variables · Partial Derivatives · The Gradient Vector · The Total Differential: Measuring Combined Effects · Second Partial Derivatives and the Hessian · Taylor Expansion in Multiple Variables · Multivariable Optimisation · Constrained Optimisation: Lagrange Multipliers · Chain Rule in Multiple Variables · The Jacobian Matrix · Summary

M03

Linear Algebra

4 lessons

Portfolios, factor models, and PCA collapse to matrix algebra. This module builds matrices, eigenstructure, and decompositions. Covariance and regression return after probability and statistics give you the right language for risk and fitting.

  1. 01
    Matrices & Linear Systems

    Includes: Why This Module Matters · Matrix Notation · Matrix Operations · The Transpose · Special Matrices · The Determinant · The Inverse Matrix · Solving Linear Systems · Matrix Multiplication as Transformation · Trace of a Matrix · Summary

  2. 02
    Eigenvalues & Eigenvectors

    Includes: Why This Module Matters · The Core Definition · Finding Eigenvalues: The Characteristic Equation · Eigendecomposition (Diagonalisation) · Properties of Symmetric Matrices · Positive Definiteness · Principal Component Analysis (PCA): The Killer Application · Computing Eigenvalues in Practice · Summary

  3. 03
    Matrix Decompositions: LU, QR & Cholesky

    Includes: Why this matters · Why decompose a matrix? · LU decomposition & solving linear systems · Pivoting & numerical stability · QR decomposition & least squares · Cholesky decomposition for SPD matrices · Cholesky for generating correlated random draws · Common pitfalls · Summary

  4. 04
    Singular Value Decomposition

    Includes: Why this matters · The SVD theorem · A fully worked $2\times2$ example · Geometric meaning (rotation-scale-rotation) · SVD vs eigendecomposition · Low-rank approximation (Eckart-Young) · SVD and PCA · Applications: denoising covariance & factor extraction · Common pitfalls · Summary

M04

Probability

9 lessons

Markets are random. Learn the rules of probability, expectation and variance, then covariance matrices, named distributions, conditional expectation, and limit theorems. Characteristic functions and Fourier transforms move to the advanced track so this module stays focused on intuition you can use immediately.

  1. 01
    Sets & Combinatorics

    Includes: Why this matters · Sets: The Language of Collections · Set Operations: Union, Intersection, Complement · De Morgan's Laws and Disjoint Sets · Counting: The Product Rule · Permutations: Counting Ordered Arrangements · Combinations: Counting Unordered Selections · Binomial Coefficients and Pascal's Triangle · Summary

  2. 02
    Foundations of Probability

    Includes: Why This Module Matters · Sample Space and Events · Probability: The Rules · Random Variables: Assigning Numbers to Outcomes · Probability Density Functions · Common Distributions in Finance · The Cumulative Distribution Function (CDF) · Connecting Distributions to Finance Models · Summary

  3. 03
    Conditional Probability & Bayes

    Includes: Why This Module Matters · Conditional Probability · Independence · The Multiplication Rule · The Law of Total Probability · Bayes' Theorem · Bayes' Theorem in Finance · Bayesian Updating: An Iterative Process · Common Pitfalls · Summary

  4. 04
    Expectation & Variance

    Includes: Why This Module Matters · Expected Value (The Mean) · Variance and Standard Deviation · Covariance: The Link Between Two Variables · Higher Moments: Beyond Mean and Variance · The Sharpe Ratio: Combining Return and Risk · Expected Value of a Function · Summary

  5. 05
    Covariance Matrices

    Includes: Why This Module Matters · Recap: Variance and Standard Deviation · Covariance: How Two Assets Move Together · Correlation: Normalised Covariance · Building the Covariance Matrix · The Portfolio Variance Formula · Positive Semi-Definiteness · The Correlation Matrix · Practical Challenges and Solutions · Risk Decomposition · Summary

  6. 06
    Common Probability Distributions

    Includes: Why this matters · Bernoulli and Binomial: Counting Successes · Uniform: Equally Likely Outcomes · Poisson: Counting Rare Events Over Time · Exponential: Waiting Times · Normal: The Workhorse Bell Curve · Log-normal: Modelling Prices That Can't Go Negative · Student-t: Fatter Tails for Real Markets · Choosing the Right Distribution · Summary

  7. 07
    Conditional Expectation of Random Variables

    Includes: Why this matters · From conditional probability to conditional expectation · Conditioning on a discrete random variable · The law of total expectation (tower property, discrete form) · Linearity and "known given $Y$" pull-out · Continuous case (light touch) · Best predictor in mean-square sense · What this is *not* (yet) · Common pitfalls · Summary

  8. 08
    LLN & Central Limit Theorem

    Includes: Why This Module Matters · The Law of Large Numbers (LLN) · The Central Limit Theorem (CLT) · The Standard Error · Confidence Intervals · CLT and Monte Carlo Methods · The CLT for Sums (Not Just Averages) · Limitations and Caveats · Summary

  9. 09
    Simulation & Monte Carlo Intro

    Includes: Why this matters · Simulating Random Variables · From Samples to Estimates: The Sample Mean · Quantifying the Error: Standard Error and the √n Rule · Crude Monte Carlo: Estimating an Expectation · Monte Carlo Option Pricing: A Sketch · A Light Word on Variance Reduction · Why This Connects Backwards and Forwards · Summary

M05

Statistics

6 lessons

Data is the raw material of every quant strategy. Estimation, hypothesis testing, and regression come first; regularisation and maximum likelihood deepen the fitting toolkit once ordinary least squares is solid. Covariance already sits in Probability, right after expectation and variance.

  1. 01
    Descriptive Statistics & Sampling

    Includes: Why this matters · Measures of Central Tendency: Mean, Median, Mode · Measures of Spread: Variance and Standard Deviation · Percentiles and Quantiles · Shape: Histograms, Skewness, and Kurtosis · Population vs Sample: Why the Distinction Matters · A First Look at the Sampling Distribution · Summary

  2. 02
    Statistical Estimation

    Includes: Why This Module Matters · Point Estimation: Making a Best Guess · Properties of Good Estimators · Maximum Likelihood Estimation (MLE): A Quick Preview · Method of Moments · Interval Estimation: Quantifying Uncertainty · Estimation Challenges in Finance · Summary

  3. 03
    Hypothesis Testing

    Includes: Why This Module Matters · The Framework · Types of Error · Worked Example: Testing a Trading Strategy · One-Tailed vs Two-Tailed Tests · Two-Sample Tests · The Multiple Testing Problem · Practical Considerations in Finance · Summary

  4. 04
    Linear Regression

    Includes: Why This Module Matters · Simple Linear Regression · Ordinary Least Squares (OLS) · Goodness of Fit: $R^2$ · Assumptions of OLS · Multiple Linear Regression · Interpreting Coefficients Correctly · Residual Analysis · Adjusted $R^2$ and Overfitting · Practical Tips for Financial Regression · Summary

  5. 05
    Regression & Regularisation

    Includes: Why this matters · Least Squares from Matrices: Normal Equations and Geometry · Multicollinearity and Ill-Conditioning · Ridge Regression: L2 Shrinkage · Lasso Regression: L1 and Sparsity · Robust Regression: The Huber Loss · Finance Applications: Factor Betas and Covariance Shrinkage · Choosing the Right Tool · Summary

  6. 06
    Maximum Likelihood & Fisher Information

    Includes: Why this matters · The likelihood function · Log-likelihood & the MLE · Properties: consistency & asymptotic normality · Fisher information & the Cramér–Rao bound · MLE for the normal: full derivation · MLE for the Bernoulli: full derivation · Preview: MLE for GARCH/volatility estimation · Summary

M06

Stochastic Processes

6 lessons

Random paths underpin pricing and risk. Start with Markov chains and discrete processes, then random walks, Brownian motion, and jumps. A fair-games bridge makes filtrations intuitive before formal discrete martingales.

  1. 01
    Markov Chains

    Includes: Why this matters · State space & the Markov property · Transition matrices · n-step transition probabilities · Stationary distributions · Absorbing chains & hitting times · Finance application: credit-rating migration · Common pitfalls · Summary

  2. 02
    Discrete-Time Stochastic Processes

    Includes: Why this matters · What is a stochastic process? · IID noise versus dependence · Filtrations: information up to time $n$ · Adapted processes · Examples: returns and the AR(1) intuition · Stationarity intuition (weak) · From discrete processes to continuous models · Summary

  3. 03
    Random Walks & Brownian Motion

    Includes: Why This Module Matters · The Simple Random Walk · Random Walk with Drift · The Random Walk Hypothesis · From Random Walks to Brownian Motion · Roadmap preview (optional) · Limitations of GBM · Bringing It All Together · Summary

  4. 04
    Poisson Processes & Jumps

    Includes: Why this matters · Counting processes · The Poisson process: definition · Interarrival times are exponential · Compound Poisson processes · Jump intuition for markets: crashes and defaults · Preview: jump-diffusion and Lévy processes · Summary

  5. 05
    Fair Games & Information

    Includes: Why this matters · A Fair Coin Game · Information Grows Over Time · Adapted Means "Use Only Known Info" · Insider vs Outsider · Risk-Neutral Pricing in One Paragraph · Preview: Martingales Are Formal Fair Games · Summary

  6. 06
    Discrete Martingales

    Includes: Why this matters · Filtration recall · Martingales, submartingales, and supermartingales · Fair game intuition · Optional stopping: a careful, light introduction · Doob decomposition intuition · Why discounted prices being martingales matters for no-arbitrage · Preview: the one-step binomial model · Summary

M07

Optimisation

5 lessons

Portfolio construction and calibration are optimisation problems. Build convexity and gradient descent, learn Lagrange multipliers with a gentle bridge, then KKT and quadratic programming for portfolios.

  1. 01
    Convexity & Convex Sets

    Includes: Why this matters · Convex sets · Convex and concave functions · First- and second-order conditions · Jensen's inequality · Why convexity guarantees a global optimum · Common pitfalls · Convexity in finance (option payoffs, risk measures) · Summary

  2. 02
    Unconstrained Optimisation & Gradient Descent

    Includes: Why this matters · Gradients and Hessians revisited · Newton's method · Gradient descent and step sizes · Convergence intuition · Line search · Pitfalls (saddle points, conditioning) · A worked Newton vs gradient-descent comparison · Summary

  3. 03
    Lagrange Multipliers: Intuition

    Includes: Why this matters · Optimise With a Constraint · Gradients Point the Same Way · The Lagrangian · What Does $\lambda$ Mean? · Worked Example: Two Assets, Weights Sum to One · Equality Only — KKT Comes Next · Summary

  4. 04
    Constrained Optimisation: Lagrangian Duality & KKT

    Includes: Why this matters · Equality constraints and Lagrange multipliers · Inequality constraints · The KKT conditions · Duality and shadow prices · Economic interpretation of multipliers · A worked constrained example · Adding an inequality: a long-only twist · Common pitfalls · Summary

  5. 05
    Quadratic Programming for Portfolios

    Includes: Why this matters · The quadratic programming form · Mean–variance optimisation as a QP · Solving the minimum-variance portfolio · Adding constraints (long-only, budget) · Sensitivity of the efficient frontier · From QP to risk parity · A worked long-only example · Common pitfalls · Summary

M08

Time Series & Econometrics

6 lessons

Systematic trading research lives in time series. Stationarity, ARMA, GARCH, and cointegration separate signal from noise in returns — placed here so the research track does not wait for measure theory or Ito calculus.

  1. 01
    Stationarity & Autocorrelation

    Includes: Why this matters · Weak vs strict stationarity · Integrated series: I(0) vs I(1) · The autocorrelation function (ACF) and PACF · White noise and random walks · Unit-root tests (ADF) — intuition · Differencing and transformations · Summary

  2. 02
    ARMA Models

    Includes: Why this matters · Autoregressive AR(p) models · Moving-average MA(q) models · The combined ARMA(p,q) model · Stationarity and invertibility conditions · Identifying orders from ACF/PACF · Estimation · Summary

  3. 03
    ARIMA & Forecasting

    Includes: Why this matters · Integration and the ARIMA(p,d,q) model · The Box–Jenkins workflow · Forecasting and prediction intervals · Information criteria (AIC and BIC) · Backtesting forecasts · Limits on forecasting financial returns · Summary

  4. 04
    GARCH Volatility Models

    Includes: Why this matters · Volatility clustering and the stylised facts · From constant variance to ARCH · GARCH(1,1): the workhorse model · Persistence: $\alpha + \beta$ and stationarity · Forecasting variance and the unconditional level · Applications: VaR, vol-targeting, and options · Common pitfalls · Summary

  5. 05
    Cointegration & Pairs TradingOptional

    Includes: Why this matters · The spurious regression trap · Cointegration: definition and intuition · The Engle–Granger two-step procedure · Pairs trading mechanics · Half-life and Ornstein–Uhlenbeck intuition · Summary

  6. 06
    State-Space Models & the Kalman FilterOptional

    Includes: Why this matters · State-space representation: state and observation equations · The predict step · The update step and the Kalman gain · Application: a time-varying hedge ratio · Nowcasting and other applications · Summary

M09

Advanced Calculus Toolkit

3 lessons

ODEs, PDEs, and Fourier/Laplace transforms are the differential-equation and transform toolkit behind heat equations, pricing PDEs, and characteristic-function methods. Parked after the core calculus path so learners meet them when paths, PDEs, and numerics are about to matter.

  1. 01
    Ordinary Differential Equations

    Includes: Why this matters · Core path · Roadmap (optional) · Common pitfalls · Summary

  2. 02
    Introduction to PDEs

    Includes: Why this matters · From ODEs to PDEs · Classification (what kind of PDE?) · The heat equation · Initial, terminal, and boundary conditions · Domain and grid (preview of numerics) · How this connects to ODEs and to SDEs · Common pitfalls · Summary

  3. 03
    Fourier & Laplace Transforms

    Includes: Why this matters · Core vs Roadmap · Periodic functions & Fourier series · The Fourier transform · Key properties (linearity, convolution, shifting) · The Laplace transform & solving ODEs · Characteristic functions as Fourier transforms · Preview: transform methods in option pricing · Common pitfalls · Summary

M10

Numerical Methods for Pricing

2 lessons

Root finding and quadrature already sit in Calculus. This module focuses on finite differences for PDEs and Monte Carlo with variance reduction — after the Advanced Calculus toolkit has introduced the equations you will discretise.

  1. 01
    Finite Difference Methods for PDEs

    Includes: Why this matters · Discretising the Black–Scholes PDE · Explicit, implicit and Crank–Nicolson schemes · Stability and convergence · Boundary conditions · Pricing American options (PSOR) · Grids and Greeks · Summary

  2. 02
    Monte Carlo & Variance Reduction

    Includes: Why this matters · The Monte Carlo estimator: a quick recap · Simulating terminal asset prices · Antithetic variates · Control variates · Importance sampling · Quasi-Monte Carlo (Sobol) · Choosing and combining techniques · Summary

M11

Measure-Theoretic Probability (Advanced)

Optional7 lessons

Optional pricing-theory track. Characteristic functions, sigma-algebras, Lebesgue expectation, and martingales in continuous time — the language of rigorous risk-neutral pricing. Skip this module if you are on the research/time-series path; return when you need continuous-time derivatives theory.

  1. 01
    Generating & Characteristic Functions

    Includes: Why this matters · Core vs Roadmap · Moment generating functions (MGFs) · Worked example: the MGF of the exponential distribution · Computing moments by differentiating the MGF · Characteristic functions & when they exist · Sums of independent random variables · Uniqueness & inversion · A gentle sketch of Fourier pricing · Use in the CLT and option pricing · Summary

  2. 02
    From Partitions to Sigma-Algebras

    Includes: Why this matters · A quick reminder: continuous random variables already have their toolkit · Information as a partition · Finer partitions carry more information · Why path space needs more than "just list the blocks" · Where this is going · Summary

  3. 03
    Probability Spaces & Sigma-Algebras

    Includes: Why this matters · Finite sample spaces: coins, dice, and binomial trees · Sigma-algebras: the finite case made precise · Probability measures and their axioms · Why we need this machinery beyond the finite case · Information as a sigma-algebra · Preview: filtrations · Summary

  4. 04
    Lebesgue Integration & Expectation

    Includes: Why this matters · Riemann vs Lebesgue integration · Measurable functions · The Lebesgue integral, built in layers · Expectation as an integral · Convergence theorems (MCT and DCT) · Change of variables · Common pitfalls · Summary

  5. 05
    Conditional Expectation

    Includes: Why this matters · Conditioning on a sigma-algebra · A fully worked discrete example · The tower property, worked through the same example · The defining properties · Projection in L-squared · Conditional expectation as best predictor · Link to regression · Common pitfalls · Summary

  6. 06
    Martingales, Filtrations & Stopping Times

    Includes: Why this matters · Filtrations and adapted processes · The martingale definition, and its discrete-martingales cousin · Examples (symmetric random walk, likelihood ratios) · Stopping times · The optional stopping theorem · Why martingales mean 'fair game' and no arbitrage · Summary

  7. 07
    Continuous-Time Martingales & Quadratic Variation

    Includes: Why this matters · From discrete history to continuous filtrations · Brownian motion as a martingale · The companion martingale $W_t^2 - t$ · Quadratic variation: the roughness that remains · Trading interpretation (preview of the Ito integral) · Roadmap (optional depth) · Summary

M12

Stochastic Calculus (Advanced)

Optional8 lessons

Optional pricing-theory track. From likelihood ratios and an Ito intuition bridge through the Ito integral, SDEs, Girsanov, and Feynman–Kac — the engine behind Black–Scholes. Take this after Measure-Theoretic Probability if you need continuous-time pricing mathematics.

  1. 01
    Radon–Nikodym & Likelihood Ratios

    Includes: Why this matters · Two probabilities on the same outcomes · The likelihood ratio $Z$ · One-step binomial (worked) · Absolute continuity (plain language) · Density processes (preview) · Roadmap · Summary

  2. 02
    From Trading Gains to the Ito Integral

    Includes: Why this matters · Discrete Buy-and-Hold Gains · Choose the Position Before the Move · Why Jagged Paths Break Ordinary Calculus · Quadratic Variation: Sum of Squared Moves · The Slogan $(dW)^2 = dt$ · Preview: The Ito Integral as a Limit of Gains · Summary

  3. 03
    The Ito Integral

    Includes: Why this matters · Why ordinary calculus fails for Brownian paths · Quadratic variation · Constructing the Ito integral · The Ito isometry · The martingale property of the integral · Worked simple integrals · A fully numeric simple-integrand example · Common pitfalls · Summary

  4. 04
    Ito's Lemma

    Includes: Why this matters · The chain rule for stochastic processes · The half-sigma-squared correction term · Applying Ito to log(S) · Worked examples: powers of $S$ and a bond-style function · Deriving geometric Brownian motion · Multidimensional Ito · Common mistakes · Summary

  5. 05
    Stochastic Differential Equations

    Includes: Why this matters · The SDE form (drift + diffusion) · Key models: GBM, Ornstein-Uhlenbeck, CIR · Existence and uniqueness (intuition) · Euler-Maruyama discretisation · Worked example: one Euler–Maruyama step by hand · Strong vs weak solutions · Simulating SDE paths and common pitfalls · Summary

  6. 06
    Change of Measure & Girsanov's Theorem

    Includes: Why this matters · Discrete intuition: risk-neutral pricing in a binomial model · Equivalent probability measures · The Radon-Nikodym derivative · Girsanov's theorem · Removing or adding drift · Real-world vs risk-neutral measure · Why this enables pricing · Pitfalls and technical fine print · Summary

  7. 07
    Feynman-Kac & the Pricing PDE

    Includes: Why this matters · Linking SDEs to PDEs · The Feynman-Kac formula · Deriving the PDE step by step (the SDE-to-PDE walkthrough) · Deriving the Black-Scholes PDE · Terminal and boundary conditions · Probabilistic vs PDE pricing · Connection to the heat equation · Common pitfalls · Summary

  8. 08
    Jump & Levy ProcessesOptional

    Includes: Why this matters · Limitations of pure diffusion · The Poisson and compound Poisson processes · Worked example: calibrating an intensity and simulating jump arrivals · Jump-diffusion (the Merton model) · Levy processes overview · Ito's lemma with jumps · Why jumps matter for tails and the vol smile · Contrast with pure diffusion: a quick reference · Summary

Technology

74 lessons

The software-engineering foundation that makes the difference between a quant who can prototype and a quant who can ship. Python from refresher to advanced, then CS fundamentals, databases, networking, cloud, optional systems programming, data engineering, machine learning, and AI/LLMs for quantitative finance.

M01

Python Onboarding (Optional)

Optional2 lessons

If you've never written code before, this is your zero-to-one ramp. Optional for everyone else — but doing it gives you the muscle memory to read every Python snippet in the rest of the curriculum without friction.

  1. 01
    Python: Zero to OneOptional

    Includes: Welcome — What Is Programming? · Your First Program · Comments — Notes to Yourself · Variables — Giving Names to Things · Data Types — Different Kinds of Data · Arithmetic — Doing Maths · String Formatting — Mixing Text and Data · Making Decisions — `if`, `elif`, `else` · Loops — Repeating Things · Lists — Collections of Things · Functions — Reusable Blocks of Code · Putting It All Together · +2 more inside the lesson

  2. 02
    Python: Building MomentumOptional

    Includes: You Know the Basics — Now Let's Build on Them · Dictionaries — Looking Up Data by Name · Strings in Depth · Tuples — Immutable Sequences · Sets — Unique Collections · List Comprehensions — Elegant Loops · File I/O — Reading and Writing Files · Error Handling — When Things Go Wrong · Imports and Modules — Standing on the Shoulders of Giants · Introduction to Classes · Bringing It All Together · Looking ahead

M02

Foundations

7 lessons

Working as a quant means living inside a terminal, a debugger, and a git repo. This module gives you the developer toolbox — running a first project, Python, the command line, version control, packaging, and how to read errors — so the rest of tech doesn't fight you at every step.

  1. 01
    Prerequisites

    Includes: Who is this course for? · What we expect you to know · Self-assessment checklist · Looking ahead

  2. 02
    Your First Project Setup

    Includes: Why this matters · Open a terminal · Make a project folder · Create and run a Python file · Why the folder matters (paths) · A private Python for this project (preview) · Optional: first Git snapshot · Looking ahead

  3. 03
    Python Fundamentals

    Includes: Why Python? · Variables and Types · Control Flow · Functions · Data Structures · Classes and Objects · File I/O · Error Handling · Imports and Modules · Looking ahead

  4. 04
    The Command Line

    Includes: Why Bother With the Terminal? · What Is the Terminal? · Navigating the Filesystem · Running Programs · Viewing File Contents · Finding Things · Putting Commands Together · Environment Variables · Essential Shortcuts · A Simple Example · Looking ahead

  5. 05
    Git & Version Control

    Includes: What Is Version Control? · Why Does This Matter? · The Core Concepts · Branches · Working With Others · GitHub · The Most Important Commands · Looking ahead

  6. 06
    Package Management

    Includes: What Is a Package? · pip: The Package Installer · The Problem: "It Works On My Machine" · Virtual Environments · requirements.txt: Recording Your Dependencies · pyproject.toml: The Modern Approach · Common Packages You'll Use · What Can Go Wrong · Looking ahead

  7. 07
    Debugging & Reading Errors

    Includes: Bugs Are Inevitable · Step One: Read the Error Message · Common Error Types · Print Debugging · Logging: Print Debugging for Grown-Ups · Using a Debugger · The Debugging Mindset · Looking ahead

M03

Systems Basics

6 lessons

Quant systems are distributed, networked, and stateful. You don't need to be a systems engineer, but you do need to know how networks, operating systems, data formats, and databases behave — because every model eventually meets one of them.

  1. 01
    Networking & The Internet

    Includes: You Already Know More Than You Think · The Internet in 60 Seconds · URLs: The Address System · Clients and Servers · HTTP: The Language of the Web · APIs: How Software Talks to Software · Latency: Why Speed Matters · A Few More Concepts · Looking ahead

  2. 02
    Operating Systems

    Includes: Why Should You Care? · What Is an Operating System? · The CPU: The Brain · Memory (RAM): The Workspace · Storage: The Filing Cabinet · Processes: Programs in Action · How Programs Run · Environment Variables · Looking ahead

  3. 03
    Data Formats

    Includes: Data Is Everywhere · CSV: The Simplest Table · JSON: Structured and Nested Data · YAML: Human-Friendly Configuration · Other Formats Worth Knowing About · Choosing the Right Format · Text vs Binary · Encoding: Why Text Gets Garbled · Looking ahead

  4. 04
    Databases & SQL

    Includes: Beyond Files · What Is a Relational Database? · SQL: The Language of Databases · Using SQLite in Python · When to Use a Database vs a File · Beyond Relational: Other Types of Databases · Why Databases Matter in Finance · Looking ahead

  5. 05
    Development Tools

    Includes: More Than Just a Text Editor · Your Editor: Where You Spend Most of Your Time · Linting: Catching Mistakes Before You Run · Formatting: Consistent Code Style · Type Checking: Catching Errors Without Running Code · Testing: Proving Your Code Works · Reading Documentation · Putting It All Together · Looking ahead

  6. 06
    Correctness in Financial Code

    Includes: Why this matters · Decimal for money · Floating-point pitfalls · Determinism and seeded RNGs · Reproducibility and audit trails (high level) · Latency vs throughput (lightly) · A testing and verification mindset · Habits to keep · Looking ahead

M04

Python Mastery

6 lessons

Python is the lingua franca of quant work. This module takes you from competent scripter to confident library author — comfortable with advanced techniques, OOP vs functional patterns, plain-English risk metrics, and the NumPy/Pandas stack that backs every research notebook in the industry.

  1. 01
    Python Advanced Techniques

    Includes: Beyond the Basics · Decorators · Generators and Iterators · Context Managers · *args and **kwargs · Lambda Functions and Functional Tools · Dataclasses · Type Hints: Going Further · Looking ahead

  2. 02
    OOP vs Functional Programming

    Includes: Two Ways to Think About Code · Object-Oriented Programming (OOP) · Functional Programming (FP) · Python's Pragmatic Approach · Looking ahead

  3. 03
    Returns & Risk Metrics (Plain English)

    Includes: Why this matters · Price vs return · Daily vs annual · Volatility (the "how bumpy" number) · Sharpe ratio (return per unit of bumpiness) · What this is not · Looking ahead

  4. 04
    NumPy Introduction

    Includes: Why NumPy? · The ndarray · Vectorised Operations · Indexing and Slicing · Common Operations · Reshaping and Broadcasting · A Financial Example · Looking ahead

  5. 05
    Pandas Introduction

    Includes: The Data Analysis Workhorse · Creating DataFrames · Selecting Data · Filtering, Sorting, and Transforming · Grouping and Aggregation · Handling Missing Data · A Financial Example · Pandas vs NumPy: When to Use Each · Looking ahead

  6. 06
    Speeding Up Research Code

    Includes: Making Research Code Run Faster · Start Here: NumPy Vectorisation · Next: Numba JIT (Just-In-Time) · SIMD (short awareness) · GPU Computing (CUDA) — awareness · FPGA — HFT specialty / optional awareness · When to Use What · Looking ahead

M05

Software Engineering Core

5 lessons

A model that breaks silently in production is worse than no model at all. Testing, debugging, environment isolation, a clean dev workflow, and design patterns are the disciplines that turn experimental code into something a desk can rely on.

  1. 01
    Testing Introduction

    Includes: Why Testing Matters · Unit Tests with pytest · What Makes a Good Test? · Fixtures · Parameterised Tests · Test Coverage · Test-Driven Development (TDD) · Looking ahead

  2. 02
    Debugging (Advanced)

    Includes: Beyond Print Statements · Logging: Print Debugging Done Right · Using a Debugger (pdb) · Profiling: Finding Performance Bottlenecks · Common Debugging Strategies · Memory Profiling · Debugging in Production · Looking ahead

  3. 03
    Package Management & Virtual Environments

    Includes: Beyond pip install · Virtual Environments in Depth · Dependency Resolution · Pinning Dependencies · Modern Python Packaging: pyproject.toml · Poetry · Dev vs Production Dependencies · Looking ahead

  4. 04
    Development Tools & Workflow

    Includes: The Professional Setup · Advanced IDE Usage · Linting with Ruff · Type Checking with mypy · Pre-commit Hooks · Makefile and Task Runners · Documentation · The Complete Workflow · Looking ahead

  5. 05
    Design Patterns

    Includes: Proven Solutions to Common Problems · Why Design Patterns Matter · Creational Patterns · Structural Patterns · Behavioural Patterns · Anti-Patterns to Avoid · Looking ahead

M06

CS Essentials

7 lessons

Big-O isn't an interview gimmick — it's why your backtest takes 30 seconds or 30 hours. This module covers how Python runs on a machine, then the CS fundamentals, OS internals, data formats, and version-control workflows that every senior quant draws on weekly.

  1. 01
    How Your Python Actually Runs

    Includes: Why this matters · Program → process · CPU, RAM, and disk (recap with a spreadsheet lens) · Why some code feels instant and some crawls · Stack scratchpad vs long-lived objects (gentle) · Why finance cares · Looking ahead

  2. 02
    Computer Science Fundamentals

    Includes: How a Computer Actually Works · The CPU: The Brain · Memory Hierarchy · Binary and Data Representation · Temporary Scratchpad vs Long-Lived Objects · Big-O Notation · Essential Data Structures · Looking ahead

  3. 03
    Operating Systems (Advanced)

    Includes: The Layer Between You and the Hardware · Process Management · Threads vs Processes · Memory Management · File Systems · Inter-Process Communication (IPC) · Signals · Looking ahead

  4. 04
    Data Formats (Advanced)

    Includes: Choosing the Right Format · CSV: Edge Cases and Large Files · JSON: Schema Validation and Streaming · YAML: Advanced Syntax · Binary Formats · Choosing the Right Format · Serialisation Performance · Looking ahead

  5. 05
    Columnar vs Row Storage

    Includes: How Data Layout Affects Performance · Row-Oriented Storage · Column-Oriented Storage · OLTP vs OLAP · Compression Benefits · Real-World Formats · Practical Impact · Looking ahead

  6. 06
    Git Essentials

    Includes: Your Daily Git Workflow · The Daily Workflow in Detail · What Is a Pull Request? · Merge Conflicts · Undoing Things Safely · Advanced / use with care — skip on first read · .gitignore and .gitattributes · Looking ahead

  7. 07
    Branching Strategies

    Includes: How Teams Organise Their Code · Feature Branching · GitFlow · Trunk-Based Development · Release Strategies · Code Review Best Practices · Monorepo vs Multi-repo · Looking ahead

M07

Databases

6 lessons

Tick data, position state, trade history — quants live on top of databases. This module takes you from SQL essentials (including joins) through advanced queries, schema design, ORMs, and the time-series stores built specifically for market data.

  1. 01
    SQL Introduction

    Includes: The Language of Data · Creating Tables · Inserting Data · SELECT: Querying Data · Aggregate Functions · GROUP BY and HAVING · UPDATE and DELETE · Foreign Keys · JOINs: Combining Tables · Using SQLite from Python · Looking ahead

  2. 02
    Databases (Advanced)

    Includes: Beyond Basic Queries · Database Engines · ACID Properties · Indexes · Query Execution Plans · Connection Pooling · Looking ahead

  3. 03
    SQL Advanced

    Includes: Powerful Query Techniques · JOINs in Depth · Subqueries and CTEs · Window Functions · CASE Expressions · Set Operations · Query Optimisation · Looking ahead

  4. 04
    Database Design

    Includes: Getting the Structure Right · Normalisation · Relationships · Entity-Relationship Diagrams · Denormalisation · Schema Migration · Looking ahead

  5. 05
    ORMs

    Includes: Bridging Python and SQL · SQLAlchemy: The Standard Python ORM · The ORM vs Raw SQL Debate · Common Anti-patterns · Migrations with Alembic · Looking ahead

  6. 06
    Time Series Databases

    Includes: When Time is the Primary Dimension · What Makes Time Series Data Special · Time Series Database Options · Key Concepts · Financial Use Cases · TSDB vs Traditional RDBMS · Looking ahead

M08

Networking & APIs

5 lessons

Trading systems live and die on latency and integration. This module covers the network internals, REST APIs, authentication patterns, and a plain-English map of desk systems that connect a research model to an exchange or counterparty.

  1. 01
    Networking (Advanced)

    Includes: Beyond the Basics · The OSI Model · TCP vs UDP · DNS (Domain Name System) · Ports · Firewalls and Security Groups · Load Balancing · Looking ahead

  2. 02
    Network Speeds

    Includes: Why Milliseconds Matter · Key Terminology · Real-World Latencies · Network Types · Co-location · Measuring Network Performance · Bandwidth vs Latency Trade-offs · Protocols and Speed · Looking ahead

  3. 03
    APIs & REST

    Includes: How Applications Talk to Each Other · REST Principles · HTTP Status Codes · Request and Response Format · Working with APIs in Python · Authentication · Rate Limiting · API Design Best Practices · Looking ahead

  4. 04
    Security & Authentication

    Includes: Protecting Systems and Data · Authentication vs Authorisation · Password Security · Tokens and JWTs · API Security · Common Vulnerabilities · HTTPS and TLS · Role-Based Access Control (RBAC) · Looking ahead

  5. 05
    Trading Desk Systems (Orientation)

    Includes: Why this matters · The job of the plumbing · Key acronyms (plain English) · Layers on a typical desk · Trade lifecycle (happy path) · Microservices vs monolith (lightly) · Looking ahead

M09

DevOps

4 lessons

Reproducibility is non-negotiable in regulated finance. Environments, SDLC discipline, CI/CD, and containers are the practices that let a small quant team ship code with confidence and roll it back when something breaks.

  1. 01
    Environments

    Includes: From Local to Production · Common Environments · Environment Configuration · Environment Variables · Secrets Management · Feature Flags · Looking ahead

  2. 02
    SDLC Best Practices

    Includes: The Software Development Life Cycle · SDLC Phases · Development Methodologies · Code Quality Practices · Version Control Best Practices · Technical Debt · Monitoring and Observability · Looking ahead

  3. 03
    CI/CD & Pipelines

    Includes: Automating the Path from Code to Production · Why CI/CD? · Continuous Integration (CI) · Continuous Deployment (CD) · Pipeline Stages · CI/CD Tools · Artifacts and Caching · Looking ahead

  4. 04
    Containers & Docker

    Includes: Running Software Consistently Everywhere · What is a Container? · Containers vs Virtual Machines · Docker · Docker Images and Layers · Docker Compose · Container Registries · Container Orchestration · Looking ahead

M10

Cloud

4 lessons

Modern quant infrastructure is cloud-first. AWS and Azure power the data lakes, model training, and risk runs at most hedge funds and investment banks. This module orients you so you can navigate either provider.

  1. 01
    Cloud Providers Introduction

    Includes: Computing on Someone Else's Servers · Why Cloud? · Core Cloud Services · Cloud Service Models · Pricing Models · Regions and Availability Zones · Looking ahead

  2. 02
    AWS Fundamentals

    Includes: The Building Blocks of AWS · Compute · Storage · Databases · Networking · Messaging · Monitoring · IAM (Identity and Access Management) · Looking ahead

  3. 03
    Azure Fundamentals

    Includes: Microsoft's Cloud Platform · Azure vs AWS — Service Mapping · Core Compute Services · Storage · Databases · Networking · Identity: Azure Active Directory (Entra ID) · DevOps · When to Choose Azure · Looking ahead

  4. 04
    S3 & Object Storage

    Includes: Storing Anything at Any Scale · Core Concepts · Storage Classes · Working with S3 in Python (boto3) · S3 for Financial Data · Access Control · Looking ahead

M11

Data Engineering

2 lessons

Quant signals are only as good as the pipelines feeding them. This module covers the big-data tools and platform thinking that keep a research desk fed with clean, timely data at scale.

  1. 01
    Big Data & Data Pipelines

    Includes: Processing Data at Scale · What Makes Data "Big"? · Batch vs Streaming · Apache Spark · Apache Kafka · ETL / ELT · Data Pipeline Architecture · Data Quality · Looking ahead

  2. 02
    Data Platform Fundamentals

    Includes: How Organisations Structure Their Data · Data Platform Layers · Data Lake vs Data Warehouse · Data Governance · Common Data Platform Tools · Financial Data Platform Architecture · Data Mesh (optional org-design idea) · Looking ahead

M12

Machine Learning

6 lessons

Modern quant desks use ML for signal combination, credit scoring, execution, and risk. This module teaches the algorithms and — more importantly — the validation discipline that separates a backtest that looks brilliant from a model that survives live markets.

  1. 01
    Supervised Learning Fundamentals

    Includes: Why this matters · The supervised learning setup · Bias–variance and the finance twist · Train / validation / test · Baseline before brilliance · Key takeaways · Looking ahead

  2. 02
    Features, Labels & Leakage

    Includes: Why this matters · Labels in finance are design choices · Feature hygiene · Point-in-time and reporting lag · Leakage checklist · Scaling and preprocessing · Key takeaways

  3. 03
    Tree Models & Ensembles

    Includes: Why this matters · A decision tree in one picture · Bagging and random forests · Boosting (the workhorse) · Practical hyperparameter instincts · Trees vs linear models · Key takeaways

  4. 04
    Validation & Walk-Forward Testing

    Includes: Why this matters · Why standard K-fold fails · Walk-forward (expanding or rolling) · Purging and embargoing · Metrics that matter · Nested validation for hyperparams · Multiple testing · Key takeaways

  5. 05
    Neural Networks for Quants

    Includes: Why this matters · Building blocks · Architectures you will hear about · Regularisation and training hygiene · When to use nets vs trees · Key takeaways

  6. 06
    Unsupervised Learning

    Includes: Why this matters · Clustering · Dimensionality reduction · Anomaly detection · Relation to factor models · Key takeaways

M13

AI & LLMs in Quant Finance

5 lessons

Large language models are changing how quants research, document, and automate workflows — but they are not magical alpha engines. This module covers how LLMs work, how to use them safely for research and ops, and the governance issues that matter in regulated finance.

  1. 01
    How LLMs Work

    Includes: Why this matters · The core objective · Transformers in one paragraph · Context windows and memory · What LLMs are good at in quant finance · What they are bad at alone · Key takeaways

  2. 02
    Prompt Engineering for Quants

    Includes: Why this matters · Anatomy of a strong prompt · Patterns that work in finance · Temperature and sampling · Prompt injection awareness · Key takeaways

  3. 03
    RAG & Document Intelligence

    Includes: Why this matters · The RAG pipeline · Chunking is a modelling choice · Evaluation · Failure modes in finance · Key takeaways

  4. 04
    Agents & Quant Workflows

    Includes: Why this matters · What an agent is · High-value quant workflows · Design constraints that keep you employed · Multi-agent patterns · Key takeaways

  5. 05
    Risks, Hallucinations & Governance

    Includes: Why this matters · Hallucinations and silent errors · Data protection and model choice · Model risk management (MRM) lens · Responsible rollout checklist · Key takeaways · Looking ahead

M14

Systems Programming (Optional)

Optional9 lessons

Optional specialization after the main path. For low-latency and platform-adjacent roles: systems literacy, then C++ and/or Rust. Research and analyst paths can treat the stream as complete after AI & LLMs.

  1. 01
    Systems Literacy for QuantsOptional

    Includes: Why this matters · Latency vs throughput (again) · Why not Python for the hottest path? · What you will (and will not) do in this track · How to use the optional track · Looking ahead

  2. 02
    C++ IntroductionOptional

    Includes: Why this matters · Why C++ in Finance? · Types, Variables, and Functions · Classes and Encapsulation · Memory: Stack, Heap, and RAII · Templates and the STL · C++ Alongside Python · Summary

  3. 03
    C++ for Low LatencyOptional

    Includes: Why this matters · Move Semantics and Cheap Transfers · Avoid Allocations on the Hot Path · Cache-Friendly Data Layout · Const, Inlining, and Branch Predictability · Concurrency Without Surprises · Interop and Measurement · Summary

  4. 04
    Modern C++ IdiomsOptional

    Includes: Why this matters · Prefer Values Over Sentinels · Views: string_view and span · Algorithms Over Loops · RAII for Locks and Handles · Rule of Zero (and Five) · Const-Correct APIs · Summary

  5. 05
    C++ ConcurrencyOptional

    Includes: Why this matters · Threads and Responsibilities · Mutexes and Critical Sections · Atomics for Simple Shared State · Message Passing Beats Shared Mutation · Data Races vs Race Conditions · Latency Habits Under Contention · Summary

  6. 06
    Rust IntroductionOptional

    Includes: Why this matters · Why Rust? · Ownership: Rust's Core Idea · Syntax Basics · Enums and Pattern Matching · Option and Result · When to Use Rust in Finance · Summary

  7. 07
    Rust for Systems ProgrammingOptional

    Includes: Why this matters · Borrowing in APIs · Traits: Interfaces Without Inheritance · Lifetimes (Intuition) · Error Handling at Scale · Concurrency Without Data Races · Rust vs C++ in Practice · Summary

  8. 08
    Rust Iterators & CollectionsOptional

    Includes: Why this matters · Vec, HashMap, and Friends · The Iterator Trait · Ownership Through Iterators · Zero-Cost Abstraction (Intuition) · Collecting and Fallible Iteration · When Not to Be Clever · Summary

  9. 09
    Rust Concurrency PatternsOptional

    Includes: Why this matters · Move Threads, Don't Share by Accident · Channels for Pipelines · Arc and Mutex When You Must Share · Send and Sync (Intuition) · Atomics and Lock-Free Caution · Async Is a Separate Gear · Summary

Finance

53 lessons

How modern markets actually work, the instruments traded on them, and the models used to price and risk-manage those instruments. From financial markets and time value of money through to derivatives pricing, structured notes, and market microstructure.

M01

Markets Foundations

6 lessons

Before models, you need a clear mental map of markets — who participates, why prices move, and how a single dollar today relates to a dollar next year. Without these foundations, every later concept floats untethered.

  1. 01
    Financial Markets & Participants

    Includes: Why this matters · The Major Asset Classes · How Markets Are Structured · Market Participants · Market Makers & Liquidity · The Role of Quants in Financial Institutions · How It All Fits Together · Summary

  2. 02
    Time Value of Money

    Includes: The Most Important Idea in Finance · Future Value: Growing Money Forward · Continuous Compounding · Present Value: Discounting Cash Flows · Net Present Value (NPV) · The Arbitrage Intuition · Annuities and Perpetuities · Summary

  3. 03
    Interest Rates & Yield Curves

    Includes: Why Rates Matter for Everything · What Is an Interest Rate? · Spot Rates · Forward Rates · The Yield Curve · Zero-Coupon Bonds · Bootstrapping: Building the Curve · Key Rate Benchmarks · Term Structure Theories · Summary

  4. 04
    FX Markets & Currency

    Includes: Why this matters · Spot, forward and the FX conventions · Covered interest rate parity · FX forwards and points · The carry trade and uncovered parity · Triangular arbitrage · FX options and the volatility smile (brief) · Summary

  5. 05
    Commodities & Convenience Yield

    Includes: Why this matters · Spot vs futures and the cost of carry · Convenience yield · Contango and backwardation · Storage and seasonality · Roll yield and total return · Commodity indices · Summary

  6. 06
    Money Markets & Repo

    Includes: Why this matters · The money market instruments (T-bills, CP, CDs) · Day-count conventions · Repo and reverse repo mechanics · Haircuts and collateral · The repo rate and funding · SOFR and the transition from LIBOR · Summary

M02

Core Instruments

4 lessons

Quants are paid to model instruments. You can't model what you don't understand — bonds, equities, and the full derivatives zoo each have economics that drive how their prices behave under stress.

  1. 01
    Bonds & Fixed Income

    Includes: What Is a Bond? · Anatomy of a Bond · Bond Pricing · Yield to Maturity (YTM) · Duration: Measuring Interest Rate Sensitivity · Convexity: The Curvature · Credit Risk Basics · Types of Bonds · Interest Rate Sensitivity in Practice · Summary

  2. 02
    Equities & Returns

    Includes: What Is an Equity? · Price Return vs Total Return · Simple vs Log Returns · Dividends · Market Indices · Volatility · Summary

  3. 03
    Derivatives Overview

    Includes: What Is a Derivative? · Forwards · Futures · Options · Swaps · Hedging Intuition · How Derivatives Are Used in Practice · Summary

  4. 04
    Swaps & Swap Pricing

    Includes: Why this matters · The interest-rate swap mechanics · Fixed vs floating legs · Valuing a swap from discount factors · The par swap rate · Currency swaps · Swap risk (DV01) and uses · Summary

M03

Risk & Return

6 lessons

Every quant decision is a trade-off between risk and reward. Portfolio theory and factor models give you the language to express that trade-off precisely — and the maths that lets you optimise it.

  1. 01
    Risk & Return Trade-Off

    Includes: The Fundamental Relationship · Expected Return · Volatility as a Measure of Risk · Risk Premium · The Sharpe Ratio · Diversification Intuition · Other Risk Measures · Summary

  2. 02
    Portfolio Theory

    Includes: The Big Idea · Portfolio Return · Portfolio Variance · The Efficient Frontier · Correlation Effects · The Capital Allocation Line · The Diversification Mathematics · Limitations of Mean-Variance · Summary

  3. 03
    CAPM & Factor Models

    Includes: From Portfolios to Pricing · Systematic vs Idiosyncratic Risk · Beta (β) · The CAPM · The Security Market Line (SML) · CAPM Limitations · Multi-Factor Models · Practical Applications · Summary

  4. 04
    Multi-Factor Models (Fama-French)

    Includes: Why this matters · From CAPM to multi-factor · The Fama-French three-factor model · Size (SMB) and value (HML) factors · Momentum and the five-factor extension · Estimating factor loadings by regression · Factor investing in practice · Summary

  5. 05
    The Black-Litterman Model

    Includes: Why this matters · Problems with naive mean-variance · Reverse optimisation and equilibrium returns · Expressing views (P, Q, Omega) · The Black-Litterman master formula · Blending views with the prior · Practical calibration · Summary

  6. 06
    Risk Parity & Portfolio Construction

    Includes: Why this matters · Equal weighting vs equal risk · Marginal and total risk contributions · The risk parity condition · The naive inverse-volatility portfolio · Leverage and risk parity · Comparison to 60/40 · Summary

M04

Derivatives & Pricing

8 lessons

This is where quants really earn their keep. From simple forwards through to Black–Scholes, you'll learn to price contingent claims, understand replication, and read the Greeks like a trader reads a screen.

  1. 01
    Forwards & Futures Pricing

    Includes: The No-Arbitrage Principle · Forward Price: The Cost-of-Carry Model · Forwards on Assets with Known Income · Futures Pricing · Basis and Basis Risk · Practical Applications · Commodity Futures: Additional Considerations · Summary

  2. 02
    Options Fundamentals

    Includes: Why Options Are Special · Calls and Puts — Review and Depth · Payoff Diagrams · Intrinsic Value vs Time Value · Moneyness · Put-Call Parity · European vs American Options · Option Strategies · Summary

  3. 03
    Binomial Option Pricing

    Includes: From Intuition to Pricing · The One-Step Model · Risk-Neutral Probability · Multi-Step Trees · Convergence to Black-Scholes · Pricing American Options · Summary

  4. 04
    Black-Scholes Model

    Includes: The Most Famous Formula in Finance · Model Assumptions · The Formula · Understanding the Formula · Lognormal Price Dynamics · Risk-Neutral Valuation · Key Inputs · Implied Volatility · Limitations of Black-Scholes · Summary

  5. 05
    The Greeks

    Includes: Why Sensitivities Matter · Delta (Δ) · Gamma (Γ) · Vega (ν) · Theta (Θ) · Rho (ρ) · The Greeks in Practice · Summary

  6. 06
    Exotic Options

    Includes: Why this matters · Path-dependent vs path-independent · Barrier options (knock-in/knock-out) · Asian options · Digital/binary options · Lookback and cliquet options · Pricing approaches · Summary

  7. 07
    Dynamic Hedging & Replication

    Includes: Why this matters · The replicating portfolio · Delta hedging · Rebalancing and discrete hedging error · Gamma and the cost of convexity · Transaction costs · P&L attribution of a hedged book · Summary

  8. 08
    Monte Carlo & PDE Pricing

    Includes: Why this matters · Risk-neutral simulation of GBM · Monte Carlo option pricing · Standard error and convergence · Variance reduction recap · The PDE (finite-difference) alternative · Choosing MC vs PDE · Summary

M05

Risk Management

5 lessons

Pricing without risk management is gambling with extra steps. Volatility models, VaR, and credit risk frameworks are how firms decide what they can stomach losing — and how they explain it to regulators.

  1. 01
    Volatility Modelling

    Includes: The Central Role of Volatility · Historical Volatility · Implied Volatility · The Volatility Smile and Skew · Realised vs Implied Volatility · Volatility Clustering · Exponentially Weighted Moving Average (EWMA) · Summary

  2. 02
    Value at Risk

    Includes: Quantifying Portfolio Risk · What Is Value at Risk? · Parametric (Normal) VaR · Historical Simulation VaR · Expected Shortfall (CVaR) · Tail Risk · Coherent Risk Measures · VaR in Practice · Summary

  3. 03
    Credit Risk

    Includes: What Is Credit Risk? · Key Concepts · Credit Spreads · Credit Rating Agencies · Structural Models (Merton Model — Intuition) · Reduced-Form Models (Intuition) · Credit Default Swaps (CDS) · Credit Risk in Quantitative Finance · Summary

  4. 04
    Expected Shortfall, Backtesting & Stress Testing

    Includes: Why this matters · From VaR to Expected Shortfall · Coherent risk measures · Computing ES historically and parametrically · Backtesting VaR (Kupiec/traffic-light) · Stress testing and scenario analysis · The Basel FRTB shift to ES · Summary

  5. 05
    XVA & Counterparty Risk

    Includes: Why this matters · Counterparty credit risk and default · Expected exposure and PFE · CVA — credit valuation adjustment · DVA, FVA and the XVA family · Wrong-way risk · Regulation and capital · Summary

M06

Structured Products

3 lessons

Structured notes are where pricing, risk, and product design collide. Understanding them is a fast track to seeing how multiple parts of the curriculum compose into a real, sellable product on a bank's balance sheet.

  1. 01
    Structured Notes: Understanding

    Includes: What Is a Structured Note? · Structured Rates: Interest That Follows Rules · Credit-Linked Notes: Lending With a Catch · How Structured Rates and Credit Notes Combine · Reading a Term Sheet · Summary

  2. 02
    Structured Notes: Modelling

    Includes: From Product to Numbers · Cashflows Over Time · Rule-Based Interest · Credit Events · Scenario Analysis · Modelling in Practice · Summary

  3. 03
    Structured Notes: Valuation

    Includes: Is This Actually a Good Deal? · Expected Returns vs Promised Returns · Downside Risk · Stress Testing · Explaining the Product: The Transparency Test · Putting It All Together: A Valuation Framework · Summary

M07

Quantitative & Advanced

3 lessons

The frontier of quant finance: how prices are made on the order book, how strategies are systematised, and the risk-neutral framework that ties pricing theory together. This is the material that separates analysts from quants.

  1. 01
    Market Microstructure

    Includes: How Trading Actually Happens · Order Books · Bid-Ask Spread · Order Types · Slippage · Liquidity · Transaction Costs · Market Making · Summary

  2. 02
    Algorithmic Trading

    Includes: Rules, Not Gut Feelings · What Is Algorithmic Trading? · Alpha Signals · Backtesting · Overfitting · Signal Decay · Execution Risk · Risk Management in Systematic Trading · Summary

  3. 03
    Risk-Neutral Pricing

    Includes: The Theoretical Backbone · What Is Arbitrage? · Arbitrage-Free Markets · The Risk-Neutral Measure · Discounted Asset Prices Are Martingales · The Replication Principle · Pricing as Expectation Under Risk-Neutral Measure · Connecting the Dots · Limitations and Real-World Considerations · Summary

M08

Fixed Income & Rates

5 lessons

Rates desks are the largest part of most banks. Curve construction, duration, short-rate and market models, and the derivatives built on them are core quant territory — and the maths is some of the most elegant in finance.

  1. 01
    Yield Curve Construction

    Includes: Why this matters · Discount factors, zero rates and forward rates · Bootstrapping the curve from instruments · Interpolation choices · Multi-curve (OIS discounting) post-2008 · Curve risk and key-rate durations · Summary

  2. 02
    Duration & Convexity

    Includes: Why this matters · Macaulay duration · Modified duration · DV01 / PV01 · Convexity · The duration-convexity price approximation · Hedging interest-rate risk · Summary

  3. 03
    Short-Rate Models

    Includes: Why this matters · The short rate and the bank account · Vasicek model · Cox-Ingersoll-Ross (CIR) · Mean reversion and calibration · Bond pricing under affine models · Limitations · Summary

  4. 04
    HJM & the LIBOR Market Model

    Includes: Why this matters · Modelling the whole forward curve · The Heath-Jarrow-Morton framework · The HJM drift condition (no-arbitrage) · The LIBOR Market Model (BGM) · Caplets, Black's formula and calibration · Choosing a model · Summary

  5. 05
    Interest Rate Derivatives

    Includes: Why this matters · FRAs and interest-rate futures · Caps, floors and collars · Swaptions · Bermudan and exotic IR products · Pricing approaches · Risk management of an IR book · Summary

M09

Credit Risk & Derivatives

4 lessons

Credit is where probability of default meets pricing. CDS, structural and reduced-form models, and the correlation products at the heart of 2008 are essential for anyone touching credit, counterparty risk, or capital.

  1. 01
    Credit Default Swaps

    Includes: Why this matters · CDS mechanics and cash flows · The CDS spread · The credit triangle (spread ≈ hazard × LGD) · Mark-to-market and the ISDA model · Index CDS (CDX/iTraxx) · Uses and risks · Summary

  2. 02
    Structural Credit Models (Merton)

    Includes: Why this matters · The Merton model: equity as a call on assets · Default at maturity · Distance to default · From distance-to-default to PD · The KMV approach · Strengths and weaknesses · Summary

  3. 03
    Reduced-Form Credit Models

    Includes: Why this matters · Hazard rates and the intensity of default · Survival probability · Pricing risky bonds · Calibrating intensity from CDS · Comparison with structural models · Summary

  4. 04
    CDOs & Default Correlation

    Includes: Why this matters · Securitisation and tranching · The waterfall · Default correlation and the Gaussian copula · Base correlation and the 2008 lessons · Tranche sensitivities (correlation risk) · Summary

M10

Advanced Volatility

4 lessons

The vol surface is where the hardest, best-paid quant work lives. Local and stochastic volatility, the smile, and variance products are how derivatives desks price and hedge beyond textbook Black-Scholes.

  1. 01
    Local Volatility

    Includes: Why this matters · The limitation of constant Black–Scholes vol · Local volatility as a deterministic function $\sigma(S,t)$ · Dupire's equation · Calibrating to the implied surface · Strengths and the dynamics critique · Summary

  2. 02
    Stochastic Volatility & the Heston Model

    Includes: Why this matters · Why volatility itself is random · The Heston model SDEs · The variance process (CIR) · The correlation and the skew · Semi-analytic pricing via the characteristic function · Calibration · Summary

  3. 03
    The Volatility Smile & Surface

    Includes: Why this matters · Implied volatility recap · The smile and skew · The term structure of volatility · The implied vol surface · Sticky strike vs sticky delta · Arbitrage constraints on the surface · Summary

  4. 04
    Variance Swaps & the VIX

    Includes: Why this matters · Realised vs implied variance · The variance swap payoff · Replication with a strip of options · The VIX construction · Volatility as an asset class · Summary

M11

Systematic Trading

5 lessons

This is the buy-side quant's craft: turning signals into a live, risk-managed book. Signal construction, honest backtesting, execution, and stat-arb are the difference between a backtest and a strategy that actually makes money.

  1. 01
    Signal Construction

    Includes: Why this matters · From raw data to alpha signals · Cross-sectional vs time-series signals · Normalisation and winsorisation (z-scores) · Combining signals · Decay and turnover · Avoiding look-ahead bias · Summary

  2. 02
    Backtesting Methodology

    Includes: Why this matters · The anatomy of a backtest · In-sample vs out-of-sample · Overfitting and the multiple-testing problem · The deflated Sharpe ratio · Transaction costs and capacity · Common biases (survivorship, look-ahead) · Summary

  3. 03
    Execution & Transaction Costs

    Includes: Why this matters · The cost of trading: spread, impact, fees · Market impact models (square-root law) · Implementation shortfall · Execution algorithms (TWAP, VWAP, POV) · Slippage measurement · Capacity and decay · Summary

  4. 04
    Statistical Arbitrage

    Includes: Why this matters · Pairs trading · Cointegration and the spread · Mean-reversion and the Ornstein-Uhlenbeck spread · Entry/exit z-score rules · Risk management of a stat-arb book · Decay of edges · Summary

  5. 05
    Systematic Portfolio Construction

    Includes: Why this matters · From signals to positions · Volatility targeting · Position sizing and the Kelly criterion · Constraints (gross, net, sector) · Rebalancing and costs · Combining strategies · Summary

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