Phase 0 Orientation and Diagnostic Assessment6/6 published What quantitative finance is, what quantitative developers actually do, how the profession is structured, and a diagnostic that maps your starting point.
foundation
The landscape of quantitative finance and where engineers fit into it.
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What Quantitative Finance Is20m finance fundamentals What a Quantitative Developer Actually Does professional skills Quant Developer vs Research vs Trading vs Software Engineering professional skills Banks, Asset Managers, Hedge Funds and Prop Trading Firms finance fundamentals Front Office, Middle Office and Back Office finance fundamentals Quant Teams and How Financial Software Reaches Production software engineering
Phase 1 Mathematics From Absolute Zero78/78 published Arithmetic through stochastic calculus: the complete mathematical spine, sequenced by prerequisites, with interactive visualisations at every step.
foundation
Numbers, operations, fractions, percentages, powers, logs, estimation and mental calculation.
Tracks: A · B · C · D · E
Number Systems and the Four Operations25m arithmetic Fractions, Decimals and Ratios arithmetic Percentages, Percentage Change and Financial Arithmetic arithmetic Powers, Roots, Exponents and Logarithms arithmetic Estimation, Approximation and Mental Arithmetic arithmetic Divisibility, Primes, GCD and LCM arithmetic foundation
From unknowns to equations: variables, expressions, order of operations and inequalities.
Tracks: A · B · C · D · E
Variables, Constants and Expressions22m algebra Solving Linear Equations algebra Inequalities and Intervals algebra Translating Problems Into Equations algebra core
Quadratics, polynomials, functions, exponentials, logarithms and sequences.
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Quadratic Equations and Parabolas28m algebra Polynomials and Factorisation algebra Simultaneous Equations algebra Functions, Composition and Inverses algebra Exponential and Logarithmic Functions algebra Sequences, Series and Induction algebra core
Coordinate geometry, triangles, the unit circle and periodic functions.
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Coordinate Geometry and Straight Lines24m geometry trig Triangles and Trigonometric Ratios geometry trig The Unit Circle and Radians geometry trig Trigonometric Identities and Graphs geometry trig core
Function behaviour, limits intuition, graph transformations and mathematical modelling.
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Function Behaviour and Transformations24m algebra Limits and Continuity — Intuition calculus Growth Models and Asymptotes algebra Mathematical Modelling Workflow quant modelling core
Limits made precise, the derivative, rules of differentiation and optimisation.
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Limits Formalised28m calculus The Derivative and the Difference Quotient calculus Power, Product, Quotient and Chain Rules calculus Derivatives of Exponential, Logarithmic and Trigonometric Functions calculus Critical Points, Maxima, Minima and Concavity calculus Taylor Approximation calculus core
Antiderivatives, the fundamental theorem, techniques of integration and applications.
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Integration and the Fundamental Theorem28m calculus Substitution, Parts and Partial Fractions calculus Numerical Integration calculus Improper Integrals and Probability Densities calculus advanced
Partial derivatives, gradients, Hessians, multiple integrals and constrained optimisation.
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Functions of Several Variables and Partial Derivatives28m calculus Gradient, Directional Derivatives and the Hessian calculus Double and Triple Integrals calculus Constrained Optimisation and Lagrange Multipliers optimization core
Vectors, matrices, decompositions, eigenvalues and the covariance matrix — the workhorse mathematics of quant finance.
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Vectors and Vector Spaces26m linear algebra Matrices and Matrix Operations linear algebra Systems of Linear Equations and Gaussian Elimination linear algebra Determinants, Rank and Linear Independence linear algebra Eigenvalues, Eigenvectors and Diagonalisation linear algebra Orthogonality, Projections and QR linear algebra SVD, Covariance Matrices and Positive Definiteness linear algebra core
Sets, logic, counting, graphs and modular arithmetic — the mathematics of computing.
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Sets, Relations and Propositional Logic25m discrete math Counting, Permutations and Combinations discrete math Graph Theory and Trees discrete math Modular Arithmetic and Recurrence Relations discrete math advanced
Convexity, gradient methods, linear and quadratic programming, duality and KKT.
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Objective Functions, Constraints and Convexity26m optimization Gradient Descent, Newton's Method and Coordinate Descent optimization Linear and Quadratic Programming optimization Lagrangian Duality and KKT Conditions optimization advanced
Floating point, error, stability, root finding and the numerical mindset.
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Floating-Point Numbers and IEEE 75428m numerical analysis Rounding Error, Cancellation and Numerical Stability numerical analysis Root Finding: Bisection, Newton-Raphson, Secant numerical analysis Interpolation and Numerical Differentiation numerical analysis Solving Linear Systems Numerically numerical analysis core
From counting to conditional probability, Bayes' theorem, expectation and the central limit theorem.
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Probability Spaces and Events26m probability Conditional Probability and Bayes' Theorem probability Random Variables, PMFs and CDFs probability Expectation, Variance and Covariance probability Law of Total Probability and Conditional Expectation probability Markov, Chebyshev, the Laws of Large Numbers and the CLT probability core
The distributions that matter in quantitative work and when to use each.
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Bernoulli, Binomial, Geometric and Poisson27m distributions The Normal Distribution distributions Uniform, Exponential, Gamma, Beta and Log-Normal distributions Chi-Square, t, F and the Multivariate Normal distributions advanced
Markov chains, martingales, Brownian motion and Poisson processes.
Tracks: B · C · D
Markov Chains and Transition Matrices28m stochastic processes Martingales and Stopping Times stochastic processes Brownian Motion and Random Walks stochastic processes Poisson Processes and Jump Processes stochastic processes specialist
Itô calculus, SDEs, change of measure and the road to Black-Scholes.
Tracks: B · D
Quadratic Variation and the Itô Integral30m stochastic calculus Itô's Lemma and Stochastic Differential Equations stochastic calculus Change of Measure, Risk-Neutrality and Feynman-Kac stochastic calculus
Phase 2 Computer Science Fundamentals31/31 published How computers actually work: hardware, Linux, operating systems, architecture, networks, databases and the discipline of software engineering.
foundation
Hardware, binary, two's complement, floating point and how programs execute.
Tracks: A · B · C · D · E
What a Computer Is: Hardware and Software22m computer fundamentals Binary, Hexadecimal and Number Representation computer fundamentals Signed Integers and Two's Complement computer fundamentals How Programs Execute: From Source to Silicon computer fundamentals foundation
The terminal, the filesystem, processes, permissions, pipes and shell scripting.
Tracks: A · B · C · D · E
The Terminal and the Filesystem Hierarchy24m linux Permissions, Users and Processes linux Pipes, Redirection and Shell Scripting linux SSH, Package Managers and System Monitoring linux core
Processes, threads, scheduling, virtual memory and synchronisation.
Tracks: B · C · D · E
Processes, Threads and Scheduling26m operating systems Virtual Memory, Paging and Memory Allocation operating systems Race Conditions, Deadlocks and Synchronisation Primitives operating systems System Calls, Interrupts and File I/O operating systems core
Pipelines, caches, branch prediction and the hardware realities behind program performance.
Tracks: B · C · D
Instruction Sets, Registers and Pipelines26m computer architecture The Cache Hierarchy and Memory Latency computer architecture Branch Prediction and Out-of-Order Execution computer architecture SIMD, NUMA and Performance Counters computer architecture core
From the OSI model to sockets, multicast and the latency properties of networks.
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Network Models, IP Addressing and DNS25m networking TCP, UDP and Multicast networking Socket Programming networking Latency, Throughput, Jitter and Packet Loss networking core
Relational modelling, SQL, transactions, indexes and query optimisation.
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Relational Model and SQL Foundations26m databases Joins, Aggregations and Window Functions databases Transactions, ACID, Isolation and Indexes databases Time-Series Data, Columnar Storage and Redis Fundamentals databases core
Git, testing, CI/CD, build systems, design patterns and production debugging.
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Git, Branching and Code Review25m software engineering Testing: Unit, Integration and TDD software engineering Build Systems, CMake and Toolchains cpp engineering API Design, SOLID and Design Patterns software engineering advanced
RPC, queues, replication, consistency and the vocabulary of large financial platforms.
Tracks: A · D · E
Client-Server Systems, RPC, REST and Message Queues26m distributed systems Replication, Partitioning and Consistency distributed systems Fault Tolerance, Idempotency and Observability distributed systems
Phase 3 Programming From Zero21/21 published No assumptions: from your first variable to production-grade Python and scientific computing.
foundation
What programming means: variables, control flow, functions, arrays and debugging.
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What Programming Means20m programming fundamentals Variables, Types and Operators programming fundamentals Conditionals and Loops programming fundamentals Functions, Parameters and Scope programming fundamentals Arrays, Strings and Debugging programming fundamentals foundation
The language of quantitative research: syntax, data structures, OOP and the ecosystem.
Tracks: A · B · C · D · E
Getting Started With Python22m python Lists, Dicts, Sets and Tuples python Control Flow, Functions and Comprehensions python Files, Exceptions and Modules python Object-Oriented Python python Iterators, Generators, Decorators and Context Managers python advanced
The object model, memory, the GIL, concurrency, profiling and C++ interop.
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The Python Object Model and Mutability26m python The GIL, Threading and Multiprocessing python Asyncio and Concurrent I/O python Profiling, Benchmarking and Performance Work python C Extensions and pybind11 python core
NumPy, Pandas, SciPy, Matplotlib and Jupyter applied to real quantitative problems.
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NumPy Arrays, Broadcasting and Vectorisation27m scientific python Linear Algebra and Random Sampling in NumPy scientific python Pandas DataFrames and Time-Series Processing scientific python SciPy: Optimisation, Integration and Statistics scientific python Matplotlib, Jupyter and Communicating Results scientific python
Phase 4 Modern C++ — The Central Engineering Course46/46 published Nine levels from first compilation to production engineering: the language that powers pricing libraries and trading systems.
foundation
Compilation, types, control flow, functions, references, pointers and structs.
Tracks: B · C · D
Compilation, Source Files and Headers26m cpp Primitive Types, Variables and Conversions cpp Control Flow, Functions and Overloading cpp References and Pointers cpp Arrays, std::string and std::string_view cpp Structs, Enums and Namespaces cpp core
Classes, RAII-friendly design, inheritance, polymorphism and the object model.
Tracks: B · C · D
Classes, Encapsulation and Constructors27m cpp Operator Overloading and Special Members cpp Inheritance and Access Control cpp Virtual Functions, Polymorphism and Virtual Destructors cpp Object Construction, Destruction and Slicing cpp core
The deepest layer of the course: stack, heap, ownership, RAII and smart pointers.
Tracks: B · C · D
Stack, Heap and Static Storage27m cpp memory Dynamic Allocation: new, delete and malloc cpp memory Dangling Pointers, Leaks and Undefined Behaviour cpp memory RAII and Resource Management cpp memory std::unique_ptr and Ownership cpp memory std::shared_ptr, std::weak_ptr and Shared Ownership cpp memory Rule of Three, Five and Zero cpp memory Move Semantics, Rvalues and Perfect Forwarding cpp memory core
Containers, iterators, algorithms and their complexity and memory characteristics.
Tracks: B · C · D
std::vector, std::array and Growth Behaviour27m cpp stl Maps, Sets and Their Hashed Counterparts cpp stl Stacks, Queues, Deques and Priority Queues cpp stl Iterators, Invalidation and the Algorithm Library cpp stl Container Complexity, Allocators and Memory Characteristics cpp stl advanced
Templates, concepts, lambdas, value categories and the modern toolbox.
Tracks: B · C · D
Function and Class Templates28m cpp advanced Concepts, Type Traits and SFINAE cpp advanced Lambdas, std::optional, std::variant and std::tuple cpp advanced constexpr, consteval and Compile-Time Programming cpp advanced Value Categories, auto and decltype cpp advanced std::chrono, std::filesystem, Ranges and Coroutines cpp advanced advanced
What happens beneath the syntax: linkage, ABI, vtables, calling conventions and optimisation.
Tracks: B · C
Translation Units, Linkage and Name Mangling27m cpp internals vtables, Object Layout, Alignment and Padding cpp internals Static vs Dynamic Linking and the ABI cpp internals What the Compiler Does: Inlining, RVO and UB Consequences cpp internals advanced
Threads, mutexes, atomics, memory ordering and the correctness arguments behind lock-free code.
Tracks: B · C · D
std::thread, jthread and Shared State27m concurrency Mutexes, Locks and Condition Variables concurrency Futures, Promises, Async and Thread Pools concurrency Atomics and Memory Ordering concurrency Lock-Free Programming and Its Correctness Arguments concurrency specialist
Cache locality, data-oriented design, SIMD, benchmarking and the measurement discipline.
Tracks: C · D
Cache Locality and Data-Oriented Design28m cpp performance Memory Pools, Custom Allocators and Alignment cpp performance Branchless Code and SIMD Fundamentals cpp performance Benchmarking, prof, Sanitisers and Latency Percentiles cpp performance advanced
CMake, sanitizers, testing frameworks, CI and production debugging.
Tracks: B · C
Compilers, Build Tools and Static Analysis26m cpp engineering GoogleTest, Benchmarking Frameworks and CI Pipelines cpp engineering GDB, Crash Analysis and Production Debugging cpp engineering
Phase 5 Data Structures and Algorithms18/18 published A dedicated problem-solving academy: complexity, core structures, algorithmic techniques and quantitative interview patterns.
core
Big-O and friends, amortised analysis and recurrence relations.
Tracks: A · B · C · D · E
Time and Space Complexity, Big-O Notation26m complexity Amortised Analysis and Best/Worst Cases complexity Recurrence Relations and Recursion Trees complexity core
Arrays to Fenwick trees: the structures every quant engineer must own.
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Arrays, Dynamic Arrays and Linked Lists26m dsa Stacks, Queues and Deques dsa Hash Tables and Hash Maps dsa Binary Trees and Binary Search Trees dsa Heaps, Tries, Segment Trees and Fenwick Trees dsa core
Searching, sorting, two pointers, graphs, dynamic programming and string algorithms.
Tracks: A · B · C · D · E
Binary Search and Sorting Algorithms27m algorithms Two Pointers, Sliding Windows and Prefix Sums algorithms Greedy Algorithms and Backtracking algorithms BFS, DFS and Topological Sorting algorithms Dijkstra, Bellman-Ford and Minimum Spanning Trees algorithms Dynamic Programming algorithms advanced
Streaming statistics, order books, simulation and the patterns quant interviews actually use.
Tracks: B · C · D
Streaming Algorithms and Running Statistics27m algorithms Order-Book Data Structures dsa Event Simulation and Monte Carlo Optimisation algorithms Randomised Algorithms and Reservoir Sampling algorithms
Phase 6 Aptitude, Logic and Problem-Solving12/12 published The numerical and logical fluency that trading firms screen for, plus a framework for attacking unfamiliar problems.
foundation
Percentages, ratios, weighted averages and speed arithmetic for assessments.
Tracks: A · B · C · D · E
Percentages, Ratios and Averages Under Time Pressure24m aptitude Profit, Loss, Compound Interest and Growth Rates aptitude Number Patterns, Sequences and Estimation aptitude core
Deduction, constraints, truth tables and structured puzzles.
Tracks: A · B · C · D · E
Deductive and Inductive Reasoning24m logical reasoning Constraint Puzzles and Arrangements logical reasoning Conditional Logic and Truth Tables logical reasoning core
Dice, cards, expected value, Monty Hall, optimal stopping and gambler's ruin.
Tracks: B · C · D
Classic Puzzles: Monty Hall, Birthday and Card Problems26m probability Expected Value in Games and Decisions probability Optimal Stopping and Secretary Problems probability Random Walks and Gambler's Ruin probability core
A repeatable ten-step process for unfamiliar problems, plus practice that cannot be memorised.
Tracks: A · B · C · D · E
The Ten-Step Problem-Solving Framework25m aptitude Unfamiliar Problem Drills aptitude
Phase 7 Financial Markets and Finance38/38 published Finance taught from zero: markets, instruments, fixed income, options, portfolios, risk and microstructure.
foundation
Money, interest, the time value of money, NPV and IRR.
Tracks: A · B · C · D · E
Money, Banking and Financial Institutions22m finance fundamentals Time Value of Money: PV, FV and Compounding finance fundamentals NPV, IRR and Discount Rates finance fundamentals Inflation, Real Returns and Nominal vs Real finance fundamentals foundation
Exchanges, order types, bid-ask spreads, liquidity and execution.
Tracks: A · B · C · D · E
Primary and Secondary Markets, Exchanges and OTC24m markets Bid, Ask, Spread and Liquidity markets Market, Limit and Stop Orders; Slippage and Execution markets Brokers, Dealers, Market Makers and Order Flow markets core
Equities to credit derivatives: what the instruments are and how they behave.
Tracks: A · B · C · D · E
Equities, ETFs, Mutual and Index Funds24m instruments Bonds, T-Bills and Government Securities instruments Futures and Forwards instruments Swaps, FX Instruments and Credit Derivatives instruments core
Bond pricing, yields, duration, convexity and the term structure.
Tracks: B
Bond Pricing, Yields and Yield to Maturity27m fixed income Duration, Modified Duration and Convexity fixed income Yield Curves, Spot and Forward Rates fixed income Interest-Rate Sensitivity and Term Structure Models Overview fixed income core
Payoffs, put-call parity, binomial and Black-Scholes models, the Greeks and volatility.
Tracks: B · C
Calls, Puts and Payoff Diagrams26m options Intrinsic Value, Time Value and Put-Call Parity options The Binomial Model options The Black-Scholes Model options Delta, Gamma, Theta, Vega, Rho and Hedging options Implied Volatility, Smiles and Volatility Surfaces options core
Mean-variance theory, factor models, performance ratios and attribution.
Tracks: A
Diversification and the Efficient Frontier27m portfolio Mean-Variance Optimisation, CAPM, Beta and Alpha portfolio Sharpe, Sortino and Information Ratios portfolio Factor Models, Rebalancing and Attribution portfolio core
VaR, expected shortfall, stress testing and the risk toolchain.
Tracks: A · B · E
Market, Credit, Liquidity, Operational and Model Risk25m risk Value at Risk: Historical, Parametric and Monte Carlo risk Expected Shortfall, Stress Testing and Scenario Analysis risk Drawdown, Exposure, Sensitivity and Hedging risk advanced
Limit order books, matching, spread dynamics and adverse selection.
Tracks: C
Limit Order Books and Market Depth27m microstructure Matching Engines and Price-Time Priority microstructure Spread Dynamics, Market Impact and Liquidity Provision microstructure Adverse Selection, Order Flow and Trade Classification microstructure advanced
Biases, costs, walk-forward methodology and honest strategy evaluation.
Tracks: A · D
Historical Data, OHLCV and Survivorship Bias26m backtesting Look-Ahead Bias, Transaction Costs and Slippage backtesting Overfitting, Train-Test Separation and Walk-Forward Testing backtesting Strategy Evaluation and Risk-Adjusted Performance backtesting
Phase 8 Statistics, Time Series and Quantitative Modelling14/14 published Estimation, testing, regression, ARIMA, GARCH and disciplined quantitative modelling.
core
Sampling, MLE, hypothesis testing, regression and the bootstrap.
Tracks: A · B · D
Descriptive Statistics, Sampling and Estimators26m statistics Maximum Likelihood and Confidence Intervals statistics Hypothesis Testing, p-Values and Power statistics Linear, Multiple and Logistic Regression statistics Bootstrap and Permutation Testing statistics advanced
Stationarity, ARIMA, GARCH and forecast evaluation.
Tracks: A · B · D
Trend, Seasonality, Stationarity and Differencing27m time series AR, MA, ARMA and ARIMA Models time series Volatility Clustering, ARCH and GARCH time series Cointegration, Unit Roots and Forecast Evaluation time series advanced
The useful foundations: supervised learning, regularisation, leakage and deployment.
Tracks: A · D
Supervised and Unsupervised Learning Foundations27m machine learning Decision Trees, Random Forests and Gradient Boosting machine learning Data Leakage, Concept Drift and Model Deployment machine learning
Phase 9 Numerical Finance and Pricing Engineering5/5 published Build real pricing engines: binomial trees, Black-Scholes, Monte Carlo, finite differences and calibration — in C++ and Python.
specialist
From forwards to finite-difference PDE pricing with production-quality numerics.
Tracks: B
Forward and Futures Pricing27m pricing Building a Binomial Pricing Engine pricing Monte Carlo Pricing and Variance Reduction pricing Finite-Difference PDE Pricing pricing Calibration, Implied Volatility and Model Validation pricing
Phase 10 Quantitative Engineering and System Design14/14 published How real financial systems are built: trading infrastructure, low-latency design, data platforms and production engineering.
advanced
Feed handlers, OMS, matching engines, risk checks and exchange connectivity.
Tracks: B · C · E
Market-Data Ingestion and Feed Handlers27m trading systems Order Management, Trade Capture and Position Keeping trading systems Matching Engines, Strategy Execution and Risk Checks trading systems Exchange Connectivity, Sessions and Reconciliation trading systems specialist
Latency budgets, kernel overheads, kernel-bypass concepts and measurement discipline.
Tracks: C
Latency Budgets and Where Time Goes27m low latency Busy Polling, CPU Affinity and Allocation Control low latency Kernel-Bypass Concepts: DPDK and Onload low latency Benchmarking Methodology and Latency Distributions low latency advanced
Tick storage, normalisation, streaming pipelines and data quality.
Tracks: A · E
Tick-Data Storage and Time-Series Databases26m data infrastructure Market-Data Normalisation, Validation and ETL data infrastructure Streaming Systems and Distributed Computation data infrastructure advanced
Monitoring, reliability, deployment and security for financial systems.
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Monitoring, Logging, Metrics and Alerting26m production engineering Fault Tolerance, Recovery and Deployment Discipline production engineering Security, Configuration and Versioning production engineering