Linear Algebra & Differential Equations for Quants : Interview Playbook

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About this resource

Most quant candidates “know” linear algebra and differential equations.

Very few know why they matter on a trading or risk desk.

This guide is written to close that gap.

Traditional textbooks teach vectors, matrices, eigenvalues, ODEs, and PDEs as abstract mathematics.

Interview prep materials reduce them to memorized formulas.

Neither explains how these objects actually show up in models, risk systems, calibration failures, or PnL attribution.

This note reframes Linear Algebra and Differential Equations as decision tools, not academic topics.

• What makes this different
• This is a desk-first mathematical guide designed for:
• Quant researchers
• Risk and model validation professionals
• Aspiring quants preparing for interviews
• Practitioners who want intuition, not proofs
• Every concept follows a consistent structure:
• Math → Geometry → Model → Risk → PnL

• What you will learn
• Linear Algebra (Applied, Not Abstract)
• Vectors as exposures and Greeks
• Norms as risk constraints and capital limits
• Eigenvalues as regimes, instability, and crisis indicators
• Condition numbers as calibration fragility
• PCA failures when eigenvalue gaps vanish
• Mahalanobis distance vs naïve risk metrics
• Differential Equations (Why They Exist in Finance)
• ODEs as mean-reversion, stability, and equilibrium forces
• PDEs as no-arbitrage constraints, not math artifacts
• Boundary conditions as product payoffs
• Free boundaries in American/Bermudan options
• Why PDEs fail in high dimensions
• When Monte Carlo dominates and why
• Numerics & Stability
• Euler vs exact schemes (and why Euler lies)
• Stability regions explained geometrically
• Why “model works in calm markets but explodes in stress”
• Sensitivity blow-ups driven by poor conditioning
• Interview & Desk Translation
• How to answer “why does this model break?”
• How eigenvalues explain regime shifts
• How gradients connect to Greeks
• How PDE choice determines hedging behavior
• What this is NOT
• No long proofs
• No measure theory
• No academic formalism for its own sake

This is mathematics as used by quants, not mathematicians.

• Who this is for
• Candidates who already studied the basics but lack intuition
• Professionals who want to understand why models fail
• Anyone who wants math to feel visual, geometric, and practical

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Disclaimer

This material is provided strictly for educational purposes.

It does not constitute financial advice, trading advice, or investment recommendations.

All examples are simplified for learning and may omit real-world constraints.

The author and publisher assume no responsibility for decisions made using this material.

What you get

• Instant digital delivery by email after purchase
• Written by a practising quantitative risk modeller
• Desk-focused material, not textbook theory

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