Numerical methods
Root finding, finite differences, quadrature and Monte Carlo, and how their errors behave.
16 planned
No page in this subject is open yet. The planned list below shows what is coming, in learning order.
Planned
In learning order. These are not pages yet.
- Floating point: why 0.1 + 0.2 isn't 0.3Intro
- Interpolation and splinesIntro
- Condition numbers: when small input errors blow upAdvanced undergrad
- Finite differences: approximating derivatives on a gridIntro
- Numerical integration: trapezoid vs SimpsonIntro
- Inverse transform sampling: from uniform to any distributionIntro
- Bisection: trapping a rootIntro
- Euler's method and the step sizeIntro
- Explicit finite differences for the heat equation and the stability limitAdvanced undergrad
- Computing eigenvalues: the power method and QR iterationAdvanced undergrad
- The discrete Fourier transform and the FFTAdvanced undergrad
- Newton's method: fast, until it isn'tIntro
- Implicit schemes and Crank-NicolsonAdvanced undergrad
- Conjugate gradient and Krylov methodsGraduate
- Monte Carlo integration and the 1/√n errorIntro
- Pseudo-random vs quasi-random pointsGraduate
How it connects
Builds on Linear algebra Calculus Differential equations Probability Complex analysis Real analysis Optimization
Leads to Monte Carlo and numerical pricing Computational statistics Hedging and calibration Stochastic calculus and SDEs Regression Corporate finance Bonds and interest rates Derivatives
Subjects marked “connection” are linked by a related idea, not by a prerequisite.