Module 17:
Convergence, large numbers and approximations

Module 17

What this module is for

Both. This module should teach not only how approximations work, but how they fail.

Lesson 17.1 · Core · QR Extension

What convergence means

Depth: Working proficiency; deeper counterexamples optional

QT/QR relevance: Both, especially QR; understanding asymptotic statements

Lesson 17.2 · Core

Weak and strong laws of large numbers

Depth: Working proficiency; strong-law proof excluded

QT/QR relevance: Both; averages and simulation

Lesson 17.3 · Core

The central limit theorem

Depth: Interview mastery

QT/QR relevance: Both; aggregate uncertainty

Lesson 17.4 · Core

Choosing and checking approximations

Depth: Interview mastery

QT/QR relevance: Both; reliable approximate calculations

Lesson 17.5 · Research Depth

Transforming asymptotic results

Depth: Advanced / quant researcher depth — Extension

QT/QR relevance: QR; later statistical estimators and nonlinear summaries

Lesson 17.6 · Research Depth

When limits and expectations do not commute

Depth: Advanced / quant researcher depth — Extension

QT/QR relevance: QR; recognising invalid asymptotic reasoning

Assessment

Module 17 assessment

Open assessment · No submitted assessment yet