Lecture 2: Mathematical Preliminaries B

Part 1 · Mathematical Preliminaries

Lecture: Monday, September 14, 2026

Topics

• Convex sets and convex functions
• Global optimality, uniqueness, and first-order certificates
• Hessian curvature, smoothness, and a justified gradient step
• Big-O notation, polynomial time, and statistical–computational gaps

Materials

• 📄 Lecture 2 Learning Sheet
• 📝 Lecture 2 Validation — Questions
• 📖 Lecture 2 Validation — With Solutions
• 📋 Lecture 2 Cheatsheet

Tutorial Notes

• Tutorial 2: Coordinates, Gradient Descent, and SOAP

Next class: Part 1 Test

The Part 1 Test covers Lectures 1–2, is worth 120 marks, and lasts 30 minutes. It contributes 14% of the course grade.

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