Course 2 · Module 2
Topology
This module covers the branch of mathematics that studies the properties of shapes that survive bending and stretching. You'll see why topologists say a coffee mug and a doughnut are the same shape, count corners, edges, and faces to find a number that never changes, and follow these ideas into DNA biology, data analysis, and physics. Topology is the mathematics of what's left when you stop caring about size and angle.
Module objectives
- Identify properties of a shape that stay the same under stretching and bending, using Euler's polyhedron formula as the example.
- Explain what topology contributes to biology, data analysis, and physics, and why the Poincaré conjecture mattered.
Lessons
- Lesson 1 Topology: What survives stretching: polyhedra, Möbius strips, and invariants You'll see what topology keeps and what it throws away when a shape is stretched or bent. You'll count vertices, edges, and faces to find a number that stays the same however a… 61111h 3m
- Lesson 2 Topology: Knots, DNA, data, and the Poincaré conjecture You'll see topology at work in cell biology, data analysis, and physics, where the question "how many holes, how tangled?" turns out to matter. You'll also meet the Poincaré… 611111h 33m