Course 5 · Module 2
Combinatorics and Graph Theory
This module covers the branches of mathematics that count possibilities and study networks. You'll see how a puzzle about crossing seven bridges became the start of network science, learn to count arrangements without listing them, and meet the mathematics behind route finding, scheduling, and coloring maps. You'll also meet a question about parties and friendships that the world's computers still can't settle.
Module objectives
- Count arrangements with the multiplication principle and decide whether a network can be traced in one path.
- Explain how graph theory models networks and scheduling, and state an open problem in Ramsey theory.
Lessons
- Lesson 1 Graph Theory: Counting arrangements and the bridges of Königsberg You'll learn to count possibilities without listing them, and you'll solve the puzzle that started graph theory: whether a walk can cross each of seven bridges exactly once… 61111h 3m
- Lesson 2 Graph Theory: Networks, scheduling, map coloring, and Ramsey numbers You'll see graph theory at work in the route your map app chooses, the way a school schedules exams, and a famous theorem about coloring maps that was the first major result… 611111h 33m