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Mathematics · Year 10 · Path · MA5-NET-P-01

Introduction to Networks

Ten lessons on a kind of mathematics that throws away almost everything. Distances, directions and shapes all disappear, leaving only which things are connected to which, and that turns out to be enough to answer questions about social media, supply chains, circuit boards and a puzzle about seven bridges that nobody could solve for two hundred years.

10lessons
19syllabus points
7hstudy
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1
What a Network Is
Vertices and edges, and why position and length carry no meaning at all
2
Vertices, Edges and Degree
Count the edge-ends and you have counted every edge twice
3
Networks in the Real World
Two modelling decisions, and what a plain network can never tell you
4
Planar and Non-Planar Graphs
A crossing belongs to the drawing; the question is whether every drawing has one
5
Faces and Euler's Formula
Count the regions, remember the outside, and three numbers lock together
6
Connected Graphs and Walks
Can you get there at all, and what a journey looks like written down
7
Trails, Paths, Circuits and Cycles
Two questions sort all four: repeated edges, repeated vertices, and closing
8
Eulerian Trails and Circuits
Every edge exactly once, and why it can never be a path
9
The Degree Rule
Count the odd vertices: zero, two, or hopeless, and where the round begins
10
The Königsberg Bridges
A city becomes four dots, and a two-hundred-year puzzle takes one line

Focus Area Snapshot

10lessons
19syllabus points
30worked examples
80questions

Where this leads

This is a Path focus area, and unlike most of the others it prepares you for Mathematics Standard rather than Mathematics Advanced. Networks return in the Year 12 Standard course, where shortest paths, minimum spanning trees and critical path analysis all build directly on the vertices, edges and degrees introduced here.

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