Further Decision (Discrete) Maths

Network Graphs on the London Underground

A series of Decision Maths activities based on the London Underground network graph. Includes shortest path, TSP, route inspection and others. Some answers included.

The Utilities Problem

James Grime explains the utilities problem, particularly in relation to Euler's formula.

Position Filled - Introduction to Matching (Bipartite) Graphs

Real life task for students to match up duties with personnel available at various retailers. Students work out which businesses enough, too many or too few staff to cover each shift. Example numbers designed to compliment the Oxford AQA Decision 1 textbook chapter. Instructions deliberately vague for students to find own methods.

Matchup the Matchings Definitions

A bipartite graph of matchup graph definitions for students to matchup. Answers included. PDF here.

Decision Introductions

A set of stand-alone worksheets to introduce students to various aspects of Decision maths including complete graphs, minimum spanning trees, route inspection and travelling salesman. (Ideas mostly taken from the AQA Decision 1 textbook).

AQA Decision Notes

Concise notes on the AQA Decision 1 module of A Level Mathematics. PDF here.

OCR Decision Notes

Notes on the OCR Decision 1 module of A Level Mathematics - thanks Ben Walker!

London Underground Map

Great for Decision maths. The standard map as a colour pdf or as a gif file. There is also a good black & white printable version.

Interesting alternate versions include where the lines really are, or on a satellite image. Which parts of the underground are actually underground. Annotated with train times between stations. Finally, showing which stations are faster to walk between.

London Underground website.

internetSorting Algorithms

A wonderful YouTube video demonstrating various sorting algorithms. See also the Hungarian Folk Dancer's version of Bubble Sort and Quicksort.


A superb website created by a student to demonstrate relative positions of nodes, weights, shortest path, one-way arcs and much more. Well worth a visit. There's even an introductory video. Great work Ed.

Travelling Salesman Problem Website

A website with many applications and puzzles based on the TSP.

Claymath P vs NP Problem

The Claymath Institute Millenium problem No.3 - P vs Np problem which is based on finding general method for solving the TSP.

Iron Maiden website

A more inspiring take on the Travelling Salesman charade, how about a world famous touring rock band. Check out the first date on this tour, a bit out of place? That was a great day!