Discrete (aka Decision) Maths Notes & Exercises

(recently added material is in green)

Topics by exam board (9 pages; 30/7/19)

Algorithms 

Bin Packing Algorithms (3 pages; 7/8/18)

Maximum Matching algorithm (4 pages; 6/9/13)

Algorithms Exs (Overview)

   Purposes of algorithms (Exs) 1 7 8 9

   Bin Packing (Exs) 3 5 6

   Sorting (Exs) 2 4     

Critical Path Analysis - Part 1 (12 pages; 22/1/20)

Critical Path Analysis - Part 2 (14 pages; 7/11/20)

Critical Path Analysis Exs 1a 1b 2 3 4

Dijkstra's algorithm: See Shortest Path

Floyd's algorithm: See Shortest Path

Game Theory Exs 1 2 3

Graphs & Networks

Graphs Glossary (3 pages; 15/1/14)

Directed Edges (incl. Incidence & Distance matrices) (5 pages; 19/11/19)

Planarity Algorithm (5 pages; 30/6/20)

Graphs Ex 2

   Kuratowski's Thm (Ex) 1

Planarity algorithm Ex 1

Hungarian Algorithm  (9 pages; 28/8/17)

Kuratowski's Thm: See Graphs & Networks

Linear Programming & Simplex method

Linear Programming (11 pages; 6/1/24)

Formulating network problems as LP problems (7 pages; 21/1/20)

Simplex method - Part 1 (15 pages; 9/1/24)

Simplex method - Part 2 (18 pages; 7/6/23)

Linear Programming Exs 1 2a 2b

   Formulate as LP problem (Exs) 3 4 5 6 7

   Simplex (Exs) 2c 8 9a 9b

Minimum Connector Problem (6 pages; 21/11/20) 

Minimum Connector Exs 1 2

Network Flows - Introduction (5 pages; 16/1/21)

Networks: See Graphs & Networks

Planarity algorithm: See Graphs & Networks

Route Inspection Problem (5 pages; 12/9/17)

Route Inspection Exs (Overview)  1 2

Shortest Path

Dijkstra's Algorithm (5 pages; 19/11/20)

Floyd's Algorithm (21 pages; 17/6/20)

Dijkstra's algorithm Ex 1

Floyd's Algorithm Exs 1 2

Simplex: See Linear Programming & Simplex method

Travelling Salesman problem (10 pages; 29/6/20)

Travelling Salesman problem Ex 1