Curriculum Mapping for Decision Mathematics


This is the curriculum mapping page for A-level decision mathematics topics.


 

AREA TOPICS COVERED
Decision D1 Algorithms; algorithms on graphs; route inspection problem; critical path analysis; linear programming; matchings.
Decision D2 Transportation problems; allocation (assignment) problems; the travelling salesman; game theory; further linear programming, dynamic programming; flows in networks.


Decision D1
Algorithms; algorithms on graphs; route inspection problem; critical path analysis; linear programming; matchings.
ALGORITHMS

The general ideas of algorithms and the
implementation of an algorithm given by a flow chart
or text. Bin packing, bubble sort, quick sort, binary search.
Zeller's Birthday
Flow Chart
Procedure Solver
ALGORITHMS ON GRAPHS
The minimum spanning tree (minimum connector) problem. Prim’s and Kruskal’s (greedy) algorithm. Dijkstra’s algorithm for finding the shortest path.  
ROUTE INSPECTION PROBLEM
Algorithm for finding the shortest route around a network, travelling along every edge at least once and ending at the start vertex.  
CRITICAL PATH ANALYSIS
Modelling of a project by an activity network, from a
precedence table. Completion of the precedence table for a given activity network.
Algorithm for finding the critical path. Earliest and latest event times. Earliest and latest start and finish times for activities.
Total float. Gantt (cascade) charts. Scheduling.		  
LINEAR PROGRAMMING
Formulation of problems as linear programs.
Graphical solution of two variable problems using
ruler and vertex methods
Consideration of problems where solutions must
have integer values.		  
MATCHINGS
Use of bipartite graphs for modelling matchings.
Complete matchings and maximal matchings.
Algorithm for obtaining a maximum matching.		  

 

 

Decision D2
Transportation problems; allocation (assignment) problems; the travelling salesman; game theory; further linear programming, dynamic programming; flows in networks.
 
TRANSPORTATION PROBLEMS
The north-west corner method for finding an initial
basic feasible solution.Use of the stepping-stone method for obtaining an
improved solution. Improvement indices.Formulation as a linear programming problem.
 
ALLOCATION ( ASSIGNMENT) PROBLEMS
Cost matrix reduction.Use of the Hungarian algorithm to find least cost
allocation.Modification of method to deal with a maximum
profit allocation.Formulation as a linear programming problem.		  
TRAVELLING SALESMAN
The practical and classical problems. The classical
problem for complete graphs satisfying the triangle
inequality.Determination of upper and lower bounds using
minimum spanning tree methods.The nearest neighbour algorithm.		  
GAME THEORY
Two person zero-sum games and the pay-off matrix.
Identification of play safe strategies and stable
solutions (saddle points).Reduction of pay-off matrices using dominance
arguments. Optimal mixed strategies for a game
with no stable solution.Conversion of 3 × 2 and 3 × 3 games to linear
programming problems.		  
FURTHER LINEAR PROGRAMMING

Formulation of problems as linear programs.

The Simplex algorithm and tableau for maximising
problems.The use and meaning of slack variables.

  
DYNAMIC PROGRAMMING
Principles of dynamic programming. Bellman’s
principle of optimality.Stage variables and State variables. Use of tabulation to solve maximum, minimum, minimax or maximin problems.		  
FLOWS IN NETWORKS
Algorithm for finding a maximum flow. Cuts and their capacity. Use of the max flow — min cut theorem to verify that a flow is a maximum flow. Multiple sources and sinks.  

 

NOTE: These NRICH problems often draw together strands from decision mathematics as a whole, and any one activity may have several possible lesson foci. For example, some problems will work well either as introduction to a topic to raise the underlying issues or as an end of module consolidation in which students' problem solving and understanding is drawn together. Others are suitable for classroom discussion and others for individual problem solving.


The topics are grouped according to a summary of the Edexcel schemes, but should be generally of use. Please note that this material is under development. New problems will arrive on a regular basis and it is intended that detailed teachers' notes will eventually accompany all of the problems. If you have any comments please do get in touch.