Contents

• Discrete and Decisions Maths syllabus topics
• Books

Discrete and Decision Maths A level syllabuses cover the following topics

Graph Theory:

applications; terms; families of graphs; isomorphism; walks, paths and trails; cycles; trees; planar graphs.

Algorithms for weights edge graphs:

shortest path (Dijkstra's algorithm); longest path; minimum connector (find the least cost edges to connect all the nodes); travelling saleman (visit all the nodes at least cost); chinese postman (visit all the edges at least cost).

Inequalities:

graphical representation.

Linear Programming:

graphical solutions; Simplex tableau.

Network flows:

bottlenecks; cuts; variations.

Matching:

match people to jobs; with preferences; the Hungarian algorithm;

Critical Path analysis:

activity-on-edge; Gantt diagrams; cascade charts; algorithm to find float times.

Difference Equations:

firstorder; non-homogeneous;

Algorithms:

generating permutations; sorting; greedy methods; recurrence for complexity measure; knapsack problems and bin packing; transportation problems;

Boolean Algebra:

sets; electrical circuits; full and half adders.

Codes:

Huffman codings; Hamming distance; error detection and correction; check digits; Mariner 9 code;

Game Theory

Zero-sum games; prisoner's dilemma; m x n games;

Books

• Decision Mathematics Editor: D Burghes, Heinemann Educational, 1992, ISBN 0 435 51553 3. £10.95
  Developed for AEB's Decision Maths Core for A and AS level
• Decision Maths Editors: J Berry, D Burghes, I Huntley. Ellis Horwood, 1986. ISBN: 0 7458 0078 5.
  UODLE inspired, produced by the Spode Group. There is also a Solution Manual 1986, ISBN 1 869931 00 9
• Decision and Discrete Maths C Compton, G Rigby. Hodder and Stoughton, 1992. ISBN 0 340 57171 3.
  MEI based
• NEAB 16-19 Unit on Networks, Information and Coding

An excellent book on Graph Theory, which is a large part of Discrete and Decision Maths courses, is Graphs: An Introductory Approach, R J Wilson, J J Watkins. John WIley, 1990. ISBN 0 471 51340 7.
It is a course book for the Open University course which is very useful for teachers. Look out for the programmes on early morning/late night TV (BBC 2). The programmes are well worth taping and showing to your students since they provide practical motivational material as well as good illustrations of the techniques involved in solving some problems. For further information, contact Ron Knott . MACTAC Home | Maths and Computing Sciences Dept | Surrey University