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Unit D1: Decision Mathematics 1

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5 topics · 15 learning objectives

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  1. D1.1 - Algorithms

    1. The general ideas of algorithms and The order of an algorithm is not expected. the implementation of an algorithm given by a flow chart or text.; Whenever finding the middle item of any list, the method defined in the glossary must be used.

    2. Students should be familiar with When using the quick sort algorithm, the pivot should be bin packing, bubble sort, quick sort, chosen as the middle item of the list. binary search.

  2. D1.2 - Algorithms on graphs

    1. The minimum spanning tree Matrix representation for Prim’s algorithm is expected. (minimum connector) problem.; Drawing a network from a given matrix and writing down Prim’s and Kruskal’s algorithm. the matrix associated with a network will be involved.

    2. Dijkstra’s algorithm for finding the shortest path.

  3. D1.3 - Algorithms on graphs II

    1. Algorithm for finding the shortest Also known as the ‘Chinese postman’ problem.; Students route around a network, travelling will be expected to use inspection to consider all possible along every edge at least once and pairings of odd nodes. ending at the start vertex.; The (The application of Floyd’s algorithm to the odd nodes is network will have up to four odd not required.) nodes.

    2. The practical and classical The use of short cuts to improve upper bound is included.; Travelling Salesman problems.; The classical problem for complete graphs satisfying the triangle inequality.

    3. Determination of upper and lower The conversion of a network into a complete network of bounds using minimum spanning shortest ‘distances’ is included. tree methods.

    4. The nearest neighbour algorithm.

  4. D1.4 - Critical path analysis

    1. Modelling of a project by an Activity on arc will be used.; The use of dummies is activity network, from a precedence included. table.; In a precedence network, precedence tables will only show immediate predecessors.

    2. Completion of the precedence table for a given activity network.

    3. Algorithm for finding the critical path.; Earliest and latest event times.; Earliest and latest start and finish times for activities.

    4. Total float.; Gantt (cascade) charts.; Scheduling.

  5. D1.5 - Linear programming

    1. D1.5.1Formulation of problems as linear programs

      Formulation of problems as linear programs.

    2. D1.5.2Graphical solution of two variable problems

      Graphical solution of two variable problems using ruler and vertex methods.

    3. D1.5.3Consideration of problems where solutions must have integer

      Consideration of problems where solutions must have integer values.