Unit D1: Decision Mathematics 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.

Use algorithms and flow-chart implementation to connect the rule to the data and decision in the question.

This matters because algorithms and flow-chart implementation determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply algorithms and flow-chart implementation to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Algorithms and flow-chart implementation is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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.

Use bin packing, sorting and binary search to connect the rule to the data and decision in the question.

This matters because bin packing, sorting and binary search determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply bin packing, sorting and binary search to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Bin packing, sorting and binary search is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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.

Use minimum spanning tree to connect the rule to the data and decision in the question.

This matters because minimum spanning tree determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply minimum spanning tree to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Minimum spanning tree is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Dijkstra’s algorithm for finding the shortest path.

Use dijkstra’s algorithm for finding the shortest path to connect the rule to the data and decision in the question.

This matters because dijkstra’s algorithm for finding the shortest path determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply dijkstra’s algorithm for finding the shortest path to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Dijkstra’s algorithm for finding the shortest path is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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.

Use algorithm for finding the shortest to connect the rule to the data and decision in the question.

This matters because algorithm for finding the shortest determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply algorithm for finding the shortest to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Algorithm for finding the shortest is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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.

Use practical and classical to connect the rule to the data and decision in the question.

This matters because practical and classical determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply practical and classical to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Practical and classical is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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.

Use determination of upper and lower to connect the rule to the data and decision in the question.

This matters because determination of upper and lower determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply determination of upper and lower to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Determination of upper and lower is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

The nearest neighbour algorithm.

Use nearest neighbour algorithm to connect the rule to the data and decision in the question.

This matters because nearest neighbour algorithm determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply nearest neighbour algorithm to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: nearest neighbour algorithm is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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.

Use project modelling with activity networks to connect the rule to the data and decision in the question.

This matters because project modelling with activity networks determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply project modelling with activity networks to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Project modelling with activity networks is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Completion of the precedence table for a given activity network.

Use completion of the precedence table for a given activity to connect the rule to the data and decision in the question.

This matters because completion of the precedence table for a given activity determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply completion of the precedence table for a given activity to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Completion of the precedence table for a given activity is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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

Use algorithm for finding the critical path to connect the rule to the data and decision in the question.

This matters because algorithm for finding the critical path determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply algorithm for finding the critical path to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Algorithm for finding the critical path is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

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

Use total float to connect the rule to the data and decision in the question.

This matters because total float determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply total float to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Total float is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Formulation of problems as linear programs.

Use formulation of problems as linear programs to connect the rule to the data and decision in the question.

This matters because formulation of problems as linear programs determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply formulation of problems as linear programs to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: use the formula and units given in the question, show the substitution and interpret the result; the calculation alone is not the conclusion.

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

Use graphical solution of two variable problems to connect the rule to the data and decision in the question.

This matters because graphical solution of two variable problems determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply graphical solution of two variable problems to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Graphical solution of two variable problems is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Consideration of problems where solutions must have integer values.

Use consideration of problems where solutions must have integer to connect the rule to the data and decision in the question.

This matters because consideration of problems where solutions must have integer determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply consideration of problems where solutions must have integer to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Consideration of problems where solutions must have integer is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.