Discrete and Decision Mathematics Option Content
Graphs, networks, algorithms, linear programming, recurrences, game theory and decision procedures mapped to AQA, Pearson, OCR A and OCR MEI option scopes.
How to study A-level Further Mathematics
Define the objects and conditions, select a representation, carry out exact mathematics, then validate, interpret and communicate the result.
Core concepts
Concept 1
An algorithm must have defined input, finite unambiguous steps and a justified output or stopping condition.
Exam cue: State the graph or network conventions before running an algorithm.
Concept 2
Graph algorithms depend on whether edges are directed, weighted, repeated or capacity constrained.
Exam cue: Record labels, permanent states and tie handling so the procedure can be checked.
Concept 3
Optimisation requires a feasible region, a correctly formed objective and interpretation of integer or modelling constraints.
Exam cue: Verify optimality and feasibility rather than accepting the first plausible route or vertex.
Risk pitfalls and guardrails
Using a minimum-spanning-tree method to solve a shortest-path problem.
Guardrail: Do not replace proof with examples, exact reasoning with unverified calculator output, or a valid awarding-body route with an invented mix of options.
Ignoring capacity, direction or repeated-edge restrictions.
Guardrail: Do not replace proof with examples, exact reasoning with unverified calculator output, or a valid awarding-body route with an invented mix of options.
Rounding a linear-programming solution without rechecking feasibility.
Guardrail: Do not replace proof with examples, exact reasoning with unverified calculator output, or a valid awarding-body route with an invented mix of options.
Memory anchors
Algorithm
An algorithm is a finite unambiguous procedure for valid inputs.
Permanent Label
A permanent label records a vertex value proved final under the stated shortest-path procedure.
Spanning Tree
A spanning tree connects every vertex without a cycle.
Feasible Region
A feasible region is the set satisfying every optimisation constraint.
Optimality Check
An optimality check proves that no feasible alternative improves the objective.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
A graph has 7 edges. Find the sum of all vertex degrees.
What is the maximum number of edges in a simple graph on 6 vertices?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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