Mathematics: Applications and Interpretation HL
Extended networks and discrete systems
Graph walks, Markov extensions, Voronoi boundaries, recurrence closed forms, and optimisation sensitivity.
Find two-step Markov probabilities
Use transition probabilities twice to find a two-step probability.
Solve two-state steady-state probabilities
Solve a two-state Markov steady-state equation.
Count walks with adjacency matrices
Use entries of powers of an adjacency matrix to count walks.
Interpret graph degree sums
Use the handshaking lemma to find edge counts or degree totals.
Find Voronoi boundary midpoints
Use midpoint and perpendicular-bisector reasoning for two-site Voronoi boundaries.
Use recurrence closed forms
Use a first-order recurrence closed form for repeated change.
Determine Euler trail conditions
Use odd-degree vertex counts to decide whether an Euler trail is possible.
Use nearest-neighbour route length
Add edge lengths from a nearest-neighbour travelling-salesperson route.
Calculate critical path float
Calculate total float from earliest and latest start times.
Find minimum cut capacity
Add the capacities crossing a proposed cut in a flow network.
Use max-flow bottleneck increments
Find the bottleneck capacity along an augmenting path.