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Decision 2: lesson checks flashcards

This deck has 9 check-yourself questions and 7 spot-the-error cards. The misconception each lesson corrects, and its check-yourself question with the worked answer. Rate each answer, and the card comes back sooner or later depending on how you rated it.

Further Maths · all 584 maths cards

How the five kinds differ

Standard results ask you to recall a formula or a value. Definitions ask you to state a mathematical term precisely. Recall prompts ask for a rule, condition or method. Check yourself cards are a short question with its answer. Spot the error cards ask you to correct a statement that is wrong.

Every card in this deck

Choose any card to try it in the player above. Each card links to the lesson that teaches it.

• The north-west corner method gives a good starting solution because it fills the cheapest cells first.Spot the error
• A transportation problem has 4 sources and 3 destinations. How many cells should a solution use, and what does it mean if it uses five?Check
• An unused cell has cost 12, its row shadow cost is 4 and its column shadow cost is 9. Find the improvement index and say what it means.Check
• In the Hungarian algorithm you can subtract the smallest entry in the whole matrix from every element.Spot the error
• A 4 by 4 reduced matrix needs only 3 lines to cover its zeros. What is the next step?Check
• The capacity of a cut is the total capacity of every arc it crosses.Spot the error
• A cut crosses arcs of capacity 7 and 5 towards the sink and one of capacity 4 back towards the source. Find its capacity.Check
• A flow-augmenting path has spare capacities 7, 3 and 9 along it. How much extra flow can it carry, and what happens to the arc that limits it?Check
• Dynamic programming works forwards from the source, choosing the cheapest step available at each stage.Spot the error
• From a vertex the options are a step of 5 to a vertex worth 9, and a step of 8 to one worth 4. Give the value of this vertex for a minimum-total problem and for a minimax problem.Check
• In a zero-sum game the column player wants the largest entries, since a large pay-off is good.Spot the error
• A game has row minima 4 and 2, and column maxima 7, 4 and 9. Is it stable, and what is the value?Check
• In a mixed strategy the player should favour the choice with the larger pay-offs, in proportion to them.Spot the error
• Against two columns the expected pay-offs are 2 + 5p and 7 − 3p. Find the optimal p and the value.Check
• The best course of action is always the one with the highest expected monetary value.Spot the error
• A chance node has a 0.3 branch paying 200 and a 0.7 branch paying 50, and reaching it costs 60. Find the expected monetary value.Check

The lessons these cards come from

• Allocation and the Hungarian algorithm
• Decision trees, expected monetary value and utility
• Dynamic programming and Bellman's principle
• Flows in networks: cuts and capacity
• Game theory: play safe and stable solutions
• Maximum flow and the labelling procedure
• Mixed strategies in game theory
• The stepping-stone method
• Transportation problems and the north-west corner method

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