Vince Knight: Mathematician at Cardiff University

Here is a collection of outreach activities I use.

Please get in touch with me if you would like any further information

Hawks And Doves

An activity looking at the mathematics of evolution

Queues And Variation

An activity based on Anscombe's quarter

Playing Games

An introduction to game theory using the Prisoners Dilemma.

Hawks And Doves

This activity is intended for later high school years and introduces students to the mathematics behind evolution. In particular using probability and Moran processes.

Requires multiple multi sided dice.

  1. Describe the Moran process image on the slides;
  2. Ask for an explanation about the equations.
  3. Ask what might be wrong about this assumption? (In particular that all individuals have “the same fitness”).
  4. Show the Hawk Dove game and discuss.
  5. Create groups of 4 and explain that we will simulate the Moran process.
  6. Discuss the probabilities that might occur and how to simulate these using the dice available.
    1. If 1 Hawk:
      • Hawk gets 9 (3 x 3)
      • Each dove gets 5 (1 x 1 + 2 x 2)
      • Total score is 24.
      • Assign numbers to each individual (roll dice)
    2. If 2 Hawk:
      • Hawks each gets 6 (1 x 0 + 3 x 2)
      • Each dove gets 4 (1 x 2 + 2 x 1))
      • Total score is 20.
      • Assign numbers to each individual (roll dice)
    3. If 3 Hawk:
      • Hawks each gets 3 (1 x 3 + 3 x 0)
      • Each dove gets 3 (0 x 2 + 3 x 1))
      • Total score is 12.
      • Assign numbers to each individual (roll dice)
  7. Get students to repeat 10 times and check probability of Hawk taking over.
  8. Put probabilities together.
  9. Discuss slide that shows theoretic probability (without going in to details).
  10. Show computer simulation.

Queues And Variation

This activity is intended for later high school years and introduces students to the importance of studying variability in systems. This feature Anscombe’s quartet but also some basic queueing theory.

Playing Games

An activity during which students are introduced to game theory by playing games.

  1. Asks students if they have played a game before.
  2. Ask them what a game is with a goal to arrive at the following 3 components:
    1. Players;
    2. Objectives/rules;
    3. Outcomes.
  3. Explain the rules to the two thirds game (handout copies of the forms). Ask students to play once.
  4. Go over rationalisation (using diagram) that the rational play is for everyone to play 0.
  5. Play again.
  6. Describe the 2/3rds game and potentially show the video.
  7. Split class in to 4 groups and play a round robin tournament with 5 repetitions.
  8. Discuss results and refer to results of tournament.
  9. Return to results of the 2/3rds game.