For Educators

gmp26's picture
Posted April 8th, 2008 by gmp26
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We hope this site may be useful to people teaching about uncertainty, whether it's the mathematics of probability and statistics, or the responses of individuals or society to risk.

The mathematics of uncertainty

The 'stories' on this site are structured at multiple levels corresponding to difficulty. For pages with mathematical content, these levels correspond roughly to

  1. level1 No maths, just pictures and text for general readership
  2. level2 Basic arithmetic and probability theory, at a high GCSE level (say up to aged 16). For example:
    • What are the chances shows probability calculations requiring multiplication of probabilities of independent and dependent events, as well as introducing ideas of expectation.
    • Lottery expectations and Luck or skill? compare observed and expected distributions: Binomial, normal and geometric expected distributions are provided but not derived.
    • Maternal death coincidence features quite a complex piece of probabilistic reasoning concerning the chance of two deaths occurring close in time and space.
  3. level3 Some algebra, probability distributions, basic statistical concepts at a high A level standard (ages 16 to 18). For example:
    • Maths of coincidence provides a general algebraic form for the probability of at least one event occurring, both for dependent and independent events. This uses the exponential $e$ and mentions the Poisson distribution.
    • Is the lottery biased? features chi-squared tests for goodness-of-fit, the derivation of the geometric distribution, and ideas of testing hypotheses by simulating distributions of test statistics under the null hypothesis.
    • May the best team win derives the mean and variance of a test statistic under a null hypothesis and uses a normal approximation to the sampling distribution to derive confidence intervals. Uncertainty about ranks is explored using Monte Carlo methods.
  4. level4 Full mathematical exposition, at university level. No level 4 pages written yet!

Non-mathematical pages also have different levels according to their conceptual difficulty