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Progress to greater stage research, corresponding to a postgraduate diploma or masters diploma. Section 1 discusses a number of ways of estimating probabilities. Section 2 critiques ideas of conditional probabilities and introduces Bayes’ theorem and its use in updating beliefs about a proposition, when data are observed, or data becomes available. Section 1 supplies a brief introduction to the kinds of drawback that come up in Number Theory. Section 2 critiques and offers a more formal method to a robust methodology of proof, mathematical induction.
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