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Postgraduate Study in Mathematics

Please take this page in conjunction with the Part III Guide to Courses Statistics and Operational Research section.

Please read in particular Introduction and prerequisites given in the Guide to Courses.

Essential, helpful or helpful for some courses as listed in the prerequisites page linked to above.

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Basic Statistics

You will need this for the following Part III courses:

  • Modern Statistical Methods
  • Applied Statistics
  • Biostatistics
  • Time Series
  • Monte Carlo Inference
  • Statistics for Stochastic Processes
  • Topics in Statistical Theory

Relevant undergraduate courses are:

Reality check

  • Basic probability theory, including common distributions such as Binomial, Normal, Poisson, Chi-squared, etc. See e.g. Basic Probability and official prerequisites page mentioned above.
  • Basic Linear Algebra (basic facts about orthogonal matrices). You can check if you are at the required level by doing the following exercises: Statistical Modelling Example Sheet 1 (2014/15) Q 1, 2a, 5, Example Sheet 2 (2014/15) Q8a.
  • Basic Real Analysis. You can check if you are at the required level by doing the following exercises: Past Exam Question Part Ia 2016 Paper 1 Q3, Part Ia 2012 Paper 1 Q3


Undergraduate statistics, including:

  • Maximum Likelihood Estimation. Common examples, consistency and asymptotic normality.
  • Hypothesis Tests and Confidence Intervals. Likelihood ratio statistics, Wilks' theorem, t-tests and F-tests.
  • The Linear Model. MLEs, hypothesis tests, confidence intervals and extensions.
  • Bayesian Statistics. Definitions, examples and comparisons with MLEs.

You can use the following exercises to check your present level and to guide your study.

Useful books and resources

  • Notes from 2014 Catch-up lecture by Tengyao Wang. Thank you! These are a summary, so a good place to start and look up things in more detail as you need to.
  • IB Statistics course page by Prof. Spiegelhalter with notes and relevant information.

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Markov Chains

Relevant Cambridge undergraduate courses are Ib Markov Chains.

Useful books and resources

  • Prof. Weber's course page with lecture notes from 2012.
  • Parts of a book by Prof. Norris.

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