Statistical Mathematics or Mathematical Statistics?

How much mathematics should there be in a statistics course? Surely there must be as much as is needed to adequately present explain and illustrate the statistics material. Can we expect that statistics students can cope with the required mathematics? Should a statistics programme have to ‘patch in’ on the mathematics it uses? John McColl explores these key issues in the following article which was originally written as a briefing note for post-experience students enrolled on the Royal Statistical Society Centre for Statistical Education distance learning course Teaching Statistics in Higher Education.