This was a one-hour talk given to talented summer school students at the 2025 LMS Summer Undergraduate Mathematics School hosted at the University of Bath.
Slide 2: I started with a short introduction to who I was and my background. I mentioned that PhD and post-PhD experiences are highly variable so you have to take my advice for what it is.
Slide 3: I then discussed the changing landscape of PhDs in the UK, notably focusing on the fact that PhD numbers can be highly variable. Bath, for instance, graduates some 15-20 students a year on account of our excellent CDT on Statistical and Applied Mathematics Doctoral Training Centre. Other departments without CDTs can suffer in terms of numbers (5, say).
Slide 4: I continued discussing the change of the landscape
Slide 5: I discussed where money comes from when funding your PhD. I discussed the challenging case of international students.
Slide 6: I discussed the pros and cons of CDTs vs traditional studentships
Slide 7: I showed where PhD adverts canbe found
Slide 8: I discussed the appliations cycle
Slide 9: How to get into a PhD
Slide 10-11: what an interview process might look like
Slide 12-13: Advertising our own excellent CDT
Slide 14: I discussed interesting industrial careers, some of which need PhDs (and others that don't).