1st Class Honours degree in mathematics, physics or engineering normally required; also desirable that students with 3-year 1st degree attend 1-year postgraduate course on advanced applied mathematics and theoretical physics; Part III of Mathematical Tripos provides such a course and graduates from outside Cambridge can come to take it as a 4th-year course; graduates who complete Part III successfully are awarded Certificate of Advanced Study in Mathematics; admission as PhD candidate is dependent on performance in Part III, or its equivalent in another university.