Certificate of Advanced Study in Mathematics

Part III of the Mathematical Tripos (officially Master of Mathematics/Master of Advanced Study) is a one-year Masters-level taught course in mathematics offered at the Faculty of Mathematics, University of Cambridge. It is regarded as one of the hardest and most intensive mathematics courses in the world and is taken by approximately 200 students each year. Roughly one third of the students take the course as a fourth year of mathematical study at Cambridge (after Parts IA, IB, and II), whilst the remaining two thirds take the course as a one-year course.

The Smith's Prize Examination was founded by bequest of Robert Smith upon his death in 1768 to encourage the study of more advanced mathematics than that found in the undergraduate course. T. W. Körner notes

Only a small handful of students took the Smith's prize examination in the nineteenth century. When Karl Pearson took the examination in 1879, the examiners were Stokes, Maxwell, Cayley, and Todhunter and the examinees went on each occasion to the examiner's house, did a morning paper, had lunch there, and continued their work on the paper in the afternoon.

In 1883 this was replaced by an exam called Part III and the Smith's Prize awarded for an essay rather than examination. In 1886 this exam was renamed Part II, and later in 1909 Part II, Schedule B. In 1934 it was again renamed Part III. In the 1980s the Certificate of Advanced Study in Mathematics was introduced, and in 2010 CASM was replaced by two new degrees, the Master of Mathematics (M.Math.) and Master of Advanced Study (M.A.St.). All those who have taken the course since 1962 have the right to proceed to these new degree titles. The first retrospective M.Math and M.A.St. degrees were conferred in October 2010. The course is often still referred to as Part III.

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