Part III of the Mathematical Tripos

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Results for parts II and III of the Mathematical Tripos are read out inside Senate House, University of Cambridge and then tossed from the balcony.

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.[1][2] 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.[3]


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.[3] 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.[3] The first retrospective M.Math and M.A.St. degrees were conferred in October 2010.[4] The course is often still referred to as Part III.

Master of Mathematics vs Master of Advanced Study[edit]

Students who have completed their undergraduate degree at Cambridge will be awarded both a Bachelor of Arts (B.A.) and the Master of Mathematics (M.Math.) degree for four years of study, provided they have not previously graduated with a B.A.[5] This allows Cambridge graduates to remain eligible for government funding for the course. Progression from Part II of the Mathematical Tripos to Part III normally requires either a first in Part II or very good performances in Parts IB and Part II.[6] Students who complete Part III of the Mathematical Tripos, but did not complete undergraduate studies at Cambridge (or have previously graduated with a B.A.) will be awarded the Master of Advanced Study (M.A.St.) in Mathematics degree for the one-year course.[7][8]

Current course structure[edit]

The course lasts one year, divided into three eight-week terms. There are a wide variety of lectures on both pure and applied maths, mostly concentrated in the first two terms. The third term is primarily for examinations (and revision for said examinations) which, together with the option of writing a part III essay (introduced in the 1970s, a miniature thesis of sorts, often in the form of a literature review), determine one's final grade entirely.


The grades available are Fail, Pass (Honours), Merit, and Distinction (the Merit grade was introduced in 2000). Cambridge recognises that in Part III of the mathematical tripos a merit is equivalent to a First Class in the other parts of the Tripos.[9][10] The level of achievement required for a distinction is yet higher. Traditionally, results are announced in the University's Senate House. Standing on the balcony, the examiner reads out the class results for each student, and printed copies of the results are then thrown to the audience below. The students' exact rankings are no longer announced, but highest-ranked student is still identified, nowadays by the tipping of the examiner's academic hat when the relevant name is read out.


In addition to the grades, there are five associated prizes. Four of these may be awarded at the discretion of the examiners: the Mayhew Prize for Applied Mathematics, the Tyson Medal for mathematics and astronomy, the Bartlett Prize for applied probability[11] and the Wishart Prize for statistics.[12] Several notable astronomers and astrophysicists have been awarded the Tyson Medal in the history of Part III maths, including Jayant Narlikar, Ray Lyttleton and Edmund Whittaker. In addition, the Thomas Bond Sprague Prize is awarded by the Rollo Davidson Trust for distinguished performance in actuarial science, finance, insurance, mathematics of operational research, probability, risk and statistics.