**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 260 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 of the Mathematical Tripos, whilst the remaining two thirds take the course as a one-year course.^{[3]}

## History

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.

— Thomas William Körner^{[3]}

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; for those students successfully completing Part III of the Mathematical Tripos in Easter Term 2011 CASM was replaced by two new degrees, the *Master of Mathematics* (M.Math.) and *Master of Advanced Study* (M.A.St.). All who have passed the course since 1962 are entitled to these new degrees.^{[3]} The first retrospective M.Math and M.A.St. degrees were conferred as part of a celebration of the University's 800th anniversary.^{[4]} The course is often still referred to as Part III.

## Master of Mathematics vs Master of Advanced Study

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]}

The program previously resulted in a Certificate of Advanced Study in Mathematics instead of a Master's degree.^{[9]}

## Current course structure

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.

## Grading

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.^{[10]}^{[11]} 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 the highest-ranked student is still identified, nowadays by the tipping of the examiner's academic hat when the relevant name is read out.

## Prizes

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^{[12]} and the Wishart Prize for statistics.^{[13]} 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.

## References

**^**"Archived copy" (PDF). Archived from the original (PDF) on 2015-08-30. Retrieved 2015-10-14.CS1 maint: archived copy as title (link)**^**https://www.dpmms.cam.ac.uk/~twk/PartIII.pdf- ^
^{a}^{b}^{c}^{d}"Discussion on the establishment of a degree of Master of Mathematics and a degree of Master of Advanced Study". Cambridge University Reporter. 2009-01-28. Retrieved 2009-04-30. **^**T. W. Körner. "Award of the Master of Mathematics and the Master of Advanced Study in Mathematics". Archived from the original on 27 November 2010. Retrieved 3 December 2010.**^**"Information for Part II students wishing to continue to Part III".*www.maths.cam.ac.uk*. September 23, 2015.**^**Bonetti, Lisa (February 1, 2019). "Mathematics".*www.undergraduate.study.cam.ac.uk*.**^**"Joint Report of the Council and the General Board on the establishment of a degree of Master of Mathematics and a degree of Master of Advanced Study". Cambridge University Reporter. 2008-12-10. Retrieved 2009-04-30.**^**"Graces submitted to the Regent House on 11 March 2009". Cambridge University Reporter. 2009-03-11. Retrieved 2009-04-30.**^**"Certificate of Advanced Study in Mathematics (Part III) : Announcement". Cambridge University Reporter. Archived from the original on 2018-02-26. Retrieved 2018-02-25.**^**"Raven login".*raven.cam.ac.uk*.**^**http://www.admin.cam.ac.uk/offices/planning/sso/studentnumbers/2014exams.pdf**^**https://www.admin.cam.ac.uk/univ/so/2013/chapter12-section2.html#heading2-28**^**https://www.admin.cam.ac.uk/univ/so/2013/chapter12-section2.html#heading2-601