Cambridge Mathematical Tripos

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

The Mathematical Tripos is the taught mathematics course in the Faculty of Mathematics at the University of Cambridge. It is the oldest Tripos that is examined in Cambridge^{[citation needed]}.

Origin

In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate students of the University of Cambridge. Prior to 1824, the Mathematical Tripos was formally known as the "Senate House Examination". From about 1780 to 1909, the "Old Tripos" was distinguished by a number of features, including the publication of an order of merit of successful candidates, and the difficulty of the mathematical problems set for solution. By way of example, in 1854, the Tripos consisted of 16 papers spread over 8 days, totaling 44.5 hours. The total number of questions was 211. The actual marks for the exams were never published, but there is reference to an exam in the 1860s where, out of a total possible mark of 17,000, the senior wrangler achieved 7634, the second wrangler 4123, the lowest wrangler around 1500 and the lowest scoring candidate obtaining honours (the wooden spoon) 237; about 100 candidates were awarded honours and the 300-odd below that level were known as poll men. The questions for the 1841 examination may be found within the Cambridge University Magazine.

Influence

According to the study Masters of Theory: Cambridge and the Rise of Mathematical Physicsby Andrew Warwick during this period the style of teaching and study required for the successful preparation of students had a wide influence:

• on the development of 'mixed mathematics' (a precursor of later applied mathematics and mathematical physics, with emphasis on algebraic manipulative mastery)
• on mathematical education
• as vocational training for fields such as astronomy
• in the reception of new physical theories, particularly in electromagnetism as expounded by James Clerk Maxwell

Since Cambridge students did a lot of rote learning called "bookwork", it was noted by Augustus De Morgan and repeated by Andrew Warwick that authors of Cambridge textbooks skipped known material. In consequence, "non-Cambridge readers ... found the arguments impossible to follow."

Early history

The early history is of the gradual replacement during the middle of the eighteenth century of a traditional method of oral examination by written papers, with a simultaneous switch in emphasis from Latin disputation to mathematical questions. That is, all degree candidates were expected to show at least competence in mathematics. A long process of development of coaching – tuition usually outside the official University and college courses – went hand-in-hand with a gradual increase in the difficulty of the most testing questions asked. The standard examination pattern of bookwork (mostly memorised theorems) plus rider (problems to solve, testing comprehension of the bookwork) was introduced.

Wranglers and their coaches

The list of wranglers, that is, the candidates awarded a first-class degree, became in time the subject of a great deal of public attention. The coaches, of whom Edward Routh was the most outstanding, assumed a para-academic status. Students were drilled with mathematical exercises driving them to a high level of technique, and there was acute time pressure in the examinations. It became common for those with a first degree in mathematics elsewhere to come to Cambridge to take part in the Tripos, as a second degree.

1909 Tripos reforms

Reforms were implemented in 1909. The undergraduate course of mathematics at Cambridge still reflects a historically-broad approach; and problem-solving skills are tested in examinations, though the setting of excessively taxing questions has been discouraged for many years.

Today's Mathematical Tripos

Today, the Mathematical Tripos course comprises three undergraduate years (Parts IA, IB and II) which qualify a student for a BA degree, and an optional one year graduate course (Part III) which qualifies a student for an MMath (with BA) if they are a Cambridge fourth year student or a MASt (Master of Advanced Studies) degree if they come from outside just to do Part III. Assessment is mostly by written examination at the end of each academic year, with some coursework elements in the second, third and fourth years.

During the undergraduate part of the course, students are expected to attend around 12 one-hour lectures per week on average, together with two supervisions. Supervisions are informal sessions in which a small group of students - normally a pair - goes through previously completed example sheets under the guidance of a faculty member, college fellow or graduate student.

During the first year, Part IA, the schedule of courses is quite rigid, providing much of the basic knowledge requisite for mathematics, including algebra, analysis, methods in calculus, and probability. The second year, Part IB, contains some further important mandatory content, but in addition there are a number of pure and applied courses that students may choose from according to their preferences. In Part II, students are free to choose from a large number of courses over a wide range of mathematical topics. Until recently, some students took options within the Tripos that allowed them to give up some Mathematics courses in exchange for courses in Physics or Computer Science, with the possibility of changing to those subjects at the end of the first year - however, the Computer Science option was discontinued from the 2008-2009 academic year.

Further reading

• Rouse Ball, A History of the Study of Mathematics at Cambridge
• Leonard Roth (1971) "Old Cambridge Days", American Mathematical Monthly 78:223–236.

The Tripos was an important institution in nineteenth century England and many notable figures were involved with it. It has attracted broad attention from scholars. See for example:

• Griffin, N.; Lewis, A. C. (1990). "Bertrand Russell's Mathematical Education". Notes and Records of the Royal Society 44: 51. doi:10.1098/rsnr.1990.0004. 
• Stray, C. (2001). "The Shift from Oral to Written Examination: Cambridge and Oxford 1700–1900". Assessment in Education: Principles, Policy & Practice 8: 33–24. doi:10.1080/09695940120033243. 

In old age two undergraduates of the 1870s wrote sharply contrasting accounts of the Old Tripos — one negative, one positive. Andrew Forsyth, Senior Wrangler 1881, stayed in Cambridge and was one of the reformers responsible for the New Tripos. Karl Pearson Third Wrangler in 1879 made his career outside Cambridge.

• A. R. Forsyth (1935) Old Tripos Days in Cambridge, Mathematical Gazette, 19, 162-179.
• Karl Pearson (1936) Old Tripos Days at Cambridge, as Seen from Another Viewpoint, Mathematical Gazette, 20, 27-36.

J. J. Thomson, a Second Wrangler in 1880, wrote about his experience in:

• J. J. Thomson Recollections and Reflections London: G. Bell, 1936.

J. E. Littlewood, a Senior Wrangler in the last years of the old Tripos, recalled the experience in:

• J. E. Littlewood A Mathematician's Miscellany (2nd edition published in 1986), Cambridge University Press.

• G. H. Hardy, A Mathematician's Apology, Cambridge University Press (1940). 153 pages. ISBN 0-521-42706-1.
• Kathryn M. Olesko (2004) Review of Masters of Theory from American Scientist magazine.
• Theodore M. Porter (2003) Review of Masters of Theory from Science.

On the importance of the Tripos in the history of mathematics in Britain: search on "tripos" in

• The MacTutor History of Mathematics archive

For statistics on the number of graduates (men and women) between 1882 and 1940 see:

• Davis archive of female mathematicians: Cambridge

For the present-day Tripos see:

• Cambridge University: Guide to the Mathematical Tripos (pdf)
• Actual examination papers from 2001-2009
• The Cambridge Maths faculty's site explaining the CASM
• Nelson, Graham. "Miss Warren’s Profession" Eureka 51, 1992. Critique of Part III.