Cambridge Mathematical Tripos
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The Mathematical Tripos is the taught mathematics course at the University of Cambridge.
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[edit] Origin of the Mathematical Tripos
In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate students of the University of Cambridge. 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.
[edit] Influence
According to the study Masters of Theory: Cambridge and the Rise of Mathematical Physics by 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; and in the reception of new physical theories, particularly in electromagnetism as expounded by James Clerk Maxwell.
[edit] 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.
[edit] 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. The level of technique required of the candidates was high, and the time pressure in the examinations acute. 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.
[edit] 1909 Tripos reforms
The reforms implemented in 1909 did much to dismantle the old Mathematical Tripos system. It continued as an examination (and a course).
The influence persists. In Cambridge terms, it has done much to support the particular kind of mathematical approach of the University's Faculty of Mathematics. G. H. Hardy, one of those most responsible for the changes, was concerned in particular to assert the importance of pure mathematics. 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.
[edit] 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 a Certificate of Advanced Study in Mathematics. Assessment is mostly by written examination at the end of each academic year, with some coursework elements in the second, third and fourth years.[1]
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.[1] 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. Each example sheet takes about 10 hours to complete, but this is highly dependent on the individual student.
During the first two years (Parts IA and IB) the schedule of courses is quite rigid, and students have relatively little choice. Courses in these years cover pure mathematics (algebra and analysis); applied mathematics (electromagnetism, special relativity, quantum mechanics and fluid dynamics); and statistics. [2] 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, these will be discontinued for the 2008-2009 academic year.
During the third year (Part II), a wider choice of courses is available and a student will typically begin to specialise in either pure mathematics or applied mathematics.
[edit] CATAM (Computer-Aided Teaching of All Mathematics)
An optional component of the mathematical Tripos is CATAM, a series of computational projects that students can undertake in an attempt to gain extra credit. CATAM projects are completed over the first two terms of the academic year, with the first set of projects due in soon after the first term (these are usually sent into the University just before Christmas). (These projects are optional in the sense that the exams are optional - if you do not do them, you will not gain marks for them.)
[edit] Specific Structure of the Mathematical Tripos
[edit] Part 1A
There are two options; Mathematics and Mathematics with Physics. Mathematics with Computer Science was recently dropped. In the second option, the Numbers and Sets and Dynamics courses are exchanged for the Physics courses from Part 1A of the Natural Sciences Tripos.
[edit] Michaelmas Term
There are four lecture courses, each consisting of twenty-four one-hour lectures each and all lectured in the Cockroft Lecture Theatre. These are 'Groups', 'Vectors and Matrices', 'Numbers and Sets', and 'Differential Equations'.
[edit] Lent Term
Again, there are four lecture courses, each consisting of twenty-four one-hour lectures each and all lectured in the Cockroft Lecture Theatre; 'Analysis I', 'Probability', 'Vector Calculus' and 'Dynamics'.
[edit] Easter Term
There is a series of lecture courses examined in the second year - attendance is optional, since they will be repeated next year, but it is generally recommended that students attend at least one or two. They are held in the Mill Lane lecture rooms, and consist of 'Metric and Topological Spaces', Numerical Analysis', 'Optimisation', 'Special Relativity' and the non-examinable 'Concepts in Theoretical Physics'.
The year is examined over four 3 hour papers in late May or early June - these are the Mathematical Tripos Examination Papers.
[edit] References
- ^ a b University of Cambridge Courses Guide : Mathematics
- ^ University of Cambridge Mathematics Course Outline
- Masters of Theory: Cambridge and the Rise of Mathematical Physics (2003) Andrew Warwick, ISBN 0-226-87375-7.
- 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:
- John Gascoigne (1984) Mathematics and Meritocracy: The Emergence of the Cambridge Mathematical Tripos, Social Studies of Science, 14, 547–584.
- Nicholas Griffin; Albert C. Lewis (1990) Bertrand Russell's Mathematical Education, Notes and Records of the Royal Society of London, 44, 51–71.
- Christopher Stray (2001) The Shift from Oral to Written Examination: Cambridge and Oxford 1700–1900, Assessment in Education: Principles, Policy & Practice, 8, 33–50.
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.
[edit] See also
[edit] External links
On the importance of the Tripos in the history of mathematics in Britain: search on "tripos" in
For statistics on the number of graduates (men and women) between 1882 and 1940 see:
For the present-day Tripos see:
