Mathematical Tripos

Mathematics course taught in the Faculty of Mathematics, University of Cambridge

The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge.

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 eight days, totaling 44.5 hours. The total number of questions was 211. It was divided into two parts, with Part I (the first three days) covering more elementary topics. The questions for the 1841 examination may be found within Cambridge University Magazine (pages 191–208).

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.

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. Example questions from 1881, before the reforms, are quoted in A Mathematician's Miscellany:(b) A sphere spinning in equilibrium on top of a rough horizontal cylinder is slightly disturbed; prove that the track of the point of contact is initially a helix. (c) If the sphere has a centrally symmetrical law of density such as to make the radius of gyration a certain fraction of the radius then, whatever the spin, the track is a helix so long as contact lasts. (Marked at 200; a second part about further details carried another 105.)