[2] 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.

Under William Whewell, the Tripos' scope changed to one of 'mixed mathematics', with the inclusion of topics from physics such as electricity, heat and magnetism.

[4] 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.

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.

Another coach, William Henry Besant published a textbook, Elementary Hydrostatics, containing mathematical exercises and solutions such as would benefit students preparing for Tripos.

Apart from intellectual preparation, the challenge of Tripos was its duration: "The examinations themselves were intended partly as tests of endurance, taking place on consecutive mornings and afternoons for four and five days together.

The coaches set the example: Routh had a two-hour constitutional walk daily, while "Besant was a mountaineer, Webb a walker, and Frost was extremely proficient in cricket, tennis, running and swimming.

[9] In 1880, Charlotte Angas Scott obtained special permission to take the Mathematical Tripos, as women were not normally allowed to sit for that exam.

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.

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.