 Results for parts II and III of the Mathematical Tripos are read out inside the Senate House, Cambridge, and then, tossed from the balcony. | |
| Type |
|
|---|---|
| Knowledge / skills tested | Mathematics |
| Duration | 3 or 4 years |
| Countries / regions | University of Cambridge |
| Languages | English language |
| Website | maths.cam.ac.uk/undergrad |
The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. [1]
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". [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. 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. [3] It was divided into two parts, with Part I (the first three days) covering more elementary topics. [4]
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. The 300-odd candidates below that level did not earn honours and were known as poll men. [5] The questions for the 1841 examination may be found within Cambridge University Magazine (pages 191–208). [6]
According to the study Masters of Theory: Cambridge and the Rise of Mathematical Physics by Andrew Warwick [7] during this period the style of teaching and study required for the successful preparation of students had a wide influence:
Since Cambridge students did a lot of rote learning called "bookwork", it was noted by Augustus De Morgan and repeated by Andrew Warwick [7] : 152 that authors of Cambridge textbooks skipped known material. In consequence, "non-Cambridge readers ... found the arguments impossible to follow."
From the 1820s to the 1840s, analytic topics such as elliptical integrals were introduced to the curriculum. 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. Students would have to study intensely to perform routine problems rapidly. [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. 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.
The list of wranglers (the candidates awarded a first-class degree) became in time the subject of a great deal of public attention. According to Alexander Macfarlane [8]
William Hopkins was the first coach distinguished by his students' performances. When he retired in 1849, one of his students, Edward Routh became the dominant coach. Another coach, William Henry Besant published a textbook, Elementary Hydrostatics, containing mathematical exercises and solutions such as would benefit students preparing for Tripos. After Routh retired in 1888, Robert Rumsey Webb coached many of the top wranglers. Warwick notes that college teaching improved toward the end of the 19th century:
A fellow of Trinity College, Robert Alfred Herman then was associated with several of the top wranglers as their coach; evidently the university was finally providing their students with education.
When A. R. Forsyth wrote his retrospective in 1935, he recalled Webb, Percival Frost, Herman, and Besant as the best coaches. Other coaches that produced top wranglers include E. W. Hobson, John Hilton Grace, H. F. Baker, Thomas John I'Anson Bromwich, and A. E. H. Love.
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." [7] : 186 Brisk walking was taken up by many candidates to build up their stamina. As the nineteenth century progressed walking turned to athletics and other competitive sports including rowing and swimming. 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." [7] : 200 By 1900, there were twenty-three recognized sports contested at Cambridge.
In 1873, Sarah Woodhead became the first woman to take, and to pass, the Mathematical Tripos. [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. She came eighth on the Tripos of all students taking them, but due to her sex, the title of "eighth wrangler," a high honour, went officially to a male student. [10] At the ceremony, however, after the seventh wrangler had been announced, all the students in the audience shouted her name. Because she could not attend the award ceremony, Scott celebrated her accomplishment at Girton College where there were cheers and clapping at dinner, a special evening ceremony where the students sang "See the Conquering Hero Comes", received an ode written by a staff member, and was crowned with laurels. [10] After this incident women were allowed to formally take the exam and their exam scores listed, although separately from the men's and thus not included in the rankings. Women obtaining the necessary score also received a special certificate instead of the BA degree with honours.
In 1890, Philippa Fawcett became the first woman to obtain the top score in the Mathematical Tripos. [11] [12]
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.)
As of 2018 [update] , 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 masters course (Part III) which qualifies a student for a Master of Mathematics (MMath) degree (with BA) if they are a Cambridge fourth year student or a Master of Advanced Study (MASt) 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. [13]
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 no mandatory content but it is recommended that students do particular courses as they are essential prerequisites for further courses. A range of pure courses, such as geometry, complex analysis and a course studying group theory, rings and modules are on offer as well as applied courses on electromagnetism, quantum mechanics and fluid dynamics. [14] In Part II, students are free to choose from a large number of courses over a wide range of mathematical topics; these are separated into more accessible C courses and D courses which are more involved. Some students choose to exchange 25% of the first-year mathematics options in exchange for the Physics option of first-year Natural Sciences Tripos with the possibility of changing to Natural Sciences at the end of the first year.
A Tripos is an academic examination that originated at the University of Cambridge in Cambridge, England. They include any of several examinations required to qualify an undergraduate student for a bachelor's degree or the courses taken by a student to prepare for these. Undergraduate students studying mathematics, for instance, ultimately take the Mathematical Tripos, and students of English literature take the English Tripos.
The British undergraduate degree classification system is a grading structure used for undergraduate degrees or bachelor's degrees and integrated master's degrees in the United Kingdom. The system has been applied, sometimes with significant variation, in other countries and regions.
At the University of Cambridge in England, a "Wrangler" is a student who gains first-class honours in the Mathematical Tripos competition. The highest-scoring student is the Senior Wrangler, the second highest is the Second Wrangler, and so on. By contrast, the person who achieves the lowest exam marks while still earning a third-class honours degree is known as the wooden spoon.
The Sixth Term Examination Papers in Mathematics, often referred to as STEP, is currently an university admissions test for undergraduate courses with significant mathematical content - most notably for Mathematics at the University of Cambridge. Starting from 2024, STEP will be administered by OCR, replacing CAAT who was responsible for administering STEP in previous years.
Part III of the Mathematical Tripos is a one-year master's-level taught course in mathematics offered at the Faculty of Mathematics, University of Cambridge. It is regarded as one of the most difficult and intensive mathematics courses in the world. 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.
The Natural Sciences Tripos (NST) is the framework within which most of the science at the University of Cambridge is taught. The tripos includes a wide range of Natural Sciences from physics, astronomy, and geoscience, to chemistry and biology, which are taught alongside the history and philosophy of science. The tripos covers several courses which form the University of Cambridge system of Tripos. It is known for its broad range of study in the first year, in which students cannot study just one discipline, but instead must choose three courses in different areas of the natural sciences and one in mathematics. As is traditional at Cambridge, the degree awarded after Part II is a Bachelor of Arts (BA). A Master of Natural Sciences degree (MSci) is available to those who take the optional Part III. It was started in the 19th century.
Sir Horace Lamb was a British applied mathematician and author of several influential texts on classical physics, among them Hydrodynamics (1895) and Dynamical Theory of Sound (1910). Both of these books remain in print. The word vorticity was invented by Lamb in 1916.
Edward John Routh was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematise the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.
The term prelim generally refers to an examination that qualifies a student to continue studies at a higher level, and/or allow the student to comprehend their studies and see how prepared they are for an upcoming examination. It can also act as a gauge on how knowledgeable one is within the chosen subject.
Charlotte Angas Scott was a British mathematician who made her career in the United States and was influential in the development of American mathematics, including the mathematical education of women. Scott played an important role in Cambridge changing the rules for its famous Mathematical Tripos exam.
The Senior Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain".
Thomas Gaskin (1810–1887) was an English clergyman and academic, now known for contributions to mathematics.
A mathematical exercise is a routine application of algebra or other mathematics to a stated challenge. Mathematics teachers assign mathematical exercises to develop the skills of their students. Early exercises deal with addition, subtraction, multiplication, and division of integers. Extensive courses of exercises in school extend such arithmetic to rational numbers. Various approaches to geometry have based exercises on relations of angles, segments, and triangles. The topic of trigonometry gains many of its exercises from the trigonometric identities. In college mathematics exercises often depend on functions of a real variable or application of theorems. The standard exercises of calculus involve finding derivatives and integrals of specified functions.
William Henry Besant was a British mathematician, brother of novelist Walter Besant. Another brother, Frank, was the husband of Annie Besant.
Robert Rumsey Webb, known as R. R. Webb, was a successful coach for the Cambridge Mathematical Tripos. Webb coached 100 students to place in the top ten wranglers from 1865 to 1909, a record second only to Edward Routh.
Robert Alfred Herman (1861–1927) was a fellow of Trinity College, Cambridge, who coached many students to a high wrangler rank in the Cambridge Mathematical Tripos. Herman was senior wrangler in 1882.
Sheila May Edmonds was a British mathematician, a Lecturer at the University of Cambridge, and Vice-Principal of Newnham College from 1960 to 1981.
The University of Cambridge is a collegiate public research university in Cambridge, England. Founded in 1209 and granted a royal charter by King Henry III in 1231, Cambridge is the second-oldest university in the English-speaking world and the world's fourth-oldest surviving university. The history and influence of the University of Cambridge has made it one of the most prestigious universities in the world. Numerous scholarships, prizes, honors, and awards specific to the university are awarded to prospective or current students.
Thomas Oliver Harding was Senior Wrangler at Cambridge University in 1873.
In the United Kingdom there are various standardized tests for admission to university. Most applicants to universities in the UK take national examinations such as A-levels or Scottish Highers. Separate admissions tests are used by a small number of universities for specific subjects, many of these administered by Cambridge University's Admissions Testing Service.
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:
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.
J. J. Thomson, a Second Wrangler in 1880, wrote about his experience in:
J. E. Littlewood, a Senior Wrangler in the last years of the old Tripos, recalled the experience in:
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:
