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

The Mathematical Tripos is the taught mathematics course at the University of Cambridge. Image File history File links Download high-resolution version (730x994, 415 KB)Picture taken by me, June 23, 2005. ... Image File history File links Download high-resolution version (730x994, 415 KB)Picture taken by me, June 23, 2005. ... Class lists for Part III of the Mathematical Tripos, June 2005 The Senate House of the University of Cambridge in the centre of the city is used mainly for degree ceremonies and formerly for meetings of the Council of the Senate. ... The University of Cambridge, located in Cambridge, England, is the second-oldest university in the English-speaking world. ... The University of Cambridge, England, divides the different kinds of honours bachelors degree by Tripos, a word which has an obscure etymology, but which may be traced to the three-legged stool candidates once used to sit on when taking oral examinations. ... The University of Cambridge, located in Cambridge, England, is the second-oldest university in the English-speaking world. ...

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. The University of Cambridge, located in Cambridge, England, is the second-oldest university in the English-speaking world. ... 1780 was a leap year starting on Saturday (see link for calendar). ... 1909 (MCMIX) was a common year starting on Friday (see link for calendar). ... A mathematical problem is a problem that can be solved with the help of mathematics. ...

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 Clark Maxwell. To meet Wikipedias quality standards, this article may require cleanup. ... Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. ... Mathematics education is the study of the practices and methods of teaching mathematics. ... A giant Hubble mosaic of the Crab Nebula, a supernova remnant. ... Electromagnetism is the force observed as static electricity, and causes the flow of electric charge (electric current) in electrical conductors. ... James Clerk Maxwell James Clerk Maxwell (June 13, 1831 - November 5, 1879) was a Scottish physicist, born in Edinburgh. ...

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 (problem to solve, testing comprehension of the bookwork) was introduced. (17th century - 18th century - 19th century - more centuries) As a means of recording the passage of time, the 18th century refers to the century that lasted from 1701 through 1800. ... Latin is an ancient [[Indo-European languages|Indo-well as the Roman CEuropean language originally spoken in Latium, the region immediately surrounding Rome. ... A coach is a person who supports and directs another person or persons via encouragement and asking questions. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ...

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. At the University of Cambridge in the United Kingdom, a wrangler is a student who has completed the third year (called Part II) of the Mathematical Tripos with first-class honours. ... Edward John Routh (1831-1907) was a British 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. ...

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. The Faculty of Mathematics at the University of Cambridge comprises the Department of Pure Mathematics and Mathematical Statistics and the Department of Applied Mathematics and Theoretical Physics. ... G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ... Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. ...

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 by written examination at the end of each academic year.^[1] CASM stands for Certificate of Advanced Studies in Mathematics. It is both the culmination of the Cambridge University mathematics degree, as an additional year for those who wish to go on beyond the BA course, and a separate graduate course which accepts many people coming from other universities. ...

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 work through problem sets, under the guidance of a faculty member, college fellow or graduate 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] Some students only take Part IA of the Mathematical Tripos, and switch to a related subject (typically Computer Science or Physics) after their first year. Broadly speaking, pure mathematics is mathematics motivated entirely for reasons other than application. ... Algebra is a branch of mathematics concerning the study of structure, relation and quantity. ... Look up Analysis in Wiktionary, the free dictionary An analysis is a critical evaluation, usually made by breaking a subject (either material or intellectual) down into its constituent parts, then describing the parts and their relationship to the whole. ... To meet Wikipedias quality standards, this article may require cleanup. ... Electromagnetism is the force observed as static electricity, and causes the flow of electric charge (electric current) in electrical conductors. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... Fig. ... Fluid dynamics is the subdiscipline of fluid mechanics that studies fluids (liquids and gases) in motion. ... A graph of a bell curve in a normal distribution showing statistics used in educational assessment, comparing various grading methods. ...

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.

References

1. ^ ^a b University of Cambridge Courses Guide : Mathematics
2. ^ 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 Andrew Forsyth was a Scottish mathematician and was Professor Emeritus at the Imperial College of Science. ... Karl Pearson (pencil sketch in notebook; there is some see-through of writing on next page) Karl Pearson (March 27, 1857 – April 27, 1936) was a major contributor to the early development of statistics as a serious scientific discipline in its own right. ...

• 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 Second Wrangler in 1880 wrote about his experience in Sir Joseph John Thomson, OM, FRS (18 December 1856 – 30 August 1940) often known as J. J. Thomson, was an English physicist. ...

• 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 John Edensor Littlewood (June 9, 1885 – September 6, 1977) was a British mathematician. ...

• 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.

G. H. Hardy Professor Godfrey Harold Hardy FRS (February 7, 1877 – December 1, 1947) was a prominent British mathematician, known for his achievements in number theory and mathematical analysis. ... A Mathematicians Apology is a 1940 essay by British mathematician G. H. Hardy (ISBN 0521427061). ...

See also

• Faculty of Mathematics, University of Cambridge

The Faculty of Mathematics at the University of Cambridge comprises the Department of Pure Mathematics and Mathematical Statistics and the Department of Applied Mathematics and Theoretical Physics. ...

External links

• Kathryn M. Olesko's Review of Masters of Theory
• Theodore M. Porter's Review of Masters of Theory

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

• The MacTutor History of Mathematics archive

For a mid-Victorian (1869) view of the Tripos and some data on the marks awarded see Francis Galton Francis Galton Sir Francis Galton F.R.S. (February 16, 1822 – January 17, 1911), half-cousin of Charles Darwin, was an English Victorian polymath, anthropologist, eugenicist, tropical explorer, geographer, inventor, meteorologist, proto-geneticist, psychometrician, and statistician. ...

• Hereditary Genius pp. 16-23

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)
• The Cambridge Maths faculty's site explaining the CASM
• Nelson, Graham. "Miss Warren’s Profession" Eureka 51, 1992. Critique of Part III.