MacTutor
IV. The Tripos coaches.
Part of a version of an address to the South-West Wales Branch of the Mathematical Association, Swansea, on 2 March, 1935, by Andrew R Forsyth. It was published in The Mathematical Gazette 19 (234) (1935), 162-179.
The Tripos coaches.
And now to turn to the actual teaching of the students by the coaches. It was excellently devised to achieve its aim, which usually was the attainment of high place in the examination; and I believe that the best of the coaches could have borne triumphant comparison with the best mathematical teachers at any epoch in any university. There must have been variations in the processes adopted by front-rank coaches in large practice: let me describe the system employed by Routh in my day.
The word system is used deliberately. Routh had fully 120 pupils in my freshman's Michaelmas term, a total which included men of four different standings because the Tripos examination was held in the Christmas vacation; and steady work on so large a scale had to be systematised. It was a marvel even of physical endurance, let alone intellectual effort. He arranged his pupils in small classes, not more than nine or ten: my own class consisted of six (being of the same year, we presumptuously called ourselves his "first" class); occasionally there was one and the same seventh member. (As an example of Routh's pre-eminent position in that little world, let me add that the said class of six were solid at the top of the list, and the occasional member was seventh in the list.) Each class was taken three times a week, on alternate days during the eight weeks of each of the three terms and the six or seven weeks of the long Vacation; and, in all, there were ten terms and three Long Vacations in the full undergraduate course. Each attendance was for one hour exactly, never more, never less. In our class he began at 8.15 in the morning, winter or summer; and in his overcrowded Michaelmas term he would be teaching until ten at night. A very few minutes at the beginning of the hour were spent in a swift examination of exercise work; the rest of the hour was devoted entirely to continuous exposition of the current subject. The topics were treated, not in connection with general underlying principles that might characterise the subject, but in the way that a student should frame his answer in the examination. We took abundant notes, scribbling our hardest (we developed a wonderful pace which told in the Tripos); the notes rarely needed working up; and the budget of these notes would be a small useful tract on its subject. Not a moment was spent in diversion, or extraneous illustration, or side-issues, or even examples. Routh had selected the topics in the whole range of subjects as he deemed best for Tripos purposes: no oral questions were asked because we were too busy writing: passing doubts had to be resolved, later, somehow: and any lack of comprehension had to be supplied outside the hour by such enquiry among fellow-students as the student cared to make. At the end of the hour some questions, always riders or problems cognate to the subject and about six in number, were given to us: their solution had to be brought to the next lecture. There might be a manuscript to be read or to be copied - the craft of manifolding had not been developed; the manuscripts, each a little tract of proofs of propositions ready to be discharged at examiners, were left in a general pupil-room that could be rather crowded. In regard to the not very numerous books - most of them being handy textbooks of a Cambridge quality - there might be a few chosen passages suggested to the student for his reading, the information to be dovetailed into his lecture-notes to the best of his own power.
Further, and this was a special feature, in every week there was a paper of problems only, given in common to all his students whatever their standing. In one week, unlimited time was allowed for the solutions; in another, the student was expected to spend only three hours on the paper, as though he were in the mill of the Senate-House. All the answers were handed in on the Friday or the Saturday of a week. On the Monday morning they had been returned to the pupil-room, together with a complete set of solutions by Routh, and with a mark-sheet which showed the mark-value of every attempt in every set of answers, as well as the respective totals. These totals were scrutinised by students, eager in their hope of ultimate high place, eager to compare themselves with one another and with men of senior standing. If a youngster scored well, in comparison with elders, he was noted; if he scored heavily in superiority to elders, his reputation blossomed - until it was nipped by his next failure. The spirit of competition had abundant stimulus, through these problem papers.
Finally, throughout the earlier years, there were occasional bookwork papers, really examination-papers of the canonical type set in the Tripos, each question consisting of bookwork and rider. In the third Long Vacation and the last term there were (I seem to remember) three of these every fortnight. The answers to these had to be written out exactly as in examination (the bookwork, be had to be written out exactly as in examination (the bookwork, be it noted, to be deliberately written out, for practice); and Routh examined these bookwork papers in class, very swiftly, spotting the deficiencies with an uncanny dexterity. Not a moment was wasted: no jesting or frivolous word over a blunder was ever spoken; and individual attention was given in public equally and impartially to all. Every subject, specified in the vast schedule for the one and undivided Tripos at that time, was covered in the first three academic years and the first two Long Vacations; the third Long Vacation and the single term of the fourth year were absorbed by revision, nothing but revision, of everything from the rudiments, upward and onward, in grim doggedness and unresting drill. Routh gave no "tips" to his students, in the usual sense of that word, meaning guesses at the minds of the examiners; and the little devices of a crammer were alien to the man and his work. He was concerned solely with the preparation of students for the examination and its demands; and anything like independence, in any direction of study or reading that led outside his scheme, was discouraged as a hazardous expenditure of precious time.
So the teaching by college lecturers counted for little over the general course compared with the coaching. Some courses of college lectures were attended, especially when related to newer subjects that had sprung up outside the old-established range. Thus in my own college W D Niven lectured on the Maxwell-Faraday theory of electricity and electromagnetism: though Routh and Maxwell were Senior and Second Wrangler in the same year, Maxwell's work was outside Routh's ambit. To Glaisher's lectures in pure mathematics I have already referred. Strangely, Routh's teaching in Rigid Dynamics was far from clear, falling far short of the standard he maintained elsewhere. He had written what was (and what still may be) the standard work of reference on the subject: one consequence to me was to stir a doubt (not applying to Routh alone) concerning the advisability of letting authors teach the subjects of books they have written, where presumably they have said what they have deemed important. In that subject I went to a course at St John's by R R Webb, a master in its range: and his course was superb.
And finally some of us made timid ventures outside the range of Cambridge textbooks. Reference has been made to T and T', a storehouse for subjects such as Potential, Attractions, Elasticity. Occasionally French books were tried, such as Verdet's Cours d'Optique and Pontécoulant's Système du Monde. Few of us had any working knowledge of German, even on a modest scale: there was Kirchhoff's Mechanik, and I ploughed through a large Durège's Elliptische Functionen. But all such ventures were exceptional and rare: there was no advice, no wish, no leisure, to urge us on those paths. The coach was the autocratic director, often the sole director.
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