# V C Morton's reports on Pure Mathematics at Aberystwyth

In 1923 Vernon Charles Morton was appointed lecturer at the University College of Wales, Aberystwyth, being promoted to Independent Lecturer and Head of the Pure Mathematics Department in 1926 and to Professor in 1933. Below we give the annual Report on the Department of Pure Mathematics of the University College of Wales, Aberystwyth, written by Morton for each of the years 1927 to 1950. We also include the Report for 1926 written by George Adolphus Schott, Professor of Applied Mathematics, since it relates to the year in which Morton became Head of Pure Mathematics. We have made some alterations to the reports. In particular we have given the full reference of papers which appear under the title 'Publications' where they tend to be reported before publication when the page numbers were not known.
1. Session 1925-26.

Report submitted 22 OCTOBER 1926.

PURE MATHEMATICS

Professor G A Schott.

The numbers of students taking courses in the department this session were almost the same as last session; so also were the numbers of passes. The chief differences were a decrease in the Subsidiary class and increases in the Final and Honours classes. The work done was very satisfactory, especially at the Final and Honours stages, and the following students are deserving of special commendation:- Subsidiary, Miss D S Meyler, W V Williams; Second Year, Honours, H Falkner, Miss C W Lucas. This session, for the first time since the re-organisation of the department, there were students (2) taking Second Year Honours in Pure Mathematics alone, of whom one, Miss C W Lucas, obtained First Class and the other Second Class, Second Division. Owing to the limited facilities provided hitherto for the study of Applied Mathematics in Girls' Schools and the consequent insufficient preparation of women students at entrance in that subject, it will be necessary for some time yet to provide an Honours course in Pure Mathematics alone, although the new Combined course in Pure and Applied Mathematics gives a much better balanced training in Mathematics and besides affords better opportunities for the student's future career. Five students, all men, took the combined Honours course, three with Theory of Functions, and two with Differential Geometry as their special subject in Pure Mathematics. The inauguration of courses in Geometry and Algebra up to the highest stages is a gratifying feature of this session's work, in so far as the training in Pure Mathematics has thereby been rendered much better balanced than hitherto, and the successful carrying out of this new departure is mainly due to and reflects great credit upon Mr V C Morton, M.A., the new Head of the Department. I wish to thank him and his colleagues, Messrs W G L Sutton, M.A., and D R Williams, M.A., for the valuable work they have done, and I am confident that under the guidance of Mr Morton the future progress of the Department is well assured.

2. Session 1926-27.

Report submitted 19 OCTOBER 1927.

PURE MATHEMATICS

Mr V C Morton.

The number of students taking courses in the Department this session was slightly less than the number last session, whilst the proportion of passes was approximately the same this year as last. The chief decrease was in the Subsidiary Class, compensated to some extent by an increase in the Second Year Honours Class. The work done was very satisfactory, especially that of the Honours students. The following students deserve special mention:- Intermediate, Mr I G Jenkins; Subsidiary, Messrs J G Nicholas and E M Williams; Final, Miss D S Meyler and Mr I G Richards; Second Year Honours, Miss D Grindley. Six students, four of whom were girls, took second year Honours in Pure Mathematics alone, four with Differential Geometry and two with Theory of Functions as special subject. One, Miss D Grindley, obtained First Class, two, Second Class, First Division, two, Second Class, Second Division, and one, Third Class. Five men sat the Combined Honours examination, two with Differential Geometry as special subject. Four obtained Second Class, First Division, and one, Third Class. The work of this double group of Honours students was keen and their enthusiasm fully justified the time spent by the staff on framing and providing for the various alternative courses.

Mr O G Sutton is continuing his research on a problem in the Theory of Functions and Mr Morton has two papers in preparation on algebraical and geometrical subjects.

In July, 1926, the Department lost the services of Mr D R Williams, M.A., who was elected to a University Fellowship, and is at present pursuing research work at Strasbourg. I should like to express my appreciation of his efficient and enthusiastic work for the Department during the two years he was here. To fill the vacancy Mr O G Sutton, BSc, an old student of this College, was appointed assistant Lecturer. He has been very successful and has ably carried out his full share of the work, both in the early and advanced stages. Mr B A Edwards, who holds a University Fellowship and who is researching at Cambridge, in geometry, gave a short but stimulating course of lectures to the Honours Class on Descriptive Geometry. Mr W G L Sutton has proved himself invaluable to the Department. His experience in both the Departments of Pure and Applied Mathematics has contributed largely to the success of the Combined Honours course which offers a thorough and well-balanced training in Mathematics as a whole.

In conclusion I wish to take this opportunity to express my appreciation of the way the Department had been re-organised and put into smooth running order ready for this last session by Professor G A Schott during the years 1923-6 and to thank him for his generous cooperation and the help of his experience.

3. Session 1927-28.

Report submitted 24 OCTOBER 1928.

PURE MATHEMATICS

Mr V C Morton.

There has been a slight increase this last session in the number of students taking courses in the Department and it is gratifying to be able to report that this increase is due to the influx of more students of improved quality from the schools. The work done was satisfactory, especially in the Subsidiary class which contained several promising Honours candidates. The Final and Honours classes were somewhat uneven. The following students deserve mention:- Subsidiary, Messrs D T Davies and C E Easthope; Final, Messrs J G Nicholas and E M Williams; Second Year Honours, Miss D S Meyler and Mr I G Richards. Miss D S Meyler was awarded a First Class in Pure Mathematics. Her work was of a very high quality.

Miss D Grindley, who holds a University Studentship, has carried out some research work on the Mathematical Theory of Mapping, with especial reference to the recent developments due to the United States Coast and Geodetic Survey. She has shown initiative and energy in collecting of material. Mr D R Williams, a former student and member of the staff, has now completed his tenure of a Fellowship of the University of Wales and the results of his research on Integral Functions will shortly be published in the "Rendiconti del Circolo matematico di Palermo."

The Department has lost the services of Mr O G Sutton, who resigned at the end of the Easter term to take up an appointment under the Meteorological Office. I take this opportunity to express my appreciation of his useful work for the Department. Mr E Davies, BSc, of Bangor, who was appointed as temporary assistant for the summer term, performed his duties competently.

In conclusion, I wish to thank Mr W G L Sutton for his enthusiastic and efficient cooperation in the work of the Department.

4. Session 1928-29.

Report submitted 23 OCTOBER 1929.

PURE MATHEMATICS

Mr V C Morton.

The number of students taking courses in the Department during the session 1928-9 was 87, a slight increase from the previous session.

The work done was satisfactory, especially that of the Subsidiary and First Year Honours classes, in both of which there are several promising students.

The following deserve special mention:- Intermediate, Miss E M Jones and Mr S C Townshend; Subsidiary : Messrs M T Chapple, H C Hum, T R James, A S T Leach, D E Morgan and J F Ractliffe; Final and First Year Honours : Messrs D T Davies and C E Easthope; Second Year Honours : Mr J G Nicholas.

Three students took Honours in Mathematics and one in Pure Mathematics. One, Mr J G Nicholas, obtained First Class, one Second Class, First Division, and two Third Class.

Miss D Grindley who has held a University Studentship for two years obtained her M.A. degree with a thesis on "Recent Developments in the Mathematical Theory of Mapping" in which she showed very good capacity for collection and arrangement of material and considerable critical ability. Her work was fully up to the requisite standard.

Mr B V Williams who took Honours in Mathematics at Aberystwyth in 1927 and who subsequently was awarded a Meyricke scholarship at Jesus College, Oxford, has recently been awarded a B.Sc. degree by the University of Oxford for a thesis on curves in manifold space, a subject in which he became interested whilst specializing in Geometry at Aberystwyth.

Mr D R Williams, who in 1926 resigned his post on the staff in order to take up a University Fellowship, has been re-appointed in place of Mr O G Sutton. Mr Williams's doctorate thesis on "Complements au théorème de M Julia" was published in the Rendiconti del Circolo Matematico di Palermo, Vol. 52. 1928.

Mr Morton has ready for publication a paper on the rational normal curve and another in preparation.

During the course of the year Mr E G Phillips of Bangor visited Aberystwyth under the exchange system and gave a short course of lectures to the Honours students; these lectures were well attended and appreciated.

I have pleasure in acknowledging the willing and efficient cooperation of my colleagues, Mr W G L Sutton and Mr D R Williams, in the work of the department.

5. Session 1929-30.

Report submitted 15 OCTOBER 1930.

PURE MATHEMATICS

Mr V C Morton.

The number of students in the Department is again slightly larger than in the previous session.

The work done was satisfactory, especially in the Honours courses. I have pleasure in being able to report that the number of Honours' candidates is increasing; next year I expect to have 11 taking Second Year Honours and 14 First Year Honours, several more than at the time a few years ago when the Department had a lecturer in addition to the equivalent of the present staff of Head of Department and two assistant lecturers.

The following students deserve special mention:- Intermediate, Miss B Wardle and Mr D A Williams; Subsidiary, Messrs G A Corfield, W H Francis, E Morgan and R H Pitman; Final and First Year Honours, Messrs M T Chapple, T A Humphries, H C Hum, T R James, J F Ractliffe and J G Thomas; Second Year Honours, Messrs D T Davies and C E Easthope.

Four students took Honours in Pure Mathematics and two in Mathematics. Two, Messrs D T Davies and C E Easthope, obtained First Class; one Second Class, First Division; one Second Class, Second Division, and two Third Class.

Miss D S Meyler, who holds a University Studentship, is researching on a branch of Algebraic Geometry. Her work during the year has been largely that of collection and arrangement of material, but already she has also carried out some original investigations.

Mr B V Williams, an old student who held a Meyricke Scholarship for research at Oxford, has been appointed to a post in the research department of the Air Force. Some of the results of his investigations on Non-Riemannian Geometry have recently been published in America.

Mr G J Nicholas, who obtained First Class Honours in Mathematics in 1929, was awarded last summer, in competition, a Meyricke Scholarship at Jesus College, Oxford. He is carrying out research there on Power Series.

During the Michaelmas term, under the Exchange of Teachers Scheme, I gave a course of lectures at Bangor, on Projectivities.

A paper by me on a problem in Differential Geometry has been accepted for publication in the Proceedings of the London Mathematical Society. Mr W G L Sutton and myself are at present working in collaboration on two geometric problems.

I am greatly indebted to my colleagues, Mr W G L Sutton and Mr D R Williams, for their ungrudging and very efficient cooperation in the work of the Department.

Publication by a former student:-

Mr B V Williams (in collaboration with J H C Whitehead).

B V Williams and J H C Whitehead, A Theorem on Linear Connections, Annals of Mathematics, Second Series 31 (1) (1930), 151-157.

6. Session 1930-31.

Report submitted 20 OCTOBER 1931.

PURE MATHEMATICS

Mr V C Morton.

The number of students in the Department is again slightly larger than in the previous session.

The work done was quite satisfactory, especially in the Subsidiary and Second Year Honours courses. The Honours classes are keeping up their numbers and their performances continue to be good.

The following students deserve special mention:- Intermediate, Mr B J Lewis; subsidiary, Messrs R A M Bound, J V Harries, B R Jones and B J Thomas; Final and First Year Honours, Messrs G A Corfield and W E Jones; Second Year Honours, Messrs M T Chapple, T R James, T A Humphries and J F Ractliffe.

Eight students took the Honours examination in Pure Mathematics and three in Mathematics. Of these, four, Messrs M T Chapple, T R James, T A Humphries and J F Ractliffe, obtained First Class; two Second Class, First Division; two Second Class, First Division; two Second Class, Second Division; and two Third Class. It is with great sorrow that I report the death of one of our promising Honours students, Mr J F Skrine. He took a full share in College life and has been greatly missed.

I regret also to have to report the serious illness of Miss D S Meyler, who has been carrying out research in a branch of Algebraic Geometry. I am very pleased to say, however, that she had the satisfaction of having a joint paper, in collaboration with me, accepted for publication in the Proceedings of the London Mathematical Society. I hope that when she has completely recovered we shall be able to continue this research.

In conclusion, I gladly take this opportunity of thanking my colleagues, Mr W G L Sutton and Mr D R Williams, for their ungrudging and very efficient cooperation in the work of the Department.

7. Session 1931-32.

Report submitted 19 OCTOBER 1932.

PURE MATHEMATICS

Mr V C Morton.

The work done in the various classes was satisfactory except that in the Intermediate class which was much below the average. Particularly good work was done in the First Year Honours classes.

The following students deserve special mention:- Subsidiary : Miss M Blackledge, Mr N F Jenkins and Mr D G Pryce; Final and First Year Honours, Miss R M Evans, Miss M Jones, Mr J V Harries and Mr B R Jones; Second Year Honours : Mr W E Jones.

Eight students took the Honours examination in Pure Mathematics and two in Mathematics. Of these, one, Mr W E Jones, obtained First Class; three Second Class, First Division; two Second Class, Second Division; and three, Third Class.

Mr B V Williams, BSc, submitted, for the M.Sc. degree, a thesis on (1) "The integration of the curvature tensor for a flat unsymmetric connection"; (2) "The Serret equations and curvature of a curve in a Riemannian n-space." He was awarded the degree.

Research. - Mr D T Davies, who has held the John Francis scholarship during the year, has been researching with me on "Poristic Configurations." He has been occupied chiefly in the collection and arrangement of material, but has also done a little original work that promises well.

I am pleased to be able to report that Miss D S Meyler, who suffered a serious illness whilst engaged in research work, is well on the way to recovery and I hope that she will return next session to continue her research work with me.

During the year Mr W G L Sutton has been working on a problem in Integral Equations. I have been collaborating with Professor A L Dixon of Oxford in some investigations on the Cubic Surface.

In conclusion, I gladly take this opportunity of thanking my colleagues, Mr W G L Sutton, Mr D R Williams and Mr T Lewis for their willing and very efficient cooperation in the work of the Department.

8. Session 1932-33.

Report submitted 18 OCTOBER 1933.

PURE MATHEMATICS

Mr V C Morton.

The number of students taking courses in the Department during the Session 1932-3 was 83.

The work done was satisfactory, especially that of the Subsidiary and Second Year Honours classes, in both of which there were several excellent students.

The following deserve special mention:- Intermediate, Mr A D Edwards; Subsidiary, Messrs E T J Davies, J G Forbister, J A Jones and H Thomas; Final and First Year Honours, Messrs N F Jenkins and D G Pryce; Second Year Honours, Messrs J V Harries and B R Jones and Miss M E Jones.

One student took Honours in Mathematics and seven in Pure Mathematics. Three obtained First Class, two Second Class, First Division, two Second Class, Second Division and one Third Class. I regret to state that one of the Second Year Honours students, Mr E Morgan, died during the course of the year.

Three postgraduate students have been carrying out research in the Department. Miss D S Meyler was awarded the M.Sc. Degree in January last for a thesis on "Modern work in the theory of the cubic surface." This thesis was considered by the Examiners to be of a very high standard indeed. I have great pleasure in being able to report that Miss Meyler has recovered from the prolonged illness which interrupted her research work and that she has recently been awarded a Fellowship of the University of Wales. She will thus have further opportunity of developing her exceptional mathematical ability.

Mr D T Davies was awarded the M.Sc. Degree in June for a thesis on "Some Algebraic Methods in the poristic theory of a rational normal curve." This thesis too was considered to be of high standard.

Mr D E Morgan has been working with Mr W G L Sutton on application of operational methods to differential equations. Mr Morgan hopes to continue this work next year.

I cannot let slip this opportunity, the last that I shall have before the retirement of Vice-Principal G A Schott from the headship of the department of Applied Mathematics, of recording my deep gratitude and thanks to him for his unfailing help, wise advice and kindness since my appointment on the staff of the College.

I have pleasure in acknowledging with gratitude the willing and efficient cooperation of my colleagues Mr W G L Sutton, Dr D R Williams and Mr T Lewis, in the work of the department.

9. Session 1933-34.

Report submitted 17 OCTOBER 1934.

PURE MATHEMATICS

Professor V C Morton.

The number of students who entered for courses in the Department during the Session 1933-4 was 86.

The work done was satisfactory, especially that of the First and Second Year Honours Classes, in both of which excellent promise was shown.

The following deserve special mention:- Subsidiary, Messrs A G Hurn, E J Richards and Miss Peggy Davies; Final and First Year Honours, Messrs E T J Davies, J G Forbister, J A Jones and H Thomas; Second Year Honours, Messrs N F Jenkins and D G Pryce.

One student took Honours in Mathematics and four in Pure Mathematics. Two obtained First Class and three Second Class, Second Division. The two First Classes were of very good standard indeed.

For some time we have felt that more tutorial work, the laboratory-work of Mathematics, has been urgently needed. I wish to thank the College Council and Senate for the recent encouragement and promise of help given in this direction.

Research. - The present severe competition for posts is heavily handicapping the student research work in the Department. Two post graduate students Mr W E Jones and Mr M T Chapple began work under, my direction during the session. Mr W E Jones was offered and accepted a teaching post in the middle of the session and Mr M T Chapple, who was holding a two-year University Studentship has just taken a teaching post at the end of his first year of tenure. Mr Chapple was working with me on Rational Normal Curves and was doing exceptionally promising work. We had already a paper in preparation for publication. One of the best men I have had in the Department, Mr B R Jones, who had already started to research towards the end of his Honours' year and who showed great promise, has obtained a teaching post and will not be returning. All these men, who earnestly wanted to continue research, came to me for advice, but in the present conditions I felt that I had no alternative but to advise them regretfully to take the posts offered.

Miss D S Meyler is now at Cambridge, holding a University Fellowship, and researching on Algebraic Geometry. She has been doing good work and has some new results.

Dr D R Williams is continuing his work on Integral Functions. Mr W G L Sutton is working on Differential Equations and allied problems. He has recently published two papers. I have been continuing my work on the Cubic Surface and have published a paper in collaboration with Professor A L Dixon of Oxford. I have another paper in preparation on the same subject in collaboration with Miss D S Meyler.

It is with great regret that I must report the resignation of my colleague and friend, Mr W G L Sutton. He is leaving to take up an appointment as Head of the Mathematics Department and Vice-Principal of the Leeds College of Technology. Mr Sutton has been with me through all the changes in the Department since 1923. An invaluable and absolutely reliable colleague and a loyal friend, his absence will be felt keenly in the work of the Department and in the everyday life of the remaining staff. We wish Mr and Mrs. Sutton all success and happiness in their new home.

Finally I have great pleasure in acknowledging with gratitude the loyal and efficient cooperation of my colleagues Mr W G L Sutton and Dr D R Williams in the work of the Department.

10. Session 1934-35.

Report submitted 16 OCTOBER 1935.

PURE MATHEMATICS

Professor V C Morton.

The number of students who entered for courses in the Department during the Session 1934-5 was 70.

The work done was satisfactory, especially that of the First and Second Year Honours Classes. The Second Year Honours Class was one of the best we have had for some years.

The following deserve special mention:- Subsidiary, Messrs T V Davies and A C S Pindar; Final and First Year Honours, Miss Peggy Davies and Mr E J Richards; Second Year Honours, Messrs E T J Davies, J G Forbister and J A Jones, all of whom obtained First Class Honours.

Five students took Honours in Mathematics and three in Pure Mathematics. Three obtained First Class, three Second Class, First Division, and two Second Class, Second Division.

Mr M T Chapple, who took First Class Honours in Pure Mathematics in 1932 and First Class Honours in Physics in 1933, and who has held a University Studentship, submitted, in candidature for the MSc. degree, a thesis on "Some congruences and a complex of Space Cubic Curves." The thesis contained considerable original work and was considered by the Examiners to be very good indeed.

11. Session 1935-36.

Report submitted 21 OCTOBER 1936.

PURE MATHEMATICS

Professor V C Morton.

The number of students who entered for courses in the department during the Session 1935-36 was 68.

The work done was, on the whole, satisfactory. That of the Second Year Honours class was not of the very high standard of the few previous years, but, on the other hand, this class contained no really weak student. In the First Year Honours class some very promising work was done. The Final Class was weaker than usual; this was due largely to the presence in it of seven students who were repeating the course after failure. The Subsidiary class was very homogeneous and, of the new entrants into College, not one failed. As usual the Intermediate class was, with two or three exceptions, weak; this will always be the case until entrance requirements are revised.

The following deserve special mention:- Intermediate, Messrs J D R Howell and E H Spoonley; Subsidiary, Messrs T G Jones and W R Thomas; Final and First Year Honours, Messrs T V Davies and A C S Pindar.

Five students took Honours in Pure Mathematics and two in Mathematics. Four obtained Second Class, First Division, and three Second Class, Second Division. Mr A H Higgs, who should have taken Honours this year, was taken ill early in the session and had to postpone the completion of his course. We hope that he will make a good recovery and be able to take Honours next session.

Two post-graduate students, Mr N F Jenkins and Mr D G Pryce, who had very good First Classes in 1934, have been doing research work in geometrical subjects under my direction and have made excellent progress.

During the session, Dr D R Williams gave a short course of lectures on a subject in the Theory of Functions at the University College, Bangor. I gave a short course at the University College, Cardiff, on a geometrical subject.

Miss Meyler and myself are continuing work on some problems in higher space.

I take this opportunity of expressing my appreciation of the efficient and loyal cooperation of Dr D R Williams and Miss D S Meyler in the work of the department.

12. Session 1936-37.

Report submitted 20 OCTOBER 1937.

PURE MATHEMATICS

Professor V C Morton.

The number and distribution of students in the Department during the session 1936-37 are shown in the table printed elsewhere in this volume.

The work done was, on the whole, satisfactory. Two men, Mr T V Davies and Mr A C S Pindar, sat for Honours in Pure Mathematics, and both, after a year of excellent work, obtained good First Classes. Both will, I hope, proceed to take Honours in Applied Mathematics next session. One student, Mr T L Phillips, carried out research work in a branch of Differential Geometry and has made good progress. Mr E T J Davies and Mr J G Forbister, who had excellent First Classes in 1935, have obtained research posts in Government departments.

The Department continues to specialise in Geometry. Miss D S Meyler and myself have papers almost ready for publication on geometrical subjects.

Publication.

Mr W T Howell.

W T Howell, A Note on Laguerre Polynomials, Philosophical Magazine (7) 23 (1937), 807-811.

13. Session 1937-38.

Report submitted 19 OCTOBER 1938.

PURE MATHEMATICS

Professor V C Morton.

The work done in the various classes throughout the Session has been, on the whole, satisfactory. The best quality was shown in the Subsidiary Class, which contained several first year men of distinct promise. For the first time for several years the Second Year Honours Class lacked first-rate men. Of the three candidates for Honours in Mathematics, one obtained Class II i; and two Class II ii.

Miss Meyler and myself have papers in preparation on geometrical subjects.

Publications.

Professor V C Morton:

V C Morton, The triple tangent planes of a cubic surface, The Quarterly Journal of Mathematics 8 (1) (1937), 238-240.

Mr W T Howell:

W T Howell, On Products of Laguerre Polynomials, Philosophical Magazine (7) 24 (161) (1937), 396-405.

W T Howell, On some Operational Representations of Products of Parabolic Cylinder Functions and Products of Laguerre Polynomials, Philosophical Magazine (7) 24 (165) (1937), 1082-1093.

W T Howell, Integral Representations for Products of Weber's Parabolic Cylinder Functions, Philosophical Magazine (7) 25 (168) (1938), 456-458.

W T Howell, A Note on Hermite Polynomials, Philosophical Magazine (7) 25 (169) (1938), 600-601.

W T Howell, On a Class of Functions which are Self Reciprocal in the Hankel Transform, Philosophical Magazine (7) 25 (169) (1938), 622-628.

14. Session 1938-39.

Report submitted 18 OCTOBER 1939.

PURE MATHEMATICS

Professor V C Morton.

The work done in the department during the Session has been, on the whole, satisfactory although the quality of the first year students was not so good as in the previous year. The best work was done in the First Year Honours Class which contained several promising students who should do well in Honours next Session. In the Honours examination in Mathematics one man had a First Class, one a Second Class, First Division, and one a Third Class.

Publications.

Professor V C Morton:

V C Morton, The general quadric primal in [5] which is at the same time inscribed and circumscribed to a given simplex, Quarterly Journal of Mathematics 9 (1938), 310-314.

15. Session 1939-40.

Report submitted 16 OCTOBER 1940.

PURE MATHEMATICS

Professor V C Morton.

The work done in the Department during the Session has been, on the whole, very satisfactory in spite of abnormal conditions. The most note- worthy feature has been the good quality of the first year students in the Subsidiary Class; several show distinct promise. In the Honours examination in Mathematics, one man had a First Class, one a Second Class, First Division, and one a Second Class, Second Division.

About twenty students of University College, London, have taken courses in the Department, Most of them have been working for their own examinations, but there has been no difficulty in fitting them into the appropriate classes.

16. Session 1940-41.

Report submitted 22 OCTOBER 1941.

PURE MATHEMATICS

Professor V C Morton.

In spite of war conditions, the work done in the Department during the Session has been very satisfactory, particularly that in the First Year Honours class, which contained several promising students. In the Honours examination in Mathematics, the one candidate was placed in the First Class and in Pure Mathematics the one candidate was placed in the Second Class, First Division. The results in other grades were rather better than usual. In my opinion the students in the Department have been working with a definite sense of responsibility.

Only a few students of University College, London, have taken courses in the Department this Session. There has been little difficulty in arranging for them.

17. Session 1941-42.

Report submitted 21 OCTOBER 1942.

PURE MATHEMATICS

Professor V C Morton.

The work done in the Department during the Session has been very satisfactory at all stages. The most noticeable change has been a sudden rise both in the numbers and quality of the Intermediate class. Of the four candidates for Honours in Mathematics, two were placed in Class I and two in Class II, Division 1. Once again, with a little extra work, we have been able to cater for a few students of University College, London.

18. Session 1942-43.

Report submitted 27 OCTOBER 1943.

PURE MATHEMATICS

Professor V C Morton.

The work in the Department has been very satisfactory at all stages particularly in the Second Year Honours class where, of three candidates for Honours in Mathematics, two were awarded First Class and one Second Class, First Division.

In order to strengthen the courses of Radio Bursars, a new College and University subject, Mathematics (combined Pure and Applied), was introduced at the Subsidiary stage. Eleven students took this course and several of them will continue the course next Session at the Final stage.

As usual, several students of University College, London, were accommodated in the Department at the appropriate stages.

19. Session 1943-44.

Report submitted 25 OCTOBER 1944.

PURE MATHEMATICS

Professor V C Morton.

Owing to war conditions our Second Year Honours Class was unusually weak. Apart from this the work done in the Department was, on the whole, good. The First Year Honours Class was particularly strong; all but one will leave this year for National Service, but will return, I hope, after the war to take Honours. This year, for the first time, we have offered a Final course in Mathematics, combined Pure and Applied, for the sake of our Radio Bursar. It may be possible, with some strengthening, to develop this course into a useful course for science specialists after the war.

Once again we have been able to fit a few London students into our classes.

20. Session 1944-45.

Report submitted 24 OCTOBER 1945.

PURE MATHEMATICS

Professor V C Morton.

The work done in the Department during the Session has been, on the whole, fairly satisfactory, although the Final Class was rather weaker than usual. Most of our senior Honours students are away on war service; the one remaining candidate for Honours in Mathematics obtained a Second Class, First Division, Once again a group of Radio Bursars took a Final course in combined Pure and Applied Mathematics. This course, modified and extended, may become very useful to Science students in future years.

21. Session 1945-46.

Report submitted 23 OCTOBER 1946.

PURE MATHEMATICS

Professor V C Morton.

The work in the Department during the Session has been satisfactory in the circumstances, except at the Intermediate stage, where the immaturity of some of the entrants made it hard to deal with the class as a group. The Honours Class has continued to be small through war conditions, our best students having been unable to finish their Honours courses. The one candidate for Honours in Pure Mathematics obtained a Second Class, First Division, and the one candidate for Honours in Mathematics obtained a Second Class, Second Division. There are one or two promising students in the First Year Honours Class, and we hope that some of our best men of past years will be able to return to complete Honours next Session or the Session after.

In my opinion the Departments of Mathematics in the College could contribute more to the needs of certain Science students by the institution of courses of Mathematics for them quite distinct from the traditional Intermediate and Subsidiary courses and extending over two or even three years. We hope that with University development it may be possible to plan such courses which should carry with them tutorial work to make them fully effective.

22. Session 1946-47.

Report submitted 22 OCTOBER 1947.

PURE MATHEMATICS

Professor V C Morton.

The work done in the Department during this Session has been the most interesting and successful for several years. The Intermediate class, which has been dull for several Sessions, was enlivened this year by a large group of ex-service students, who have worked excellently; the staff have enjoyed taking this course. In the Honours group, Mr J G Brennan, whose course was broken by war service, returned last October and obtained First Class Honours in Pure Mathematics. Four other students took Honours in Mathematics, combined Pure and Applied. Of these, two had First Class, one a Second Class, First Division, and one a Third Class. Our First Year Honours Class has been unusually large and next year we expect to have about ten Honours candidates.

I would like to make a special reference to the work of the ex-service students at all stages. Some of them, after an absence of five or six years, have had a very difficult task. We have been impressed by the determined way in which these men and women have settled down to work.

23. Session 1947-48.

Report submitted 27 OCTOBER 1948.

PURE MATHEMATICS

Professor V C Morton

The work in the Department during the Session was, on the whole, satisfactory. For various reasons our best Honours students have not come back from war service and, although there were 8 students in the second year Honours class in Mathematics, there was no one of first class calibre. The most promising man in the first year Honours class, Mr P H Roberts, has been awarded an open scholarship at Cambridge, but his plans are not yet certain. The Subsidiary class was larger than usual with a few quite promising students at the head but with a fairly long tail of weak ones.

I am very pleased to be able to say that the first stages of a project for more powerful cooperation between the departments of Mathematics and Physics will probably be carried out in the near future I take this opportunity of thanking Professor R M Davies and Mr T Lewis for their friendly and unselfish cooperation in this plan which is being built up by the three departments.

Research. - Mr D G Pryce, a former student, obtained the degree of MSc, in December for a sound thesis on a geometrical subject.

A joint paper, on systems of curves, by Mr M T Chapple and myself has been accepted for publication by the Oxford Quarterly Journal of Mathematics.

Publication.

Professor V C Morton and Mr M T Chapple:

V C Morton and M T Chapple, A point representation of a system of space cubic curves which pass through four given points and whose chords belong to a given tetrahedral complex, Quarterly Journal of Mathematics 19 (1948), 133-139.

24. Session 1948-49.

Report submitted 28 OCTOBER 1949.

PURE MATHEMATICS

Professor V C Morton.

The work in the Department during the Session has been satisfactory. Six students took Honours in Mathematics. Of these one obtained a Class I and two Class II, Division I The First Year Honours Class was weaker than usual, but there are several promising students who hope to take Honours in 1951.

Mr J G Brennan, who has begun research under Miss Meyler and myself, has been appointed to the staff of University College, Swansea. There are now at least twelve old students of the Pure and Applied Mathematics Departments, who are Mathematical Professors or Lecturers in Universities or University Colleges in England and Wales. I have great pleasure in reporting that Professor O G Sutton, a former student and Lecturer in the Department has been elected a Fellow of the Royal Society.

A paper by Miss D S Meyler on a geometrical subject has been accepted for publication by the Oxford Quarterly Journal of Mathematics.

The appointment of Dr D R Davies during the Session has now made practicable our plans for closer cooperation with the Department of Physics. The College should, in future, benefit greatly by the strong links between the three Departments of Pure Mathematics, Applied Mathematics and Physics.

Publications.

Professor V C Morton and Mr M T Chapple:

V C Morton and M T Chapple, A point representation of a system of space cubic curves which pass through four given points and whose chords belong to a given tetrahedral complex, The Quarterly Journal of Mathematics, Oxford Series 19 (1948), 133-139.

Miss D S Meyler:

D S Meyler, A point representation of a system of rational normal curves of order $n$ through $n+1$ fixed points, The Quarterly Journal of Mathematics, Oxford Series (2) 1 (1950), 33-40.

25. Session 1949-50.

Report submitted 25 OCTOBER 1950.

PURE MATHEMATICS

Professor V C Morton.

The work done in the Department has been, on the whole, satisfactory. The main feature was the increase of numbers in the Subsidiary and Final classes without however, in the case of the Subsidiary class, a corresponding increase in the number of very good students. The First Year Honours class on the other hand contained several quite promising members. The Second Year Honours class was unusually small. In the Honours Examination in Mathematics one man had a First Class and another had a Second Class, First Division.

We are having great difficulty in finding a suitable new member of staff to help with the proposed new course of Final Mathematics (combined Pure and Applied) designed for Honours students in Physics. I do not yet know if we shall be able to begin this course next Session.

Research. - I am still directing the research work of Mr J G Brennan, who is now on the staff at Swansea.

Publication.

Miss D S Meyler

D S Meyler, A point representation of a system of rational normal curves of order $n$ through $n+1$ fixed points, The Quarterly Journal of Mathematics, Oxford Series (2) 1 (1950), 33-40.

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