A course of one lecture per week throughout the year.
Svunпus. The object of the course is to consider the nature of mental phenomena. It is specifically intended not to overlap with the work of the Depart- ment of Psychology. The questions raised will be of the sort, What is an image?
What is thinking ?—as opposed to, e.g. In what way do we get images?
Booxs. There is no prescribed text-book. Students should read:
Ryle, G.—The Concept of Mind. (Hutchinson.) Russell, B.—The Analysis of Mind. (Allen & Unwin.) Price, H. H.—Thinking and Experience. (Hutchinson.) The following books should be referred to:
Mach, E.—The Analysis of Sensations. (Open Court.) James,
W.—The
Principles of Psychology. (Macmillan.) McTaggart, J. E. Philosophical Studies, Chap. 3. (Arnold.)Watson, J. B. Psychology from the Standpoint of a Behavioa4rist. (Lippincott.) Stout, G. F.—Analytic Psychology. (Macmillan.)
Kohler, W.—Gestalt Psychology. (Bell.)
D. SCHOOL OF MATHEMATICS
1. The Honours course in Mathematics covers four years, during which the following subjects must be taken:
Pure Mathematics Parts I, II, III, IV.
Applied Mathematics Parts I, II, III, IV.
Also, candidates must take additional subjects (one of which must be Physics Part I), so as to make up a total of eleven in all, and must present a thesis on some approved topic in the final year. The full course will normally be as follows:
First Year: Pure Mathematics I Applied Mathematics I Physics I
Chemistry I or Philosophy I 147
Second Year : Pure Mathematics II Applied Mathematics II
Logic or Physics II or Theory of Statistics I Third Year : Pure Mathematics III
Applied Mathematics III Fourth Year : Thesis
Pure Mathematics IV Applied Mathematics IV
The details of the Mathematics subjects of this course are given below.
Students in Combined Honour Courses which include Mathematics will take Pure Mathematics Parts I, II, III, IV, and the following provisions, so far as they are relevant, apply to them.
Students proposing to take the Honour School of Mathematics should normally have obtained Honours in Pure Mathematics and Calculus and Applied Mathematics at the Matriculation Examination. Candidates who have not this qualification are advised to consult the Professor of Mathematics before they enter. It is most desirable that candidates should have a fair knowledge of Physics and some acquaintance with French and German.
2. The Honour syllabuses in Pure Mathematics Part I and Applied Mathe- matics Part I contain the sane general topics as the corresponding Pass syllabuses, but more advanced treatment may be given. Candidates for Honours are expected to attend the Higher Grade lectures and to reach a high standard in the examination, in which they will be given opportunities to show knowledge and skill in both the elementary and the more advanced aspects of the course. However, a student who has attended the Standard grade lectures and has done really well in the exam- inations will be eligible to proceed to the second and higher years of the Honour course, and will be advised what reading he should undertake in the following long vacation so as to make up the additional ground that was covered in the higher grade lectures.
Admission to the second and higher years of the Honour School must be approved by the Faculty ; candidates should make application as soon as possible after the examination results of the first year are published.
3. In the Fourth Year, candidates will carry out, under direction, a study of a special topic, involving the reading and collation of the relevant mathematical literature, and will present a thesis embodying this work. The topic will be chosen, in consultation with the staff of the department, at the beginning of the First Term, and the thesis will be presented at the beginning of the Third Term. The thesis will be taken into account in determining the Class List for the Final Examination.
4. The examinations in Pure Mathematics Part III and Applied Mathematics Part III, hield at the end of the Third Year, will count as the first section of the Final Examination. The second section of this examination, held at the end of the Fourth Year, will cover the work of that year, and will include also two general papers. The results in both sections will be taken into account in determining the Class List.
5. At the Final Examination the Dixson Research Scholarship of f80 in Mathematics, and the Wyselaskie Scholarship of f140 in Mathematics, are awarded.
These awards may be held in conjunction with each other or with a University Research Grant. Normally, the Dixson Scholar will be required to devote his year of tenure to advanced study ana research in Mathematics, and to assist in the tutorial work of the Department, and the Wyselaskie Scholar will be required to pursue study or research in Mathematics or some other subject. See Calendar, Chap. IV, Regs. VII and XIII.
6. The Professor Wilson Prize and tli Professor Nanson Prize are awarded in alternate years for the best original memoir in Pure or Applied Mathematics.
Candidates must be graduates of not more than seven years' standing from Matriculation. See schedule to Chap. IV, Reg. LXXII in the University Calendar.
VACATION READING
The following books, relevant to the study of Mathematics, are suitable for rending in the Long Vacations. In addition, reference to books bearing specifically ou the work of each Year is given in the Details of individual subjects, and addi- tional references may be made in Lectures.
148
Historical
Turnbull, H.
W.—The
Great Mathematicians. (Methuen.)Sullivan, J. W.
N.—The
History of Mathematics in Europe. (O.U.P.) Hobson, E. W. john Napier and the Invention of Logarithms. (C.U.P.) Hobson, E. W.—Squaring the Circle. (C.U.P.) O.P.Ball, W. W.
R. —A
Short History of Mathematics. (Macmillan.) Smith, D. E.—Source Book of Mathematics. (McGraw-Hill.) Bell, E. T.—Men of Mathematics. (Pelican.)Hooper, A.—Makers of Mathematics. (Faber.) Popular
Whitehead, A. N. Introduction to Mathematics. (H.U.L., Butterworth.) Perry, J.—Spinning Tops. (S.P.C.K.)
Ball, W. W. R. Mathematical Recreations and Problems. (Macmillan.) Darwin, G. 1.—The Tides. (Murray.)
Rice,
J. Relativity.
(Benn.)Titchmarsh, E. C.—Mathematics for the General Reader. (Hutchinson.) Read, A. Н.—Signpost to Mathematics. (Thrift Books.)
Northrop, E. P.Riddles i,i Mathematics. (lodder and Stoughton.) Philosophy of Mathematics and Science
Courant, R., and Robbins, H. K.--What is Mathematics? (O.U.P.) Mach, E.—Thе Science of Mechanics. (Open Court.) O.P.
Poincaré, J. H.—The Foundations of Science: Science and Hypothesis, Chaps.
I-VIII;
Science
and Method, Book I, Chaps. I, II, and Book II, Chaps I, II. (Science Press.)Dantzig, T. Number, the Language of Science. (Allen & Unwin.) Jeffreys, Н.—Scientific Inference. (C.U.P.)
Klein, F.—Elementary Mathematics front the Advanced Standpoint. (Mac- millan).
PURE MATHEMATICS PART I
A course of three lectures and one tutorial class per week throughout the year.
SYLLлвvs. (i) Algebra and Geometry. Review of algebraic principles and methods. Complex numbers. Methods of planе analytical geometry. The most important properties of the conics. Polar co-ordinates. Determinants. Introduction to solid analytical geometry.
(ii) Calculus. The standard elementary functions. Differentiation and system- atic integration, with the usual applications. Partial differentiation. Approxi- mations and an introduction to infinite series. Introduction to differential equations.
Students will attend the higher grade course of lectures mentioned in the Pass details, and should have obtained honours in either Pure Mathematics or Calculus and Applied Mathematics at the Matriculation Examination. A knowledge of the Matriculation work in both these subjects will be assumed in the lectures.
Books. (a) Prescribed text-books:
1. Courant, R. Differential and Integral Calculus, Vol. I. (Blackie.) or Michell, J. H., and Belz, M. I —Elements of Mathematical Analysis. 2 vols.
(Macmillan.)
or Lamb, H. Infinitesimal Calculus. (C.U.P.)
or Caunt, G. W.—Introduction to Infinitesimal Calculus. (Clarendon.) 2. Duren, C. V., and Robson, A.—Advanced Algebra, Vols. 1, 2. (Bell.) 3. Durell, C. V., and Robson, A. Advanced Trigonometry. (Bell.) 4. Castle—Logarithmic and Other Tables. (Macmillan.)
or Knott—Four Figure Mathematical Tables. (Chambers.) (b) Recommended for reference:
Hardy, G. 1.—Pure Mathematics. (C.U.P.)
Courant, R., and Robbins, H. E.—What is Mathematics? (O.U.P.)
Osgood, W. F., and Graustein, W. C.—Plane and Solid Analytic Geometry.
(Macmillan.)
Michell, J. H., and Belz, M.
1.—Elements
of Mathematical Analysis. 2 vols.(Macmillan.)
149
EXAMINATION. Two 3-hour papers. The first paper will test candidates' know- ledge of the work covered in the standard course and will be taken by all students, irrespective of whether they have attended the standard or the higher course. The second paper, also taken by all students, will consist of two alternative sections, one on the work of the standard course and the other on that of the higher course.
Honours may be awarded to candidates who have done really well in the examination, regardless of which section of the second paper they have chosen ; but the award of first class honours will be restricted to those who have shown superior ability in the work of the higher course.