A course of one lecture per week throughout the Year.
SУLLAnus. The object of the course is to consider the nature of mental Phenomena. It is specifically intended nit 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 've get images?
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BØкs. There are no prescribed text-books. The following books will be referred to :
B. Russell—The Analysis of Mind. (Allen and Unwin.) E. Mаch----Tize Analysis of Sensations. (Opеn Court.) W. James—The Principles of Psychology. (Macmillan.) J. E. Mcтaggart—Phil osophicаi Studies, Chap. 3. (Arnold.)
J. B. Watson—Psychology frein the Stпnd point of a ь еhаъrioіrist. (J. B.
Lippincott.)
G. F. Stout—Analytic Psychology. (Macmillan.) W. Kohler---Gestalt Psychology. (Bell.)
S. Freud—Introductory Lectures orz Psycho-Analysis. (Allen and Unwin.) S. Freud---An AгutoЬiographical Study. (Hogarth Press.)
D. SCHamL aF MATHEMATICS
1. For students entering the first year in I950 or later, the Honours cour,,c in Mathematics will cover 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 snake 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 Maths. I Applied Maths. I Physics I Philosophy I or
Chemistry I Second Year : Pure Maths. II
Applied Maths. II
Logic or Physics II or Theory of Statistics 1 Third Year : Pure Maths. III
Applied Maths. III Fourth Year: Thesis
Pure Maths. IV Applied Maths. IV
The details of subjects for Pure Mathematics Part I, and Applied lathe- maties Part I, for this four-year course are given below. The details for the higher parts of these subjects are not given in this year's Handbook ; in place of them are given the details for Pure and Applied Mathematics Parts II and III for the three-year course which is bÝing taken by students who began before 1950.
Students in Combined Honour Courses which include Mathematics will take Pare Mathematics Parts I, II, III, IV.
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 theу enter. It is most desirable that candidates should have a fair knowledge nť Physics and some acquaintance with French and German.
2. The Honour syllabuses and examinations in Pure Mathematics Part I and Applied Mathematics Part I are the same as the Pass syllabuses and examinations, but Honour candidates will be expected to reach a higher standard and to attend the Higher grade lectures. However, a student who has attended the Standard grade lectures and has done really well in the examinations will be eligible to proceed to the second and higher years of the Honour course, and will be advised what reading lie 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 he approved by the Faculty; candidates should make application as soon as possible after the examination results of the first year are published.
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з. The following particulars relate to the three-year course which is being taken by students who began before I950 :
In their Second Year, candidates will take the Honour courses in Pure lathe- maties Part II, and Applied Mathematics Part II, together with the additional subject.
In their Third Year, candidates will take the Honour courses in Pure Mathe- matics Part III, and Applied Mathematics Part III. They will also 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, at the beginning of the Third Term.
The Final Examination in the School of Mathematics will cover the work of the Second and Third Years, and consists of eight papers, four on Pure Mathe- matics and four on Applied Mathematics. The work done in the study of a special topic, referred to in the preceding Section, will be taken into account in deter- mining the Class List and in awarding the Dixson Research Scholarship of u1h0.
The Dixson Scholar will normally be required to devote his year of tenure to advanced study and research in Mathematics, and to assist in the tutorial work of the Department of Mathematics.
The provisions of this and the preceding Sections, so far as they are relevant, apply also to candidates taking Mathematics as part of a Combined Honour Course.
4. The following four-year course for the degrees of Bachelor of Arts (Degree with Honours) and Bachelor of Sciencе was approved* :
First Year. Pure Mathematics Part I (Honours) , Applied Mathematics Part I (Honours) , Physics Part I, Chemistry Part I.
Second Year. Pure Mathematics Part II (Honours), Applied Mathematics Part II (Honours) , Physics Part II.
Third .Year. Pure Mathematics Part III (Honours) , Applied Mathematics Part III (Honours) .
Fourth Year. Physics Part III, and either Theory of Statistics Part I or Logic.
The В.A. Degree is obtained at the end of the Third Year, and the В.Sc.
Degree at the end of the Fourth Year.
In the case of a student pursuing this course, the conditions of tenure of the Dixson Research Scholarship will be modified as follows : The Scholar will he required ta assist in the tutorial work of the Department during his Fourth Year, and will receive three-fifths of the value of the Scholarship, in that year. He will receive the remaining two-fifths in the following year if he devotes this year to advanced study and research in the Department of Mathematics.
5. The Professor Wilson Prize and the 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.
VACATION READING
The following books, relevant to the study of Mathematics, are suitable for reading in the Long Vacations. In addition, reference ta books bearing specifically on the work of each Year is given in the Details of individual subjects, and addi- tional references may be made in Lectures.
Historical
Turnbull—The Great Matherzacticiaпs. (Methuen.)
Sullivan----The History of Mathematics iп Europe. (0.U.P.) Hobson—.Tohn Napier and the Invention of Logarithms. (C.U.Р. ) Hobson----Squаri;sg the Circle. (C.U.P.) O.P.
Ball—A Short History of Mathematics. (Macmillan.) Smith—Source Book of Mathematics. (McGraw-Hill.)
Popular
Whitehead---Introduction to Mathematics. (H.U.L., Butterworth.) Perry—Spinning Tops. (S.P.C.K.)
Ball—Mathematical Recreations and Problems. (Macmillan.)
-.For students entering their first year in 1950 or later, this course will not satisfy the requirements for Bachelor of Arts (Degree with Honours).
1У7
Darwin--The Tides. (Murray.) Rice—Relativity. (Benn.)
Philosophy of Mathematics and Sciencč Courant and Robbins—What is Mathematics? (0.U.P. ) Mach—The Science of Mechanics. (Opera Court.) 0.P.
Puiпcaré--The Foi ndations 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--Nuinzber, the Language of Sciепce. (Allen and Utiwin.) Jeffreys--Scientific Inference. (C.U.P.)
Pearson—The Grammar of .Science. (Everyman, Na. 939. Dent.)
Mein-- Е1еіnеntary Mathematics from the Advanced Stand point. (Macmillan.)
PURE MATHEMATICS PART I
A course of three lectures and one tutorial class per week throughout the Year.
SYLLЛnus. (i) Algebra and Geometry. Review of algebraic principles and methods. Complex numbers. Co-ordinates in two and three dimensions. Graphs.
Methods of plane 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 in- tegration, with the usual applications. Partial differentiation. Curvature. Approxi- mations and an introduction to infinite series. Introduction to differential equations.
Candidates for Honours should have reached at least second class honours standard in Pure Mathematics and in Calculus and Applied Mathematics at the Matriculation Examination. They will attend the higher grade course of lectures mentioned in the Pass details.
Bоores. (a) Prescribed text-books : One of
1. Michell and BeIz—Elea rents of 1lIаthematřcal Analysis. 2 vols. ( ) lаc- millan. )
Lamb---In finitesi gal Calculus. (C.U.P.)
Count—I n troduuction to Infinitesimal Calculus. (Clarendon.) 2. Duren and Robson—Advanced Algebra, Vols. 1, 2. (Bell.) 3. Duren and Robson—Advanced Trigonotiiсtry. (Bell.) 4. Castle—Logarithmiс and Other Tables. (Macmillan.)
(b) Recommended for reference:
Osgood and Graustein—Plane and Solid Analytic Geometry. (Macmillan.) Knapp----Theory and Application of Infinite Series. (Blackie.)
Michell and Belz---Elements of Mathematical Analysis. 2 vols. (Macmillan.) ЕхAМrхAТrох. Two 3-hour papers.