A course of three lectures and one practice class per week throughout the year

SYLLABUS

Topics selected from the following:

(i)

Potential theory, with applications

to

electrostatics and gravitation.

(ü)

Cartesian tensors, with applications to continuum mechanics.

( iii) Fluid dynamics, mainly of inviscid fluids.

(iv) Linear elasticity.

(v) Calculus of variations.

(vi) Ordinary differential equations; Laplace transforms.

BOOKS: Recommended for reference:

Ramsey, A. 8. Newtonian Attraction. ( C.U.P. ) Jeffreys, H.—Cartesian Tensors. ( C.U.P. )

Temple, G.—An Introduction to Fluid Dynamics. (O.U.P.)

Sokolnikoff, I. S.—М athem

аtical Theory of Elastić

ity.- ( McGraw-Hill.)

Hildebrand, F. B.—Methods of Applied Mathematics. ( 2nd ed., Prentice-Hall.) Jaeger, J. C.—The Laplace Transformation. (Methuen.)

Other references will be given in lectures.

EXAMINATION. Two 3-hour papers.

HONOURS DEGREE D. SCHOOL OF MATHEMATICS

( For possible combinations with this school see p. 250)

1. The course for B.A. with honours in

Mathematics covers four years, during which the following subjects must be taken:

First Year: Pure Mathematics part I Applied Mathematics part I Physics part I

sAn Arts subject (see below).

Science Language

Second

Year: Pure Mathematics part II Honours Applied Mathematics part II Honours

Epistemology, Logic and Methodology or Theory of Statistics part I or an approved substitute

Third Year: Pure Mathematics part III Honours Applied Mathematics part III Honours

• The fourth subject in First Year is to be chosen from any of one of Chemistry. Biology or Geology.

the groups, but must

not

^be 184

МАТHЕМАTICS Fourth Year: Thesis (see §3 below)

Pure Mathematics part IV Applied Mathematics part IV

The details of the Mathematics subjects of this course are given below.

Tutorial classes are held in the earlier years only. Students are expected to do reading and exercises related to the lectures throughout the course, and the work so done each year may be taken into account in the examinations.

Students in combined honour courses which include Mathematics will take Pure Mathematics parts I, II H, III H, IV and the following provisions, so far as they are relevant, apply to them.

2. Students proposing to take the Second Year of the honour school of Mathe- matics should normally have obtained at least second class honours in Pure lathe matics part I and Applied Mathematics part I. In exceptional circumstances students may be admitted without these qualifications; if admitted they will be advised what reading to undertake in the long vacation.

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 have been published.

з. In the Fourth Year, candidates will carry out, under direction, a study of a special topic in pure or applied mathematics, 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 or before the beginning of the first term, and the thesis will be presented not later than the be- ginning 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 ( two papers in each) , held 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 ( two papers in each of Pure and Applied Mathematics part IV ), and will include also two general papers relating mainly to the work covered in the second and third years. The results in both sections, as well as the thesis and other mathematical work done during the course, will be taken into account in determining the class list.

5. At the final examination the Wyselaskie Scholarship of $346 in Mathematics is awarded. This award may be held in conjunction with a University research grant.

Normally the Wyselaskie scholar will be required to pursue study or research in Mathematics or some other subject. See Calendar, regulation 6.7.

6. For students majoring in Mathematics who wish to pursue Physics or Chemistry to part II level the B.Sc. degree is available under the provisions of section 9, regulation 3.20, in the Calendar. Such students may further proceed to the degree of B.Sе. with honours on completing the Fourth Year of the honours school of Mathematics.

7. The Professor Wilson Prize and the Professor Nanson Prize are awarded in alternate years for the best original memoir in Pure or Applied Mathematics. Candi- dates must be graduates of not more than seven years' standing from Matriculation.

See regulation 6.72 ( 2 ) and (14) in the University Calendar.

VACATION RØING

Students are expected to read ( especially during the summer vacations) substantial portions of at least two of the books listed under "Preliminary Reading' for the several subjects. Many of the books are available in paperback editions.

In addition, attention is called to the following books on the history of mathematics.

Struik, D. J.—Concise History of Mathematics. (Dover.) Turnbull, H. W.—The Great Mathematicшns. ( Methuen.) Bell, E. T.—Men of Mathematics. (Pelican.)

Sarton, G.—History of Mathematics. (Dover.) Hooper, A.—Makers of Mathematics. (Faber.)

van der Waerden, B. L.—Science Awakening. (Groningen.) Dantzig, T.—Bequest of the Greeks. (Allen & Unwin.) Boyer, C. B. нistогy of the Calculus. (Dover.)

• ТЪе fourth subject in First Year is to be chosen from any of the groups, but must not be one of Chemistry, Biology or Geology.

FACULTX OF Alas HANDBOOK 384-1. PURE MATHEMATICS PART I

(Seepage 158)

384-3. PURE MATHEMATICS PART I1 HONOURS

A course of four lectures per week in the first two terms, and three in the third term, with tutorial work and a project.

This course may be taken by those who have obtained adequate honours in Pure Mathematics I and by those who have passed satisfactorily in Pure Math&

matics II, subject to the approval , of the faculty.

SYLLABUS

(i) Numerical Mathematics

or

Theory

of

Numbers

or an alternative pro co

t,

to be dona in the long vacation preceding the

course;

no lectures given. Intending students should obtain the exercises and instructions from the Mathematics Depart- ment in December or January before the course be¢iпs. and should hand in their work complete not later than 31 March. This work will carry some weight in the examina- tien. The details of these assignments are as follows:

Nиm

е

r cal

Мathematics. Exercises on summation of series, difference tables, inter- polation, integration solution of differential equations, curve fitting, simultaneous linear equations anti determinants. Calculating machines will be available for this work on request, and may be used in the Mathematics Department. It will be necessary to obtain, and to read relevant parts of:

Node,

B.—Numerical Methods,

vols. I and II. ( Oliver & Boyd.)

Theory of Numbers.

Exercises on prime numbers, factorization, congruences, quadratic residues, continued fractions, Diophantine approximation, quadratic forms.

In addition to the exercises and instructions referred to above, it will be necessary to obtain and read:

Davenport, 11.—The

Higher

Arithmetic. (Hutchinson.)

(ii) A

пalusů (about 60 lectures) :

Convergence of sequences and series.

Differentiable and continuous functions of one real variable. Riemann integration of step functions and bounded functions. Convergence of infinite integrals.

Double series, multiplication of series, partial fraction expansions.

Uniform convergence of series of functions. Power series, including the elementary functions of a complex variable. Fourier series. Integral transforms.

Continuous functions of several variables. Differentiability, change of variables, implicit functions. Functions defined by integrals.

Multiple integrals.

( iii) Algebra and Geometry

⁽ about 30 lectures):

Vector spaces. Linear transformations. Matrix algebra. Characteristic polynomial.

Quadratic forms. Systems of linear equations.

(iv) Additional

topic

in Geometry, Algebra or Analysis. ( Not more than 10 lectures.)

BOOKS

(a) Recommended for preliminary reading:

Courant, R. and Robbins, H. Е.—Whаt ů

uthemattc*F (0.U.P. )

Ѕаwvег

, W. W. Prelude to Mathematics. ( Pelican. )

НеК, Constance—IntfidUClOfl

to Higher Mathematics. (Routledge,

Kegan Paul.)

Bell, E.

т.—Mathептиdks, Queen and Servant of Science. ( McGraw-11iц. ) Coxeter, H.

S. Introduction to Geometry. ( Wiley

Hilbert, D., and Cohn-Vossen—Geometry

and the Imаgiп atioп.

(Chelsea.)

Kasoer,

E., and Newman, J.

R.—

Маthеmа

has and the Imagination. ( Simon

^&

Schuster. )

Stab

er,

E. R.-Introduction

to Mathematical Thought. (Addison-Wesley.)

WgissmØ,

F.—Introduction to Mathematical Thinking. (Harper

Torc book.)

(b) Prescribed textbooks:

Ferrar, W.

L.—Textbook of Convergence. (O.U.P.) )

Hyslop, J.

M.—Infinite

Series. ( Oliver & Boyd.) j (altern. ) Brand, L.—Advanced Calculus. (Wiley.)

Fucks,

W.—Advanced Calculus.

(Wiley.)

Olmsted, J. M. H.—Advanced

Calculus. ( Appleton.) (altera.

)

lc

Buck, R

C.—Advanced Caulus. ( McGraw-Hill. )

186

MATØMATICs

Murdoch, D. C.—Linear

Algebra for Undergraduates.

(Wiley.)

Ferrar,

W. L.—Algebra: Determinants, Matrices, etc.

(О.ц.Р.) (altern.) Hohn,

F. E. Elementary Matrix Algebra.

(Macmillan. )

EXAMINATION.

Two 3-hour papers.