DEPARTMENT OF MATHEMATICS
98. APPLIED МАТНЕМАТICS PART III
Students may not receive credit; for degree purposes, for both this subject and Pure Mathematics part III, course C.
A course of three lectures per week throughout the year, together with practical work for three hours per week during about half the year.
137
FACULTY OF ARTS ØВOOК SYLLABUS
(i) Numerical analysis and computation. Solution of linear and non-linear equations; inversion of matrices; finite differences with application to interpolation, differentiation, integration and summation of series; numerical solution of ordinary and partial differential equations; curve-fitting and harmonic analysis.
(ii) Elementary hydrodynamics.
( iii) Cartesian tensors and elementary elasticity.
(iv) Variational principles.
Students who studied Applied Mathematics Part II ( Pass) in years prior is 1962 will not have received the section of that course on Field Theory.
As this knowledge will be assumed in lectures, they should carry out the fol- lowing preliminary study:
Hildebrand, F. B.—Advanced Calculus for Engineers, Ch. 6. ( N.Y., Prentice- Hall ), possibly supplemented by
Weatherbum, C. E.—Advanced Vector Analysis, Ch. 1-2. (London, Bell).
BOОKS
(a) Prescribed textbooks:
Hartree, D. R. Numerical Analysis. (O.U.P. ) (b) Recommended for reference:
Hildebrand, F. B.—Advanced Calculus for Engineers. (N.Y., Prentice-Hall).
Jeffreys, H., and B. S.—Methods of Mathematical Physics. (O.U.P.) Rutherford, D. E.—Fluid Dynamics. (Oliver and Boyd. )
Sokolnikoff, I. S.—Mathematical Theory of Elasticity. (McGraw-Hill.) Temple, G.—Cartesian Tensors. (Methuen Monographs.)
Temple, G.—An Introduction to Fluid Dynamics. (О.U.P.) EXAMINATION. Two 3-hour papers.
HONOURS DEGREE D. SCHOOL OF MATHEMATICS (For possible combinations with this school see p. 220.)
1. The course for B.A. with honours 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 qualify in Science French or Science German or Science Russian as prescribed for the B.Sc. degree, 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 part I Applied Mathematics part I Physics part I
Chemistry part IA or Philosophy part I Science Language
Second Year Pure Mathematics part II Applied Mathematics part II Logic or Theory of Statistics part I Third Year: Pure Mathematics part III
Applied Mathematics part III Fourth Year: Thesis
Pure Mathematics part IV Applied Mathematics part IV
The details of the Mathematics subjects of this course are given below.
Students in combined honour courses which include Mathematics will take
MATHEMATICS
Pure Mathematics parts I, u, II, 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- maties should normally have obtained honours in Pure Mathematics part I and Applied Mathematics part I. In exceptional circumstances students may qualify from a pass course; they will be advised what reading to undertake in the following long vacation so as to make up the additional ground that was covered in the honours lectures. It is most desirable that candidates should have a fair knowledge of Physics.
and some acquaintance with French and German.
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 litera- ture, 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 ( 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.
The results in both sections will be taken into account in determining the class list.
5. At the final examination the Wyselaskie Scholarship of 2173 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 В.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 В.Sc. 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 READING
The following books, relevant to the study of Mathematics, are suitable for reading in the long vacations. In addition, reference to books bearing specifically on the work of each year is given in the details of individual subjects, and additional references may be made in lectures.
Historical
Turnbull, H.
W.—The Great Mathematicians. (Methuen. )
Sullivan, J. W.
N.-The History of Mathematics
inEurope. ( O.U.P. )
Hobson,
E. W. John Napier and the Invention of Logarithms. (C.U.P.)
Ball, W. W. R. —AShort History of Mathematics. ( Macmilan. )
Smith, D.
E.—Source Book of Mathematics. ( McGraw-Hill. )
Bell, E.T.—Men of Mathematics. ( Pelican.)
Hooper,
A.—Makers of Mathematics.
(Faber.) van der Waerden—ScienceAwakening.
(Groningen.)Popular
Whitehead, A.
N.—Introduction to Mathematics. ( H.U.L.,
Butterworth.) Perry, J.—SpinningTops.
(S.P.C.K.)Ball, W. W.
R.-Mathematical Recreations and Problems.
(Macmillan.) Darwin, G.H.—The Tides.
(Murray.)Rice,
J.—Relativity.
(Benn.)Titchmarsh,
E. C.—Mathematics for the General Reader.
(Hutchinson. ) Read, A. H.—Signpostto Mathematics.
(Thrift Books.)Northrop,
E. P.—Riddles in Mathe
matics.
(Hodder and Stoughton.)Philosophy of Mathematics and Science Courant, R., and Robbins, H. E.-What is Mathematics? ( O.U.P. ) Mach, E.—The Science of Mechanics. (Open Court.) O.P.
Рoineаг