Burnet, *J.—Greek Philosophy, Part I, Thales to Plato. *(Macmillan.)
Nietzsche, *F.—Early Greek Philosophy. *(Vol. II of *Collected Works.) *
Cherniss, H. *F. Aristotle's Criticism of Pre-Socratic Philosophers. *(Johns

Hopkins.)

Raven, J. E.-Pythagoras and Eleatics. (C.U.P.)
Lee, H. D. *P.—Zeno of Elea. *(С.U.P.)

Cornford, F. *M. Plato and Parmenides. *(Kegan Paul.)
Hardie, W. F.

### R. —A

*Study in Plato.*(O.U.P.) Lodge, R.

*C.-The Philosophy of Plato.*(Routledge.) Ross, W.

*D.—Plato's Theory of Ideas.*(O.U.P.) Collingwood, R.

*G.—The Idea of Nature.*(О.U.P.) Allan, D.

*J.—The Philosophy of Aristotle.*(H.U.L.) Jaeger,

*W.—Aristotle.*

**(O.U.P.)**. . ЕХА

**. iN**Ат

**roN.**One 3-hour paper.

### (b) PURE MATHEMATICS

**INTRODUCTION **

**For those who are interested primarily in the principles and uses of mathe-**
**matics and mathematical methods Pure Mathematics Part I is the basic course; **

**but for those whose formal mathematical studies are to be confined to one year, **
**General Mathematics is an alternative providing a somewhat wider and more **
**superficial cover. **

**Tutorial Classes will be held in Pure Mathematics Part I and General Mathe-**
**matics, and Practice Classes in Pure Mathematics Parts II and III. The work **
**done in these classes will carry some weight in the Annual Examination. **

**EXTERNAL STUDIES **

**Candidates in any of Pure Mathematics.. Parts I, IIA, Applied Mathematics **
**Parts I, II, by External Study, will be supplied with a full synopsis of the **
**appropriate course, with detailed references to text-books. They will be supplied **
**also with sheets of Practice Examples and, in certain subjects, with typed notes **
**on isolated topics. They may submit examples for correction and may consult the **
**appropriate Lecturer or Professor as to points of difficulty which they encounter **
**in their studies, but apart from this they cannot be given detailed tuition. **

**Entries for External Study in the above subjects at the Honour Standard, **
**or in any other mathematical subjects, will not be accepted. **

**VACATION READING **

**The following books, relevant to the study of Mathematics, are suitable for **
**reading in the summer vacations. In addition, references to books bearing specifi-**
**cally on the work of each year will be found in the details for individual subjects. **

**Additional references will be given in the lectures. **

**Sawyer, W. W.—Mathemati**ć

**ian's Delight.****(Pelican.)**

**Read, A.**о

*H.—SignQ*

**st to Mathematics.****(Thrift Books.)**

**Titchmarsh, E. C.--Mathematics for the General Reader. (Hutchinson.) **

**Whitehead, A.**

*N. Introduction to Mathematics.*(H.U.L., Butterworth.)**Dantzig, T. Number,**

*the Language of Science.*(Allen & Unwin.)**Sawyer, W.**

*W.—Prelude to Mathematics.*(Pelican.)**Northrop, E. P.—Riddles in Mathematics. (Hodder & Stoughton.) **

**Bell, E.**

*T.—Mathematics, Queen and Servant of Science.*(McGraw-Hill.)**Hooper,**

*A. Makers of Mathematics.*(Faber.)**Bell, E. T. Men of Mathematics. (Pelican.) **

**Hobson, E. W. John Napier and the Invention of Logarithms. (C.U.P.) **

**Turnbull, H.**

*W.—The Great Mathematicians.*(Methuen.)**PURE MATHEMATICS PART I **

**A course of three lectures and one tutorial class per week throughout the year. **

**In third term there will be two alternative syllabuses. Option A continues **
**the study of calculus ; Option **В ** is concerned with consolidating the previous **
**studies. Either **option **is acceptable for all purposes. **

**SYLLABUS. ****Numbers, including complex numbers. Functions. Sketching graphs. **

**Differentiation and integration, with the usual applications. The standard elementary **
**functions. Introductions to infinite series and to differential equations. Systematic **
**integration. One of the following alternatives : **

**Option A. ****Analytical solid geometry. Determinants. Conic sections. Intro-**
**duction to functions of two variables. **

**Option. ****B. Matters of principle in algebra, geometry, trigonometry and **

**calculus.**

**It will be assumed that students attending this course have a knowledge of the **
**work prescribed for Pure Mathematics at the Matriculation Examination. ** ,

**Books. ****(a) Prescribed text-books : **

**Cooley, H. R. First Course in Calculus. (Wiley.) ** . •

Tuckey, C. 0., and Armistead—Co-ordinate

*Geometry. *

(Longmaпs.)
Ferrar, W. *L. Higher Algebra for Schools. *

^{(Oxford.) }

Kaye and Laby—gaur-figure

*Mathematical Tables. *

(Longmans.)
**or**Тurnег—Four-figure

*Mathematical Tables. *

(Cheshire.)
(b) Recommended for reference:

Caunt, G.

*W.—Infinitesimal Calculus. *

(Clarendon.)
Middlemiss, R.

*R. Differential and Integral Calculus. *

(McGraw-Híll.).
Keils, L.

*M. Analytic Geometry and Calculus. *

(Prentice Hall.)
Maxwell, E. *A.—Analytical Calculus, *

Vols. I, II. (C.U.P.)
Clarke, L. *H.* *—* *Notebook in Pure Mathematics. *

(Heinemann.)
Clarke, L. *H.—General Certificate Calculus. *

(Heinemann.)
Lamb, Н.—Iпfiпitesimal *Calculus. *

(C.U.P.)
Randolph, J.

*F.—Calculus. *

(Macmillan.)
Maxwell, E.

*A.—Elementary Coordinate Geometry. *

(Oxford.)
Osgood, W. F., and Graustein—Plane

*and Solid Analytic Geometry. ***(Mac- **

**millan.)**

**EXAMINATrON. **Two 3

### -

hour papers.**PURE MATHEMATICS PART II **

A course of three lectures per week in first term and two lectures per week in the remaining terms, together with practice classes throughout the year.

After the first term the course is divided into two alternative syllabuses.

Option A is devoted to the further study of calculus, Option В to the more fundamental study of algebra and geometry. Either syllabus is open to all who have passed Pure Mathematics Part I, no matter which alternative syllabus they have chosen in that subject.

It is not necessary to decide which option will be chosen until the end of the first term. Those intending to proceed subsequently to Pure Mathematics.

Part III should choose Option A in preparation for Pure Mathematics Parts IIIA or IIIC, Option В for Pure Mathematics Part IIIB.

**Sv**гΡтл**ws. **

*Complex Functions. *

Exponential and related functions of a
complex variable.
*Differential Equations. *

Standard types of ordinary differential equations **of**the first and second orders.

*Integrals. *

Infinite and improper integrals. Reduction formulae. Curvilinear
integrals. Multiple integrals.
*Functions of Two Variables. *

Analytical solid geometry. Determinants. Direc-
tional derivatives. Stationary points. Envelopes.
*Series. *

Taylor's theorem for functions of one variable. Power series for the
standard elementary functions, and combinations of them.
In second and third terms the following alternative syllabuses will be given:

*Option A: Functions of Two Variables. *

Change of variables. Polar co-
ordinates. Surface integrals.
*Series *

Approximate calculations with series. Convergence. Absolute con-
vergence.
*Differential Equations. *

Further linear differential equations, including solutions
by series and simultaneous systems.
*Option *

В*: Geometry.*Critical study of Euclidean geometry.

*Number. *

Number notations. Factorization. Prime numbers. Directed numbers.
Books. (a) Preliminary reading:

Books listed on p. 132 and

Courant, R., and Robbins, H.

*E.—What is Mathematics! *

^{(O.U.P.) }(b) Prescribed text-books:

**One***of-*

Сооleу, H. R.—First

*Course in Calculus. *

^{(Wiley.) }Lamb,

*H.—Infinitesimal Calculus. (C.U.P.) *

**133 **

Caunt, G. *W.—Introduction to Infinitesimal Calculus. * (Clarendon.)
Kells, L. -*M. Analytic Geometry and Calculus. * (Prentice Hall.)

(c) Recommended for reference:

Courant, *R.—Differential and Integral Calculus. * (Blackie.)

Ferrar, W. *L. Higher Algebra, *the sequel, starting with Ch. XV. (O.U.P.)
Bowman, *F. Elementary Algebra, *Part II. (Longmans.)

Duren, C. *V. Advanced Algebra, *Vol. I. (Bell.)

Maxwell,

### Е.

А*.—A*п

*alytical Calculus,*vols. III and IV. (C.U.P.) Ford, L.

*R. Differential Equations.*(McGraw-Hill.)

Ince, E. *L. Integration of Ordinary Differential Equations. *(Oliver & Boyd.)
Relton, F. *E. Applied Differential Equations. *(Blackie.)

Sokolnikoff, I. *S. Higher Mathematics for Engineers and Physicists. *

(McGraw-Hill.)

Green, S. *L. Differential Equations. * (Univ. Tutorial Press.)
Tuckey, C. O., and Armistead.—Coordinate * Geometry. *(Longmans.)
Forder, H.

*G.-Euclidean Geometry.*(C.U.P.)

Forder, H. *G.—Geometry, *(Hutchinson.)

Ore, O. Number *Theory and its History. *(McGraw-Hill.)
MacDuffee, C. *C.—Theory of Equations. *(Wiley.)

**ExAMINATiON. ** Two 3-hour papers.