A First Course inMathematical Analysis

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A clear, logical and straightforward course, based on the idea of a limit,written for students reading mathematics or physics who already have aworking knowledge of the calculus. 'Books of this quality are rare enoughto be hailed enthusiastically.... fresh in conception . . . lucid in style'.Times Educational Supplement. 22s. 6d. net

Elementary Real AnalysisH. G. E G G L E S T O N

A rigorous textbook on the theoretical aspects of real variable analysis,covering the work for the first two years of an honours degree course inmathematics. Definitions are stated explicitly and the whole developmentof the subject is logical and self-contained. There are many examples, withhints for solution, which will be of particular value to students working ontheir own. 375 6d. net

Principia Mathematica to -̂A. N. W H I T E H E A D & BERTRAND R U S S E L L

A paperbound edition of the most famous work ever written on the founda-tions of mathematics. The abridged text of Volume I contains the materialmost relevant to an introductory study of logic and the philosophy ofmathematics: the whole of the preliminary sections, the whole of Part I,Section A of Part II and Appendices A and C. Cambridge Paperback.

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CAMBRIDGE UNIVERSITY PRESS

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THE QUARTERLY JOURNAL OF

MATHEMATICSOXFORD SECOND SERIES

Edited by T. W. CHAUNDY, U. S. HASLAM-JONES, E. C. THOMPSON

VOLUME 13 No. 52 DECEMBER 1962

CONTENTSA. O. Morris: The Spin Characters of the Symmetric GroupsM. S. P. Eastham: On Hilbert TransformsS. Orey: Non-Differentiability of Absolute Probabilities of Markov Chains-E. C. Titchraarsh: On the Nature of the Spectrum in Problems of Relativistic Quantum Mechanics (II)J. Knopfmacher: Universal Envelopes for Non-Associative AlgebrasJ. B. McLeod: On a Recurrence Formula in Differential EquationsR. Crittenden: Covariant DifferentiationL. Carlitz: Some Identities over a Finite FieldM. S. P. Eastham: An Eigenvalue Problem with the Parameter in the Boundary Condition

Quarterly Journal of Mathematics (Oxford Second Series) is published in March, June, Septemberand December at 18s. 6d. net for a single number with an annual subscription (for four numbers) of65s. post free. Orders may be placed with any bookseller or sent direct to the Publisher.

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VOLUME 13 (Scries 2) June 1962 PART I

1.1. DAVIES: Enumeration of Certain Subgroups of Abelian ̂ -Groups.I. S. LOWNDES : Parseval Relations for Kontorovich-Lebedev Transforms.W. D. COLLINS: On the Solution of some Axisvmmetric Boundary Value Problems by means of Integral Equations. VII.

The Electrostatic Potential Due to a Spherical Cap Situated Inside a Circular Cylinder.M. H. MARTIN : Some Aspects of Uniqueness for Solutions to Boundary Problems.I. H. WILLIAMSON : The Vviener-Pitt Phenomenon on the Half-Line.M. LOWENGRUB and I. N. SNEDDON : An Axisymmetric Boundary Value Problem of Mixed Type for a Half-space.H. S. M. COXETER : The Abstract Group G9 • ' • u .A. McD. MERCER : On Integral Transform Pairs Arising from Second Order Differential Equations.W. D. COLLINS : Some Axial I y Symmetric Stress Distributions in Elastic Solids containing Penny-shaped Cracks. III. A

Crack in a Circular Beam.P. H. DIANANDA : A Cyclic Inequality and an Extension of It. I.W. H. INORAM: The/-Differential and its Integral.D. L. GEORGE : Numerical Values of Some Integrals involving Bessel Functions.BOOK REVIEWS.MATHEMATICAL NOTES.

R. WILSON : An Existence Theorem for Second Order Linear Differential Equations.H. H. TEH: A Note on {.-Groups.

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