Table Of ContentHOW TO FIND OUT IN
MATHEMATICS
A Guide to Sources of Information
SECOND REVISED EDITION
BY
JOHN E. PEMBERTON, BA, FLA
PERGAMON PRESS
Oxford • London • Edinburgh • New York
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Copyright © 1969 John E. Pemberton
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
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wise, without the prior permission of Pergamon Press Ltd.
First edition 1964
Second revised edition 1969
Library of Congress Catalog Card No. 74-94058
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This book is sold subject to the condition
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08 006824 3 (hard cover)
TO MY WIFE
List of Illustrations
FIG. 1. British Museum Subject Index. (By kind permission of the
Trustees of the British Museum). 21
FIG. 2. James and James, Mathematics Dictionary. (By kind per-
mission of D. Van Nostrand Company Inc.) 29
FIG. 3. Baker, Dictionary of Mathematics. (By kind permission of
Butterworths.) 31
FIG. 4. International Dictionary of Applied Mathematics. (By kind
permission of D. Van Nostrand Company Inc.) 35
FIG. 5. Herland, Dictionary of Mathematical Sciences. (By kind per-
mission of George G. Harrap & Co. Ltd. and Frederick
Ungar Publishing Co. Inc.) 36
FIG. 6. Hyman, German-English Mathematics Dictionary. (By kind
permission of Plenum Publishing Corp.) 37
FIG. 7. Index to Theses Accepted for Higher Degrees in the Universities
of Great Britain and Ireland. (By kind permission of Aslib.) 45
FIG. 8. Ulrich's Periodicals Directory. (By kind permission of R. R.
Bowker Company.) 49
FIG. 9. Mathematical Reviews. (Reprinted with permission of the
publisher, the American Mathematical Society, Copyright
© 1965, vol. 29, no. 3, p. 1.) 58
FIG. 10. Bulletin Signaletique—Mathematiques Pures et Appliquees. (By
kind permission of the Centre National de la Recherche
Scientifique.) 61
FIG. 11. Fletcher, Index of Mathematical Tables. (By kind permission
of Blackwell Scientific Publications.) 95
FIG. 12. Cumulative Book Index. (By kind permission of H. W. Wilson
Company.) 121
FIG. 13. British National Bibliography. (By kind permission of the
Council of the British National Bibliography Ltd.) 124
FIG. 14. Library of Congress Catalog—Books: subjects. (By kind
permission of the Library of Congress.) 125
FIG. 15. Buckland, Bibliography of Basic Texts and Monographs on
Statistical Methods. (By kind permission of Oliver & Boyd
Ltd.) 130
FIG. 16. Wold, Bibliography on Time Series and Stochastic Processes.
(By kind permission of Oliver & Boyd Ltd.) 131
XI
Xll LIST OF ILLUSTRATIONS
FIG. 17. Kendal and Buckland, A Dictionary of Statistical Terms, (By
kind permission of Oliver & Boyd Ltd.) 135
FIG. 18. International Abstracts in Operations Research, (By kind
permission of the International Federation of Operational
Research Societies.) 149
FIG. 19. Lohwater, A. J., Russian-English Dictionary of the Mathe-
matical Sciences. (Reprinted with permission of the pub-
lisher, the American Mathematical Society, Copyright ©
1961, p. 1.) 165
FIG. 20. Burlak, Russian-English Mathematical Vocabulary. (By kind
permission of Oliver & Boyd Ltd.) 166
FIG. 21. US Government Research and Development Reports. (By kind
permission of the Clearinghouse for Federal Scientific and
Technical Information.) 171
Preface to the Second Edition
FOR this second edition every section of the book has been revised
and updated. New titles have been added, in particular to the
chapters on probability and statistics, dictionaries and encyclo-
pedias, computing and mathematical education—in all, over 200
new works and new editions have been incorporated throughout
the text. Account has been taken of developments of interest to
students, teachers, and practitioners, for example the modifications
to the content of professional actuarial examinations, the assimila-
tion of modern mathematics into the school curriculum, and the
establishment of government departments to administer financial
support for mathematical research. Also recorded are the latest
efforts to improve communication between mathematicians, for
instance the inception of the Mathematical Offprint Service and
the publication of Contents of Contemporary MathematicalJournals
by the American Mathematical Society. And perhaps special
mention should be made of the specimen pages from important
reference works—three times as many as in the first edition—
which, it is hoped, will encourage the reader to acquire a greater
familiarity with his subject's bibliographical apparatus.
The purpose of this book is to give those studying, teaching,
or applying mathematics an insight into the vast amount of in-
formation which is available and to act as a guide to its exploita-
tion. To this end a balance has been sought between descriptions
of actual sources and the principles of biblio-science—the effective
use of books and libraries. The text has been designed to facilitate
continuous reading. Its chapters are arranged according to the
Mathematics class of the Dewey Decimal Classification, which
provides a convenient and progressive grouping of material, and
a number of exercises are included under each heading. At the
xiii
Xiv PREFACE TO THE SECOND EDITION
same time, a detailed contents list and a comprehensive index
enable the book to be used for reference purposes.
Sources of Russian mathematical information are treated
separately in an appendix because of their unique interest, whilst
references to the works of other countries are incorporated in the
body of the book. Both actuarial science and the role of govern-
ment departments are similarly dealt with as appendixes.
The individuals, societies, and publishers who have willingly
given both advice and factual information are now too numerous
to mention by name, and I am obliged to make my acknowledge-
ment to them collectively. I owe a special debt, however, to
Dr. Chandler, the series editor, for his unfailing advice and
encouragement.
University of Warwick JOHN E. PEMBERTON
CHAPTER 1
Careers for Mathematicians
"With the post-war eruption in mathematics the problem of
supply [of mathematicians] has become a serious one, and in
some countries has taken on the character of a political as well
as a social crisis."
E. R. Duncan, in the Year Book of Education, Evans,
London, 1961.
General Survey
The past 5 years have witnessed a tremendous upsurge in the
number of qualified mathematicians. In the United States alone
the number of earned bachelor's and first professional degrees in
mathematics and statistics has doubled, and the annual produc-
tion of PhD's has more than trebled. Demand, however, con-
tinues to increase, and the purpose of this chapter is to draw atten-
tion to the main areas of employment, giving at the same time a
brief guide to. sources of relevant information.
Before the question of careers can be discussed it is necessary to
define the word mathematician. Mathematics is an essential train-
ing for many scientific and technical as well as commercial and
business occupations, but to attempt to cover all the fields in which
some mathematical knowledge is required is beyond the scope of
the present work. The mathematician is here considered as a
person who has specialized in mathematics at degree level.
Approximately one-half of each year's product of mathe-
maticians find employment in teaching of one form or another.
The other half are spread through a wide range of situations.
Qualified mathematicians are indeed to be found in almost every
1
2 HOW TO FIND OUT IN MATHEMATICS
sector of industry, though, as might be expected, many are grouped
in electronics, aeronautics, and space exploration.
Two developments which have in recent years opened up bright
new horizons for mathematicians, and which will continue to offer
good prospects for many years to come, are high-speed computers
and operational research.
The now established concept of automation has affected many
industries and brought in its wake new openings for those with the
necessary skills. Industries which are particularly concerned in
this development include chemical processing, nuclear engineering,
iron and steel and, of course, those which produce the necessary
control systems.
The specialized field of actuarial science is facing growing
competition for new recruits, but continues to offer good prospects
for suitably qualified men and women.
Patterns of mathematical employment are constantly changing,
but they are accurately reflected in the reports of the Mathematical
Sciences Section of the National Register of Scientific and Tech-
nical Personnel. This is maintained by the American Mathematical
Society in co-operation with the National Science Foundation.
Ten other societies, representing such fields as statistics, electronic
computation, actuarial science, and operational research, assist
in the work. Data covering the year 1960 are analysed in a report
entitled: Professional Characteristics of Mathematical Scientists,
American Mathematical Society, Providence, RI, 1962. Among
the questions with which the report deals are employment trends
among younger mathematicians, patterns of degree attainment,
the proportion of qualified persons absorbed by the individual
subfields of mathematics, and salaries. Two especially interesting
inferences are drawn which are equally valid for many countries
outside the United States. The first is the "enormous growth of
opportunities for non-academic employment of mathematicians";
and the second is that "mathematicians in industry, business and
non-profit organizations are getting higher salaries at earlier ages
than those in other types of employment". The discernible shift
away from teaching is largely due to a strong attraction from new
CAREERS FOR MATHEMATICIANS 3
specialities which do not demand as high a level of academic
attainment.
It will be stated on several occasions in this book that the work
of the mathematician is often geared to the task of helping to solve
the problems of workers in apparently unrelated fields. The con-
tribution which the application of mathematical techniques can
make in terms of efficiency and hard cash has created an un-
precedented demand for the services of competent mathematicians.
They are now being taken on in industry for their knowledge of
mathematics itself rather than of the fields to which it is applied.
It is significant that in the United States the number of mathe-
maticians employed in private industry increased by nearly 100 per
cent between 1954 and 1960. Organizations both large and small
have found that their volume of experimentation can be consider-
ably reduced by the elaboration of mathematical formulations.
The aircraft industry is one which has particularly benefited in
this respect. However, many less obvious areas of research are also
directly concerned in this movement.
Guides to Careers
Guides to careers in mathematics appear under three main
headings: general guides to occupations for scientists, particularly
graduates; those dealing with the entire range of mathematical
opportunities; and very specific guides which restrict themselves to
individual mathematical professions. The following examples
represent the first and second categories. More detailed informa-
tion on particular professions is given in succeeding sections.
Careers Encyclopedia, Cleaver-Hume, 5th edn., 1967.
Directory of Opportunities for Graduates, Cornmarket Press,
London, Annual.
FORRESTER, GERTRUDE, Occupational Literature: an Annotated
Bibliography, Wilson, New York, rev. edn., 1964.
GEHMAN, HARRY MERILL, Opportunities in Mathematics
Careers, Vocational Guidance Manuals, New York, 1964.
