Table Of ContentRussian
for the
Mathematician
S. H. Gould
Russian
for the
Mathematician
With 12 Figures
Springer-Verlag
Berlin· Heidelberg· New York 1972
S. H. GOULD
Editor of Translations
American Mathematical Society
Providence, R. I. 02904/USA
AMS Subject Classifications (1970): OOA20
ISBN·13: 978·3·540·05811·3 e·ISBN·13: 978·3·642·65384·1
001: 10.1007/978·3·642·65384·1
All rights reserved. No part of this book may be translated or reproduced in any form by print, photoprint,
microfilm, or any other means without written permission from the publishers.
© by Springer·Verlag New York Inc.
Library of Congress Catalog Card Number 72 -76 762
Preface
The Board of Trustees of the American Mathematical Society, expressing
its belief that a great deal of time would be saved for mathematicians if
they could study a textbook of Russian precisely adapted to their needs,
granted to the present author nine months leave of absence from his duties
as Editor of Translations. To the Board, and to Gordon L. Walker, the Exec
utive Director of the Society, who took the initiative in this matter with
his customary energy and good will, the author is deeply gratefUl for the
opportunity to write such a book.
For indispensable help and advice in the preparation of the book, which
was written chiefly in Gottingen, Moscow and Belgrade, gratitude is due to
many people, especially to Martin Kneser of the Mathematics Institute in
Gottingen, S. M. Nikol'skii and L. D. Kudrjavcev of the Steklov Institute in
Moscow, T. P. Andjelic of the Mathematics Institute in the Yugoslav Academy
of Arts and Sciences, G. Kurepa and B. Terzic of the Mathematics and Slav
istics Departments in the University of Belgrade, and Alexander Schenker of
the Department of Slavic Languages and Literatures in Yale University. For
expert assistance, both secretarial and linguistic, the author is indebted
to his wife Katherine and his son William, for proficient typing of the
Reading Selections to Tamara Burmeister, Secretary of the Slavistics Depart
ment in Belgrade, and Christine Lefian, editorial assistant in the American
Mathematical Society.
Providence, USA S. H. Gould
June, 1972
vi
Most helpful among the books of reference have been:
Bruzguhova, E.A.: Practical phonetics and intonation of the Russian language
(Russian), Moscow, 1963
Spagis, A.A.: Formation and use of the aspects of the Russian verb (Russian),
Mosco,r, 1961
Vlolkonsky, C.A. and Poltoratzky, M.A.: Handbook of Russian Roots, New York, 1961
Vasmer, M.: Russisches etymologisches Vlorterbuch, Heidelberg, 1953
Daum, K. and Schenk, 11.: Die russischen Verben, Leipzig, 1954
Milne-Thomson, L.M.: Russian-English Mathematical Dictionary, Madison: Uni-
versity of Vlisconsin Press, 1962
Lohwater, A.J., with the collaboration of S.H. Gould:
Russian-English Dictionary of the Mathematical Sciences, Providence:
American Mathematical Society, 1961.
Table Qlf Contents
Introduction
Plan of the book
2 Inheritance, transliteration and
loan-translation 2
3 Roots and prefixes 4
4 The Indo-European language and its descendants 4
5 Vowel gradation 5
6 Consonant variation 5
7 The alphabet 6
Chapter ~ Alphabet
The Cyrillic alphabet 8
2 Memorizing the alphabet 9
3 History of the Cyrillic consonants 10
4 The vowel-symbols; the basic vowel-scheme 11
5 Hard and soft consonants 12
6 The spelling rule 13
Chapter II Pronunciation
Importance of pronunciation 16
2 The six Russian vowel-sounds 16
3 Monosyllables for practice in pronunciation 17
4 Remarks on hard and soft consonants 20
5 Hard and soft consonants in English and Russian 20
6 A first approximation to Russian pronunciation 24
7 The letter H when pronounced but not written 25
8 The "separating" hard and soft signs 25
9 The letter H when written 25
10 Assimilation of voiced and voiceless consonants 25
11 Consonant clusters 27
12 Words of more than one syllable; accents 28
viii
Table of Contents
Chapter III Inflection
The concept of declension 33
2 The three declensions 34
3 Frequency of occurrence of nouns of the eight types 37
4 Declension in the plural 37
5 Remarks on the exercises 38
6 The concept of grammatical gender 39
7 Declension of pronouns 40
8 Declension of adjectives 43
9 The numerals 47
10 Adjective-noun phrases; italics 47
11 Comparative and superlative of adjectives and adverbs 49
12 The uninflected parts of speech 50
13 The verb; present imperfective and future perfective 54
14 The future imperfective and the past tense 57
15 The adjectival and adverbial participles 59
Chapter IV Aspect
Difference in meaning between the two aspects 65
2 Aspect regarded as a correspondence 66
3 Perfective partners and lexical compounds 67
4 The imperfectivizing suffixes 68
5 Table of aspectual and lexical compounds of verbs 69
6 Notes on the table 72
Chapter y Vocabulary
Plan of the chapter 73
2 The three "verbs of motion" 74
3 The root 6 ep- (SI-) take 78
4 The roots JIar- lay and C Ta- stand 80
5 Verbs formed from adjectives 86
6 Twenty roots of considerable productivity 91
7 Forty roots of moderate productivity 104
8 Other nouns and adjectives 107
Table of Contents
ix
Readings
Preliminary remarks 108
Section ~ Extracts from elementary analytic geometry and calculus
A1 Distance between points 109
A2 Division of a segment 110
A3 Polar coordinates 110
A4 Parallel translation of axes 111
A5 Rotation of axes 112
A6 Equations of the straight line 112
A7 The line through a point in a given direction 113
A~ Normal equation of the line 114
A9 General linear equation of the line 114
A10 The line through two given points 115
A11 Segments on the axis (i.e. intercepts) 116
A12 Definition of a vector 116
A13 Sum of vectors 117
A14 Scalar products 111
A15 General equation of the plane 118
A16 Parametric equations of a line in space 118
A17 Introduction of irrational numbers 119
A18 Continuity of the domain of real numbers 120
A19 Least upper and greatest lower bounds 120
A20 Fundamental theorem on real numbers 121
A21 The elementary functions 121
A22 Limit of a function 122
A23 Continuity of a function 122
A24 Heine-Borel and Weierstrass theorems 123
A25 Derivative of a function 124
A26 Equation of the tangent to a curve 125
A27 Maximum and minimum of a function 125
A28 Differentiation of a sum, difference, product 126
A29 Derivative of a composite function 127
A30 Indefinite integral 127
A31 Integration by change of variable 128
A32 Integration by parts 128
A33 Fundamental theorem of the integral calculus 129
x Table of Contents
Section B Extracts from elementary algebra and analysis
Bl Operations on sets 131
B2 Properties of the operations on sets 131
B3 One-to-one correspondence 132
B4 Equivalent sets 132
B5 Ordered sets 132
B6 Similar sets 133
BI Algebraic operations 133
B8 Rings 133
B9 Examples of rings 134
Bl0 The zero of a ring 134
Bl1 Domains of integrity 134
B12 Fields 135
B13 Unit element 135
B14 Division 136
B15 Characteristic of a field; prime fields 136
B16 Isomorphism 136
Bl1 Ordered rings 131
B18 Properties of ordered rings 131
B19 Axiom of Archimedes 138
B20 The natural numbers 138
B21 Addition and multiplication of natural numbers 139
B22 Order of the natural numbers 139
B23 Subtraction and division of natural numbers 140
B24 Fundamental theorem of arithmetic 140
B25 The extension principle 141
B26 Performability of operations in an extension 142
B21 Equivalence classes 142
B28 The ring of integers up to isomorphism 142
B29 The ring of integers 143
B30 The field of rational numbers 144
B31 Quotient fields 144
B32 The field of real numbers 145
B33 The field of complex numbers 145
Table of Contents xi
Section C More advanced topics
C1 Functions of a real variable 146
C2 Functions of several complex variables 147
C3 Summability theory of divergent series 149
c4 Generalized functions 151
C5 Calculus of variations 155
c6 Theory of groups and generalizations 157
C7 Theory of numbers 160
c8 Mathematical logic 163
C9 Partial differential equations 166
C10 Hilbert space 169
C11 Differential geometry 173
C12 Topology 178
Glossary 181
Name and Subject Index 207
