Russian for the Mathematician

Transcription

1 Russian for the Mathematician

2 S. H. Gould Russian for the Mathematician With 12 Figures Springer-Verlag Berlin Heidelberg New York 1972

3 S. H. GOULD Editor of Translations American Mathematical Society Providence, R. I /USA AMS Subject Classifications (1970): OOA20 ISBN 13: e ISBN 13: : / 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

4 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 Executive 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 Slavistics 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 Department in Belgrade, and Christine Lefian, editorial assistant in the American Mathematical Society. Providence, USA June, 1972 S. H. Gould

5 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: University 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.

6 Table Qlf Contents Introduction Plan of the book 2 Inheritance, transliteration and loan-translation 3 Roots and prefixes 4 The Indo-European language and its descendants 5 Vowel gradation 6 Consonant variation 7 The alphabet Chapter ~ Alphabet The Cyrillic alphabet 2 Memorizing the alphabet 3 History of the Cyrillic consonants 4 The vowel-symbols; the basic vowel-scheme 5 Hard and soft consonants 6 The spelling rule Chapter II Pronunciation Importance of pronunciation 2 The six Russian vowel-sounds 3 Monosyllables for practice in pronunciation 4 Remarks on hard and soft consonants 5 Hard and soft consonants in English and Russian 6 A first approximation to Russian pronunciation 7 The letter H when pronounced but not written 8 The "separating" hard and soft signs 9 The letter H when written 10 Assimilation of voiced and voiceless consonants 11 Consonant clusters 12 Words of more than one syllable; accents

7 viii Table of Contents Chapter III Inflection The concept of declension 2 The three declensions 3 Frequency of occurrence of nouns of the eight types 4 Declension in the plural 5 Remarks on the exercises 6 The concept of grammatical gender 7 Declension of pronouns 8 Declension of adjectives 9 The numerals 10 Adjective-noun phrases; italics 11 Comparative and superlative of adjectives and adverbs 12 The uninflected parts of speech 13 The verb; present imperfective and future perfective 14 The future imperfective and the past tense 15 The adjectival and adverbial participles Chapter IV Aspect Difference in meaning between the two aspects 2 Aspect regarded as a correspondence 3 Perfective partners and lexical compounds 4 The imperfectivizing suffixes 5 Table of aspectual and lexical compounds of verbs 6 Notes on the table Chapter y Vocabulary Plan of the chapter 2 The three "verbs of motion" 3 The root 6 ep- (SI-) take 4 The roots JIar- lay and C Ta- stand 5 Verbs formed from adjectives 6 Twenty roots of considerable productivity 7 Forty roots of moderate productivity 8 Other nouns and adjectives

8 Table of Contents ix Readings Preliminary remarks 108 Section ~ Extracts from elementary analytic geometry and calculus A1 Distance between points 109 A2 A3 A4 A5 A6 A7 A~ A9 A10 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A27 A28 A29 A30 A31 A32 A33 Division of a segment Polar coordinates Parallel translation of axes Rotation of axes Equations of the straight line The line through a point in a given direction Normal equation of the line General linear equation of the line The line through two given points Segments on the axis (i.e. intercepts) Definition of a vector Sum of vectors Scalar products General equation of the plane Parametric equations of a line in space Introduction of irrational numbers Continuity of the domain of real numbers Least upper and greatest lower bounds Fundamental theorem on real numbers The elementary functions Limit of a function Continuity of a function Heine-Borel and Weierstrass theorems Derivative of a function Equation of the tangent to a curve Maximum and minimum of a function Differentiation of a sum, difference, product Derivative of a composite function Indefinite integral Integration by change of variable Integration by parts Fundamental theorem of the integral calculus

9 x Table of Contents Section B Extracts from elementary algebra and analysis Bl B2 B3 B4 B5 B6 BI B8 B9 Bl0 Bl1 B12 B13 B14 B15 B16 Bl1 B18 B19 B20 B21 B22 B23 B24 B25 B26 B21 B28 B29 B30 B31 B32 B33 Operations on sets Properties of the operations on sets One-to-one correspondence Equivalent sets Ordered sets Similar sets Algebraic operations Rings Examples of rings The zero of a ring Domains of integrity Fields Unit element Division Characteristic of a field; prime fields Isomorphism Ordered rings Properties of ordered rings Axiom of Archimedes The natural numbers Addition and multiplication of natural numbers Order of the natural numbers Subtraction and division of natural numbers Fundamental theorem of arithmetic The extension principle Performability of operations in an extension Equivalence classes The ring of integers up to isomorphism The ring of integers The field of rational numbers Quotient fields The field of real numbers The field of complex numbers

10 Table of Contents xi Section C More advanced topics C1 C2 C3 c4 C5 c6 C7 c8 C9 C10 C11 C12 Functions of a real variable Functions of several complex variables Summability theory of divergent series Generalized functions Calculus of variations Theory of groups and generalizations Theory of numbers Mathematical logic Partial differential equations Hilbert space Differential geometry Topology Glossary Name and Subject Index