482 Abstracts #406-613 HM4

ABSTRACTS

EDITED BY KENNETH 0. MAY

The purpose of this department is to give sufficient infor mation about the subject matter of each publication to enable readers to decide whether to read it. The indexing terms (in boldface capitals) refer only to aspects of the publication of interest to historians of mathematics, including some topics in general history of science and historiography, but not other topics unless there is a fairly close link with mathematics or its history.

Readers are invited to send reprints, autoabstracts, corrections, additions, and notices of publications that have been overlooked. Be sure to include complete bibliographic information. We need volunteers willing to cover one or more journals for this department.

MR 46 #3255 means that the item is numbered 3255 in volume 46 of Mathematical Reviews. RZ 1973 #3Al4 means that the item is numbered 3Al4 in the third number of the 1973 volume of the Referativny Zhurnal. Z 50 4 means volume 50, page 4 of the Zentralblatt.

The department is composed on the University of Toronto Computer text editing system (ATS/360), which allows easy correction, permanent availability for computer processing, right justification or variations in format of printout, and above all the quick automatic production of subject and author indices.

In order to facilitate reference and indexing, entries are given serial numbers (underlined for books) which appear -- at the end following the symbol #, and names are given surname first.

A name in parentheses at the end of an entry indicates the abstractor. In this issue there are abstracts by V. Albis, J. Albree, A. R. Amir-MO&z, J. W. Dauben, N. Dudley, S. M. Eisenberg, C. Eisenhart, D. E. Kullman, A. C. Lewis, J. Mathews, L. F. Meyers, B. M. Schein, H. Skala, S. Termini, H. S. Tropp, and D. E. Zitarelli. Other entries are by the editor.

Copyright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved

HM4 Abstracts #406-418 483

E;ANUNOV N F 1975 Pervyi ocherk teorii algebr F E Molina. 1st~mat issl 20, 150-170. ALGEBRA. MOLIEN T E. #406.

KATSIVELI G and SHILOV G E editor Matemaiki i deistvitelnost. Publikatsiya, predislovie i primechaniya G E Shilova. 1st~mat issl 20, 11-27. Mathematics and Reality, by Katsiveli, with preface and notes by Shilov.. PHILOSOPHY OF MATHEMATICS. NATURE OF MATHEMATICS. 4'407.

ERNbST JOHN 1976 Mathematics and Sex. (Mathematics Department, Univ of Calif, Santa Barbara). 31 p. EDUCATION. WOMEN. Preprint of an article to appear in the Amer Math MO. A report on a study of sex differences in the educational environment environment that might explain the gross sex differences in mathematical achievement and employment. The main conclusion is that there are modifiable practices that "tend to defer women from aspiring " to achievement in mathematics. #408. -

CHINENOVA V N 1975 K ponyatiyu tsentrostremitelnoi uskoryayushchei sily u Nyutona. Problemy ist mat i mekh 2, 37-39. CENTRIPEDAL ACCELERATION. NEWTON. #409.

COHEN I B 1975 Benjamin Franklin, Scientist and Statesman. New York (Charles Scribners). 95 p. FRANKLIN B. First of a series called DSB Editions, each volume being an article from the Dictionary of Scientific Biography, with partial bibliographies, sometimes with revisions, plus photographs. Brief reference to Franklin's work on MAGIC SQUARES and ALMANACS. #410. -

EVES HOWARD 1976 An Introduction to the History of Mathematics. Fourth Edition. (Molt Rinehard and Winston). 603 p. This GENERAL HISTORY, written as a TEXTBOOK for undergraduates and long popular for reacher training courses, has been expanded by three more chapters on the last three centuries, material on Chinese mathematics, more maps and portraits. Revisions include a more strictly chronological order and attention to various pedagogical and epimathematical matters. #411.

COPERNICUS 1972 COMPLETE WORKS. Warsaw-Krakow (Polish Scientific Publishers) & London (Macmillan) & New York (Johnson Reprint). Three volumes in five language versions (Latin, Polish, English, French, Russian). Vol. 1 contains the FACSIMILE MANUSCRIPT (in color) of the De revolutionibus with introduction, history and analysis of the MANUSCRIPT. Vol 2 contains the printed version , notes and commentary. #412 -

KAUCHIKAS A P 1975 Chisla i simboly v 'Algebre' R Bombelli. Problemy ist mat i mekh 2, 94. NUMERATION. BOMBELLI. #413.

GAMBLEN F 1976 Charles Ernest Weatherburn. J of the Australian Math Sot 21, l-4. Brief biography of WEATHERBURN C E. PORTRAIT. BIBLIOGRAPHY of his publications. DIFFERENTIAL GEOMETRY. (David E Zitarelli). #414.

GARDNER W D 1974 Will the inventor of the first digital computer please stand up? Datamation ZO(Feb), 84, 88-90. COMPUTERS. ATANASOFF J V. MAUCHLY J. ECKERT J P. LARSON E R. BERRY C. ENIAC. PENNSYLVANIA U. IOWA S C. PRIORITIES. SPERRY-RAND. HONEWELL. PATENTS. The court decision to invalidate the basic Eniac patent and assign priority to Atanasoff. Brief biography. PORTRAITS. (H S Tropp). ff415.

CROWE D W 1976 Geometric patterns in ancient ART. J of Undergrad Math 8(2), 35-36. ANCIENT MATHEMATICS. PREHISTORIC MATHEMATICS. The author suggests investigating primitive cultures to see the extent to which SYMETRY and the CRYSTALLOGRAPHIC GROUPS are represented in their art. #416.

CUVIER G L C F D 1970 (1810) Rapport historique sure les progres des sciences naturelles depuis 1789. Amsterdam (B M IsraWl). 411 p. Facsimile REPRINT of the original edition of 1810. The "natural sciences" (chemistry, natural history, geology, physiology, medicine, agriculture, etc.) are placed between the "mathematical sciences" and the "moral sciences." #417 -*

GERLO ALO'IS 1974 COPERiiICUS en Simon STEVIN. In Commemoration du 500me Anniversaire de las naissance de Nicolas Copernic, organisee le 4 avril 1974. Brussels (Ed de l'llniv), 39-52. #418.

484 Abstracts #419-430 HM4

DISTROVSKY SIGALIA 1975 Early vibration theory: PHYSICS and MUSIC in the seventeenth century. Archive Hist Exact Sci 14(3), 169-218. VIBRATIONS. MUSICAL ACOUSTICS. XVII. MBRSENNE. HUYGENS. SAUVEUR J. WALLIS. GALILEO. #419.

KOVALEV B D 1975 I istorii ponyatiya davleniya. Problemy ist mat i mekh 2, 32-36. PRESSURE. GALILEO. LEONARDO DA VINCI. ARCHIMEDES. NEWTON. STEVIN. #420.

BERKSON WILLIAM 1974 Fields of Force. The Development of a World View from Faraday to Einstein. London (Routledge and Kegan Paul). 383 p. Very little mathematics. Poorly indexed. #421. -

KOROLYUK L G & SIMONOV N I 1975 0 nachalncm periode issledovanii differentsialno- raznostnykh uravnenii. Problemy ist mat i mekh 2, 106-112. DIFFERENTIAL- DIFFERENCE EQUATIONS. #422.

GIURESCU CONSTANTIN 1974 Contributions to the History of Romanian Science and Technique from the 15th to the early 19th Century. Bucharest (Academiei Republicii Sot Romania). 226 p. In English. Largely on TECHNOLOGY, but includes chapters on SURVEYING and on CARTOGRAPHY in ROMANIA. #423 --

GODDARD L S 1976 Eamon DE VALERY--a mathematical portrait. Mathematical Spectrum 8, 75-77. IRELAND. (N Dudley). #424.

HERIVEL JOHN 1972 The influence of FOURIER on British Mathematics. Centaur-us 17, 40-57. GREAT BRITAIN. GREEN G. HAMILTON W R. STOKES G G. THOMSON W. MAXWBLL J C. PHYSICS. The author argues that his most important influence was in mathematical physics, largely on an emotional, inspirational level. (J W Dauben). #425.

HERMANN ROBERT editor and translator 1975 Ricci and Levi-Civita's TENSOR ANALYSIS paper. (LIE GROUPS: History, Frontiers and Applications, vol. 3). Brookline, Mass (Math Sci Press). 272 p. A translation with commentary and additional material of 'Methodes de calcul differentiel absolut et leurs applications" by RICCI and LEVI- CIVITA (1900 Math Ann 54), which is taken to be the source of the mathematics used by EINSTEIN tin his work on RELATIVITY, and which the editor considers "a model of the sort of synthesis and interaction between mathematics and the disciplines which use mathematics that I am trying to develop in this series." PURE AND APPLIED MATHEMATICS. #426 A

HERMANN ROBERT editor g ACKERMAN M translator 1976 Sophus Lie's 1884 Differential Invariant Paper. (LIE GROUPS: History, Frontiers and Applications, vol 3). Brookline, Mass (Math Sci Press). 281 p. GALOIS THEORY OF DIFFERENTIAL EQUATIONS. DIFFERENTIAL INVARIANTS. LIE S. DIFFERENTIAL GEOMETRY. INTEGRAL INVARIANTS. VESSIOT E. PICARD E. Translation of "Differentialinvarienten" (1884 Math Ann 24(4), 537-578 = Werke 6, 95-138), preceded by a discussion of the work in modern terms and followed by several chapters of commentary containing 'new or improved material that can serve as a basis for further research." #427. -

HILTS VICTOR L 1975 A Guide to Francis Galton's English Men of Science. Philadelphia (Amer Phil Sot). 84 p. (Transactions of the AI'S (NS)65(5)). Though very valuable for the SOCIOLOGY OF SCIENCE in XIX century GREAT BRITAIN, this survey (1874) of members of the ROYAL SOCIETY includes only four mathematicians (CAYLBY. HIRST T. SMITH Archibald. SPOTTISWOODE.) Todhunder and Sylvester did not reply to Galton's questionnaire. J E Routh and W K Clifford were not asked. #428. -

GOLDSTEIN SIDNEY 1969 FLUID MECHANICS in the first half of this century. In Sears W R editor, Annual Review of Fluid Mechancis 1 (Palo Alto), l-28. XX. Expository discussion of significant contributions by key figures. (H S Tropp). #429.

KRAMAR F D 1970 Ob algebre kvaternionov Gamiltona i vektornom analize Maksvella. Matemaika i mekhanika (Alma Ata) 1, 210-216. DIFFERENTIAL OPERATORS. VECTOR SPACES. MAXWELL C, using ideas on QUATERNIONS and VECTORS of HAMILTON W R. introduced such concepts as CURL, VECTOR TUBES, CONVERGENCE OF VECTORS. (RZ 1973 fflOAl0). [Helen Skala). #430.

HM4 Abstracts #431-444 485

SAID LEILA MOHAMMED AL- 1975 Neopredelnye uravneniya vtoroi stepeni u al-Karadzhi. Problemy ist mat i mekh 2, 90-93. DIOPHANTINE EQUATIONS QUADRATIC. DIOPHANTUS. KARAJI. #431.

SCHIRO MICHAEL ANTHONY 1974 An introduction to the theory of P-GROUPS, its development and group theoretic applications. Doctoral thesis at New York Univ, supervised by William Zlot. 212 p. (Disseration Abstracts 35, 4996-B. Order no. 75-8563). GROUP THEORY. XIX. XX. BIBLIOGRAPHY. (S M Eisenberg). #432. -

SERGESCU PIERRE 1973 Les mathematiques en Roumanie au XVIII siecle. Acta his rer nat net tech, Special issue 6, 310-311. Originally a communication to the 4th Int Con Hist Sci, Prague 1937. ROMANIA. #433.

KUDRYASHOVA L V 1975 Pervoe soobshchenie Dalambera ob uravneniyakh dvizheniya tverdogo tela. Problemy ist mat i mekh 2, 40-43. D'ALEMBERT. EQUATIONS OF MOTION. #434.

KUDRYASHOVA L V 1975 K istorii formirovaniya osnovykh ponyatii gecznetrii mass. Problemy ist mat i mekh 2, 44-48. CENTER OF I&%. CENTROIDS. #435.

GOULD H W 1976 Research Bibliography of Two Special Number Sequences. Revised Edition. Morgantown, W Va (Combinatorial Research Inst, 1239 College ave, 26505). CATALAN NUMBERS. BELL NUMBERS. BIBLIOGRAPHY (431 and 172 items respectively). #436 -*

GRANT EDWARD editor 1974 A SOURCE BOOK in Medieval Science. (Harvard Univ Press). 882 p. Of the 190 selections there are 25 on MEDIEVAL MATHEMATICS. one on LOGIC, one on ASTROLOGY, and others on ASTRONOMY, MECHANICS, etc. Commentary and annotations, detailed subject index, and brief biographies of the authors. Mainly Latin authors, very few Greek or Arabic, and none farther east. #437. -

KOLATA GINI BAR1 1977 Structure in large sets: two proofs where there were none. Science 195, 767-768. Excellent exposition of the impact of recent proofs by SZMEREDI E and FURSTENBERG H of a coniecture of ERDOS P and TURAN P relating to the length of ARITIBiETIC PROGRESSIONS in the set of integers. CCMBINATORICS. - RAMSEY THEORY. ERGODIC THEORY. CURRENT HISTORY. VAN DER WAERDEN B L. ROTH K. (H s Tropp). #438.

MDSTOW G D 1976 Abraham Robinson 1918-1974. Israel J of Math 25, 5-14. This volume contains the proceedings of the memorial conference for ROBINSON ABRAHAM at Yale University in May - 1975. BIBLIOGRAPHY (127 items). M)DEL THEORY. LOGIC. FOUNDATIONS. NONSTANDARD ANALYSIS. PORTRAIT. (HS Tropp). X439.

KAPLAN ALAN R 1977 An informal history of the hobby computer market. Personal Computing l(l), 36-39. COMPUTERS. PERSONAL COMPUTERS. (H S Tropp). #440.

DIEUWNNE JEAN 1976 L'idea de progress0 in matematica. In AGAZZI EVANDRO 1976 I1 concetto di progress0 nella scienza. Milan (Fellrinelli), 121-133. PROGRESS. HISTORICAL THEORY. #441.

GALLUZZI P 1976 Evangelista TORRICELLI. Concezione della matematica e segreto degli occhiali. Annali dell'ist e museo di storia della scienza di Firenze l(1). 71-96. OPTICS. EYE-GLASSES. #442.

ECCARIUS WOLFGANG 1976 August Leopold CRELLE als Herausgeber des Crelleschen JOURNALS. J f d reine u angew Math (Crelle!) 286/287, 5-25. QUANTITATIVE METHODS IN HISTORY. Part of this paper was published in Annals of Science (See X118). It443.

ORAYEN R A no date. La ontologie de FREGE. La Plata (Univ Nat de la Plata). The structure of his ONTOLOGY in relation to set type ontology. PHILOSOPHY OF MATHEMTICS. (Victor Albis). #444.

486 Abstracts #445-457 HM4

CARRIZOSA V J 1937 Recuento historico de1 desarrollo de las matematicas en COLOMBIA. In Primer Seminario Colombiano sobre la ensenanza de las matematica en el nivel universitario. Bogota (Fond0 Universitario National), 15-24. COMNIAL AMERICA. XIX. (Victor Albis). #445.

THORIN C L 1957 La Estadistica en COLOMBIA. In the source of #445, 25-33. STATISTICS. EDUCATION. Discusses teaching, texts, and schools up to 1957. (Victor Albis). U446.

RUEFF MARCEL 1976 Ferdinad Gonseth 1890-1975. Elemente der Math 31(S), 105-109. GONSETH F. PHILOSOPHY OF MATHEMATICS. PORTRAIT (H S Tropp). #447.

tiUWARIZM1 $ KHADEEV-JAM HOSSEIN translator 1969 Mafatih al-ulum (Key of the sciences) by Abu Abd Alla Muhammad ibn Ahmad ibn Yusuf al-Khuwarizmi. Teheran, Iran (Cultural Center of Iran). Persian translation. Complimentary to foreign scholars. Translator's introduction containing historical comments, preface, and two books. Tne first covers theology, grammar, writing, poetry, administration, etc. The second, philosopny, logic, medicine, arithmeetic, geometry, astronomy, music, mechanics, alchemy. ARAB SCIENCE. X. ENCYCLOPEDIAS. He is not to be confused with the more famous Abu Jafar Muhammad ibn musu al-KHWARIZMI . (A R Amir-Moez). #448. -

CHARBONNEAU LOUIS 1976 FOURIER, l'homme et le physicien d'apres John lierival. Rev hist Sci 29(l), 63-72. #449.

CLOSS MICHAEL P 1977 The nature of the Maya chronological count. American Antiquity 42(l), 18-27. MAYAN MATHEMATICS. NUMERATION. TIME. #450.

EISENSTEIN GOTTHOLD 1975 MATHEMATISCHE WERKE. Two volumes. New York (Chelsea Publishing Co). 952 p. The first complete COLLECTED WORKS. There was an earlier incomplete collection , the Mathematische Abhandlungen (Berlin 1847) with a preface by Gauss, reproduced here, 917-918. In addition to all his published works, published letters, and miscellanea (including a deposition concerning his imprisonment for political activity), included are ten LETTERS to GAUSS published for the first time and a biobibliographic article on Eisenstein by BIERMANN K-R. #451 --

KEEN LINDA 1977 Sonya Kowaleskaya - her life and work. Assoc for Women in Math Newsletter 7(2), 2-6 KOVALEVSKYA S V. t4.52.

GRATTAN-GUINNESS I 1974 Tne rediscovery of the Cantor-Dedekind Correspondence. Jb Deu Math Ver 76(2/3), 104-139. CAITOR. DEDEKIND. MANUSCRIPTS. LETTERS. Summarizes the state of the correspondence. Describes the materials found in the files of the lawyer of I~OETHER EMMY and now housed at EVANSVILLE UNIVERSITY. BIBLIOGRAPHY and list of 98 letters. #453.

GREENBAUM JOHN 1976 DIVISION OF LABOR in the COMPUTER field. Monthly Review 28(3), 40-55. MATbEMATICAL TECHNOLOGY. #454.

DOU ALBERT0 1963 Julio REY PASTOR. Razon y Fe 167, 133-146, 273-282. Biography with BIBLIOGRAPHY. #455.

GRIFFITHS H B & HOWSON A G 1974 Mathematics, Society and Curricula. (Cambridge University Press). 438 p. Though not intended as a history, it begins with an interesting two page chronological "panorama" and includes much historical information, commentary, and insight, especially on the XIX and XX century GREAT BRITAIN and USA. BIBLIOGRAPHY and exercises. Suitable for a course in CURRENT HISTORY of mathematics EDUCATION. #456. -

DRAKE STILLMAN 1976 GALILEO and the first mechanical computing device. Scientific American 234(l), 104-113. SECTORS. CALCULATING INSTRUMENTS. PROPORTIONAL COMPASSES. #457.

HM4 Abstracts #458-468 487

HINDLE BROOKE editor 1976 Early American Science. New York (Science History Publications). 227 p. REPRINTS from Isis, beginning with an interesting preface by SARTUN GEORGE to vol. 8 (1925). No papers explicitly on mathematics, but several tangential. ROBIE THOMAS. FRAIiKLIN F. LOGAN JAMES. CLAP THOMAS. RITTENHOLISE D. ASTRONOMY. COLONIAL AMERICA. USA. #458. -

SHIOKALO I 2 & BOGOLYUBOV 0 M 4 SOLOGUB V S 1972 Iosip Benedikovich Pogrebiskii. Narisi z ist prirod i tekn. Resyublikanskii mizhvid. zbirnik 17, 89-90. Obit of POGREBYSSKII I B. (B M Schein). #459.

LE NOIR TIMOTHY W 1974 The social and intellectual roots of discovery in seventeenth century mathematics. Doctoral thesis at Indiana University. 583 p. (Dissertaion Abstracts 35, 3450-B. Order no. 75-1718) CARTESIANISM. NEWTON. XVII. SOCIOLOGY OF MATHEMATICS. (S M Eisenberg). #460. -

HOOKER C A editor 1975 The Logico-Algebraic Approach to QUANTUM MECHANICS. Vol. 1: historical Evolution. Dordrecht (D Reidel). 622 p. This SOURCE BOOK reprints 31 "pioneering" papers by mathematicians, physicists, and philosophers, beginning with "The logic of quantum mechanics (1936) by BIRKHOFF G and VON NEUMAN J. The LOGICO- ALGEnRAIC APPROACH formulates questions of PHYSICS in terms of ALGEBRAIC STRUCTURES and related LOGICS. Volume 2 will deal with conceptual/philosophical issues in current mathematical research. #461 --

MARION WILLIAM ALEXANDER 1975 The SCHWARZ-CHRISTOFFEL TRANSFORMATION-- a mathematical development and a numerical solution. Doctoral thesis at the University of Northern Colorado. 140 p. Includes a history of the problem. (Dissertation Abstracts 36, 3430-B. Order No. 76-214). (S M Eisenberg). #462. -

MARTIN DENNIS SCOTT 1974 The DIFFERENTIAL in beginning calculus. Doctoral thesis at the State Univ of New York Buffalo. 251 p. A history of the concept in TEXTBOOKS and EDUCATION journals. NONSTAIIDARI ANALYSIS. (Disseration Abstracts 35, 3451-B. Order No. 74-29,240) (S M Eisenberg). #463. -

DUDLEY UNDERWOOD 1970 The first recreational mathematics book. J of Recreational Math 3, 164-169. Brief sketch of the life and work of BACHET de Meziriac and of his Problemes plaisants et delectables qui se font par les nombres (Lyon 1612). RECREATIONS. (Ii S Tropp). #464.

RAPPAPORT DAVID 8 DAVIS H T & MACLANE S & SACHS J M & ZYGWND A & ALLEN F B & GUNDLACH B B & HILDEBRANDT E H C & HEWITT GLENN 1965 A Half Century of Mathematics Progress. Chicago (Men's Mathematics Club of Chicago and Netropolitan Area). 235 p mimeographed. XX. CHICAGO. USA. A series of lectures on the period 1913-1963 prepared for the fiftieth anniversary of the MEN'S MATHEMATICS CLUB which initiated the formation of the NATIONAL COUNCIL OF TEACHERS OF IMATHEMATICS and played an important role in mathematics EDUCATION in the Midwest. Historical articles by Davis (general history of the period), Maclane (ALGEBRA), Sachs (GEOMETRY), Zygnumd (ANALYSIS and SET THEORY), Allen (EDUCATION), Gundlach (ELEMENTARY EDUCATION), Hildebrandt (TEACHER EDUCATION), and Hewitt (the club). Appendices include the certificate given the club as the first affiliate of the NCTM, summary of sample programs, "Takala's puns," lists of officers, and the membership list for 1963-1964. It is abstracted here at this later date because it seems never to have been reviewed (in spite of the eminence of some of its authors) and to have become rare. #465 -*

RASHED ROSHUI 1974 L'aritbmetisation de l'algebre au XIeme siecle. Proc 13 Int Con Hist Sci 1971 Set 4, 63-69. ARITHMLTIZATION. ARAB MATHEMATICS. ALGEBRA. ff466.

REID WILLIAM T 1976 A historical note on Sturmian theory. J of Differential Equations 20, 316-320. STURM THEORY. STURM THEOREM ON ZERUS OF POLYNOMIALS.. ORDINARY DIFFERENTIAL EQUATIONS ORDER 2. BIBLIOGRAPHY. (II S Tropp). #467.

PETROV V F 1975 Zagadka ustroistva Orfireusa. Problemy ist mat i mekh 2, 49-52. PERPETUAL MOTION. ORFFYREUS (= BESSLOR J E E). #468.

488 Abstracts #469-483 HM4

POVSTENKO V V 1975 Razvitie metoda kasatelnykh i normalei k krivym, opisannym v ploskom dvizhenii. Problemy ist mat i mekh 2, 59-64. KINEMATICS. TANGENTS. NORMALS. PLANE CURVES. #469.

PROBLEMY ISTORII MATEMATIKI I MEKHANIKI 1975 Moscow (Moscow U Press). Issue 2. 132 p. This series of collections, of which the first issue appeared in 1972, is published by the Chair of History of Mathematics and Mechanics of the Mechanico- Mathematical Faculty of Moscow State Univ and contains work of participants in its seminar on the history of mathematics and mechanics. Individual articles are abstracted separately. #470.

PROCEEDINGS 1975 Al-FARABI i razvitie nauki i kultury stran vostoka. Alma-Ata (Nauka). 112 p. Abstracts of papers given at the 1975 International Congress on this great scholar. MEDIEVAL MATHEMATICS. ARAB MATHEMATICS. TRIGONOMETRY. BIRUNI. EDUCATION. PHILOSOPHY OF MATHEMATICS. INDIAN MATHEMATICS. t471 --

PAEV M 1974 0 dvukh matematicheskikh mestakh v sochineniyakh Platona. Proc 13 Int Con Hist Sci 1971 Set 3, 34-36. CONTINUED FRACTIONS. ROOT EXTRACTION. PLATO. An obscure and controversial passage in the Republic. #472.

NEWTON THEOWRE HEBERT 1975 The duality function and some applications in undergraduate mathematics. Doctoral thesis at Columbia University supervised by B. K. Vogeli. 123 p. Contains a history of the DUALITY concept. (Disseration Abstracts 36, 1259-B. Order No. 75-20,215) (S M Eisenberg). #473. -

MUKHERJEE RABINDRA HATH 1975 Discovery of ZERO and its effect on HINDU MATHEMATICS. Thesis at Bihar Univ, India. INDIAN MATHEMATICS. Author's address: Nawrattan, P.O. & Dist. Purnea, Bihar, India. ff474. ..--

REINGOLD NATHAN 1976 Science in America since 1820. New York (Science History Publications). 334 p. REPRINTS from Isis. Nothing on mathematics. #475. -

RFMEZ E YA & SKOROKHOD A V & GAVRILYUK V G 1972 K 150-letiyu so dnya rozhdeniya P L Chebysheva. Ukrainskii mat zhurnal 24, 137-140. CHEBYSHEV. (B M Schein). W476.

WREN WILLIAM L JR 1976 Graduate student at Chicago in the twenties. Amer Math MO 83, 243-248. DUREN E L. HUSTON ANTOINETTE KILLEN. REMINISCENCES. SOCIOLOGY OF MATHEMATICS. CHICAGO UNIVERSITY. The people, their work, the quality of EDUCATION, areaa of RESEARCH during a period the author describes as a "down cycle" at the University. Concluding paragraph lists a large number of WOMEN who were graduate students at the time. (H S Tropp). #477.

MOVCHAN V 0 1972 Matematichna statistika i teoriya imovirnostei u pratsyakh M P kravchuka. Narisi z ist prirod i tekh. Respub. mizhvidomstvennii zbirnik 17, S-15. STATISTICS. PROBABILITY. KRAVCHUK M P. (B M Schein). #478.

HOWSE DEREK 1975 GREENWICH OBSERVATORY. Vol 3: The Buildings and ASTRONOMY INSTRUMENTS. London (Taylor and Francis). 197 p. 130 fine plates. #479. -

SKURATOVSKII M V 1975 Rozvytok fundamantalnoyi totozhnosti teoriyi prostykh chysel. Narysy z ist pryrodoznavstva i tekh 21, 36-41. Prehistory of DIRICHLET SERIES. EULER IDENTITY for the RIEMANN ZETA-FUNCTION. GOLDBACH. DIRICHLET. CHEBYSHEV. RIEMANH. DEDEKIND. CHEBOTAREV. INGAM. (B M Schein). 11480.

MARRINELLI EN20 1976 Enrico BCMPIANI. Annali di Mat Pura e Applicata 197, i-iii. Brief summary of major accomplishments. (H S Tropp). #481.

MITROPOLSKII YU A 1973 0 roli matematiki v nauchno tekhnicheskom progresse. In Matematika i nauchno-tekhnicheskii progress. Kiev (Naukova dumka), 5-16. ROLE OF MATHEMATICS. PROGRESS. NATURE OF MATHEMATICS. HISTORICAL THEORY. MATHEMATICAL TECHNOLOGY. DIFFERENTIAL EQUATIONS. (B M Schein). #482.

KUTTNER FRITZ A 1975 Prince CHU TSAI-YU's life and work; re-evaluation of his contribution to equal temperament theory. Ethnomusicology 19, 163-206. CHINESE MATHEMATICS. MUSICAL SCALES. STEVIN. n483.

Abstraots #984-495 489

HOWLE.TT J 1976 International Research Conference on the History of Computing, Los Alamos, June 10-15, 1976. Communications of the ACM 19(8), 481-482. COMPUTERS. Newsy sumnary of this meeting, featured by the presence of many of the computer pioneers. #484.

LYASHKO I I 1974 Vychislitelnaya matematika v sovremennom nauchno-tekhnicheskom progresse. In Nauchnaya konferentsiya "Vychislitelnaya matematika v sovremennom nauchno-tekh progress. Kanev, 34-39. A survey of directions presented in reports at the Conference on COMPUTER SCIENCE in modern technological PROGRESS. MATHEMATICAL TECHNOLOGY. (B M Schein). #485.

LEiiZEN V F 1968 Benjamin Peirce and the U. S. Coast Survey. San Francisco (San Francisco Press). 60 p. PEIRCE 8. uses. PERTURBATIONS. LINEAR ALGEBRA. An informal essay, based on a paper read to the Herbert M. Evans History fof Science Dinner Club in Berkeley, California. PORTRAITS of Peirce and of HASSLER R. BACHE A D. DAVIDSON G. PEIRCE C S. FACSIMILE of part of a letter from Peirce. Photograph of the author with the the USCGS ship Peirce. #486. -

KURDYUMDVA A I 1975 0 Faktorialakh Krampa. Problemy ist mat i mekn 2, 113-118. FACTORIALS. KRAMP C. W487.

GRIGORYAN E S & DDVLATOVA L I 1974 Traktat Kutbeddina Shiraze "0 dvizhenii kacheniya i ob otnoshenii mezhdu ploskim i krivym. Proc 13 Int Cong Hist Sci 1971 Set 4, 106- 107. ROULETTES. CURVES. PLANE GEOMETRY. ANGLES. AP.AB MATHEMATICS. #488.

LORINGHOFF B B V FREYTAG 1973 Prof. Schickards TUbinger Rechenmaschine von 1623 im TUbinger Rathaus. Kleine TUbinger Schriften Heft 4. Tubingen (TUbingen Chronik). 15 p. SCHICXARD WILLHELM. CALCULATING MACHINES. His machine was constructed in 1623. PORTRAIT. W489.

HOWSON A G 1975 University courses for future teachers. Educational Studies in Mathematics 6, 273-292. HISTORY OF MATHEMATICS COURSES. HISTORY OF MATHEMATICS IN EDUCATION. Describes an optional course in the secondary teacher training program at Southampton University, which includes a general survey, extended class discussion of a special theme from mathematics since 1800 (e.g. invariance, genus, Gauss, structure), student seminar reports on projects, an essay, and a final examination. Sample topics, projects, and examination questions. #490.

DUFFIE WILLIAM BURKE 1975 An historical development of the asymptotic evaluation of functions defined by integrals. Doctoral thesis at Univ of Illinois at Chicago Circle. 139 p. LAPLACE. STOKES. KELVIN. POINCARE. WATSON G N. RIEMANN. DEBYE P J W. VAN DER CORPUT. (Dissertation Abstracts 36, 1745-B. Order No. 75-23,352.) (S M Eisenberg). #491. -

MAXWELL E A 1976 William Valiance Douglas Hodge. Math Gazette 60, 61-62. HODGE W V D. Obit. (H S Tropp). #492.

MITROPOLSKII YU A 1974 0 roli matemaiki v nauchno-tekhnicheskom progresse i vliyanie vychislitelnoi matematiki na ee razvitie. In Nauchnaya konferensiya "Vychislit mat v Sovremennom nauchno- tekh progressee". Kanev . CURRENT HISTORY. MATHEMATICAL TECHNOLOGY. (B M Schei$:

40-53. COMPUTER SCIENCE. w493.

DUDLEY RICHARD M 1976 Unvolvable problems in mathematics. Science 191, 807-808. UNSOLVABILITY. Letter to editor in response to L Steen (18 July 1975, p. 209). demonstating that unlike the axiom of choice, the proof that conjectures such as FERMAT LAST THEOREM, GOLDBACH CONJECTURE, and FOUR COLOUR CONJECTURB are in such a form that if they are not disprovable in Zermelo-Frankel SET THEORY, then they are ttrue. (H S Tropp). (H S Tropp). #494.

MEDVEDEV F A 1974 Vydayushchiisya matematik Rene Ber. Voprosy ist estestvoznaniya i tekh 4(49). 77-78. On the occasion of the 100 ANNIVERSARY of the birth of BAIRE RENE. In the journal's translated and transliterated table of contents in French, German and English, Baire is renamed Rene Bohr, illustrating the typical disastrous results of transliterative round trips! X495.

490 Abstracts #496-506 HM4

GRUSHKOV S S 1975 Algebre Albera Zhirara. Problemy ist mat i mekh 2, 97-105. ALGEBRA. GIP.ARD ALBERT. #496.

RGDIN E Y 1975 Seven short biographical notes and reminiscences on Cornelius LANCZOS C. Computers and Mathematics with Applications 1(3-4), 257-268. EINSTEIN. FOURIER SERIES. DUBLIN. One note lists four videotapes and one audiotape of lectures and interviews (available from the University of Manchester Audio-Visual Service). (Joe Albree). #497.

RUZSA IWRE 1976 Die Begriffswelt der Mathematik. Budapest (Akademiai Kiado). 471 p, Almost entirely POPULARIZATION of elementary concepts of FOUNDATIONS, with little history and a few passages on PHILOSOPHY OF MATHEMATICS, of which the most interesting is on p. 449, where the author concludes from the LUwenheim-Skolem theorem that "Every consistent axiom system has an interpretation that relates it to objective reality." #498. -

ROBINSON R DE B 1974 Samuel Beatty: 1881-1970. Ontario Math Gazette 13(l), 27-29. BEATTY SAMUEL. Obit reprinted from Proc of the Royal Sot 4(9), 33-34. #499.

BUTZER P L & STARK E L editors 1975 Dissertationen in Mathematik an den hochschulen der Bundesrepublik Deutscnland in der Zeit from 1961 bis 1970. Stuttgart(Teubner). ;;;,,p,;* (= Jb* der Deu Math Ver 76(Suppl)). DISSERTATIONS. GEPMANY. CURRENT

Gives references to previous BIBLIOGRAPHIES of dissertations, back to 1850. Author index. Subject indexes would make such lists far more valuable. #500. -

BIERMANN KURT-R 1977 Friefwechsel zwischen Alexander van Humboldt und Carl Friedrich Gauss. Zum 200, Geburtstag van C. F. Gauss im Auftrage des Gauss-Komitees bei der Akademie der Wissenschaften der DDR neu herausgegeben durch Kurt-R. Biermann. Berlin (Akademie-Vsrlag). 202 p. (BeitrLge zur Alexander-von-Humboldt-Forschung 4) GAUSS C F. HUMBOLDT A v. 53 letters between them amd 7 others. Chronologies. PORTWITS. FACSIMILES. BIBLIOGRAPHY. Well indexed. #SO1 --*

FREGE GOTTLOB & editors GABRIEL GOTTFRIED & hERMES hANS & KAMBARTEL FRIEDRICH 4 THIEL CHRISTIAN & VERAART ALBERT 1976 Wissenschaftlicher Briefwechsel. Hamburg (Felix Meiner). (Nacngelassene Schriften und Wissenschaftlicher Brisfwechsel, vol. 2) 336 p. LETTERS to (mostly) or from FRBGE G and AVENARIUS R. BALLUE L E. BAUCH B. BRIX W. C. G. BUCHHOLZ H. CARNAP R. COUTURAT L. DARMSTAEDTER L. DINGLER H. ENGERT H. EUCHEN R. FALCKENBERG R. GOETZ G. HAUSSNER R. HILBERT D. tiOFFMANN A. HONIGSWALD R. HUNTINGTON E V. HUSSERL E. JONES E E C. JOURDAIN P c B. KLEIN F. KNOCH E. KOEBNER W. KORSELT A R. LEON X. LIEBMANN H. LINKE P. LOWENHEIM L. MARTY A. MAYER A. OGDEN C K. PASCH M. PEANO G. RICKERT H. RUSSEL B. SCHEFFER. SCHLOMILCR 0. SPIESER H. STUMPF C. THO-MAE J. ULRICI I!. VAILATI G. WIENER N. WITTGE!!STEIN L. ZSIGMONDY h. REPRINT of an article on Frege by JOURDAIN P E B from the Quart J of Pure and Appl Math 43 (1912). 237-269. Index of both persons and subjects (bravo!). #502.

SIMONOV R A 1977 Matematicheskaya mysl drevnei rusi (Mathematical concepts of old Russia). Moscow (Nauka). 120 p. RUSSIA. XI. XII. XIII. NUMERATION. ARITHMETIC. BIBLIOGRAPHY. #503.

TATON R ed 1976 Sadi Carnot et l'essor de la thermodynamique. Table Ronde du Centre National de la Recherche Scientifique. Paris, Ecole Polytechnique 11-13 juin 1974. Paris (Edition du CNRS). 435 p. 35 papers on CARNOT SAD1 and a previously unpublished MANUSCRIPT on ECONOMICS. #504

PRUDNIKOV V E & editor OZHIGOVA E P 1976 Pafnutii Lvovich Chebyshev 1821-1894. Leningrad (Nauka). 282 p. CHEBYSHEV P L. CHRONOLOGY. BIBLIOGRAPHY. List of honors. About 32 p devoted to his scientific work. Preface by editor. #505.

AL-DAFFA' AL1 ABIIULLAH 1977 The MUSLIM Contribution to Mathematics. London (Groom Halm), Atlantic Highlands NJ (Humanities Press), in Canada (Macmillan of Canada). 121 p. ISLAMIC. ARAB. MEDIEVAL. POPULARIZATION with many references to the literature. BIBLIOGRAPHY of books, articles, and MANUSCRIPTS. #506. -_

HM4 Abstracts #507-519 491

BOLZANO BERNARD & editor BERG JAN 1976 Reine Zahlenlehre. Stuttgart-Bad Cannstadt (Friedrich Frommann). 173 p. (Bernard Bolzano-Gesamtausgabe, Reihe II Nachlass, A. Nachgelassene Schriften, Band 8 GrUssenlehre II). NUMBER CONCEPT. REAL NUMBERS. INFINITESIMALS. TRANSFINITE NUMBERS. Many anticipations. 1507

MARACCHIA SILVIO 1975 La matematica come sistema ipotetico-deduttivo. Profilo storico. Florence (Felice Le Monnier). 227 p. (La Matematica nella Cultura e nella Scuola 7, Quaderni di "Archimede") AXIOMATICS. PLATO. ARISTOTLE. EUCLID. NON-EUCLIDEAN GEOMETRY. MODELS. HILBERT D. GODEL THEOREMS. 21 FACSI~IILES of title pages of "importanti opere." #508.

GRAEF MARTIN ed 1973 350 Jahre Rechenmaschinen. VortrWge eines Festkolloquiums veranstaltet vom Zentrum fUr Datenverarbeitung der Universitlt TUbingen. Munich (Carl Hanser). 124 p. CALCULATING MACHINES. COMPUTERS. CHRONOLOGY' 1623-1964, pp. 90-94. Numerous ILLUSTRATIONS. #509.

LORINGHOFF B v FREYTAG 1973 Wilhelm Schickard und seine Rechenmaschine von 1623. In #509, 11-20. SCHICKARD W. CALCULATING MACHINES. #510.

MACKENSEN L v 1973 Von Pascal zu Hahn. Die Entwicklung von Rechenmaschinen im 17. und 18. Jahrhundert. In #509, 21-33. CALCULATING MACHIMES. XVII. XVIII. #511.

HOWLETT J 1973 Cnarles Babbage and his computer. In #509, 34-42. BABBAGE C. COMPUTERS. #512.

REINECKB H 1973 Neuere Entwicklungen mechanischer Recnenmaschinen. In #509, 43-50. CALCULATING MACHINES. XIX. XX. #513.

ZUSE h 1973 Die ersten programmgesteuerten Relais-Rechenmaschinen. In #509, 51-56. COMPUTERS. STORED PROGRAM COMPUTERS. #514.

SYRBE M 1973 Die Rechenmaschinen in der Zukunft. In #509, 80-89. COMPUTERS. FUTUROLOGY. #515.

LAKATOS IMRE & editors WORRALL JOHN & ZAHAR ELIE & bibliographer and indexer CURRIE GREGORY 1976 Proofs and Refutations. The Logic of Mathematical Discovery. Cambridge (Cambridge Univ Press). 186 p. HEURISTIC. HISTORICAL THEORY. An attempt to carry through what Lakatos hoped to do. Ch 1 is an essay with the book's title published in 1963-4 in the J of Phil of Sci 14, originally an amended version of Ch 1 of his 1961 Cambridge thesis on the EULER POLYHEDRON FORMULA. Ch 2 is a discussion of the vector-algebra proof of the same by POINCARE H, based on Ch 2 of the thesis. The two appendices are based on Ch 3 of the thesis, on CAUCHY A on the limits of sequences of CONTINUOUS FUNCTIONS and implications for EDUCATION. Extended BIBLIOGRAPHY. Subject and name indexes (good!). #516 -*

MARSCHAK ALEXANDER 1972 The Roots of Civilization. The Cognitive Beginnings of Man's First Art, Symbol and Notation, New York (McGraw-Hill). 413 p. PRHEtiISTORIC artifacts suggestive of NUMERATION. CALENDARS. Many ILLUSTRATIONS. Well indexed. BIBLIOGRAPHY. SOURCES. #517.

LINDBERG DAVID C 1975 A Catalogue of Medieval and Renaissance Optical Manuscripts. Toronto (Pontifical Institute of Mediaeval Studies) 142 p. (Subsidia Mediaevalia IV) OPTICS. MEDIEVAL. BIBLIOGRAPHY. FtiUSCRIPTS. Indexes. #518 -*

WIENER NORBERT & editor MA&&N1 P 1976 Collected Works. With Commentaries. Volume I. Mathematical PHILOSOPHY and FOUNDATIONS. BROWNIAN MOVEMENT. WIENER INTEGRALS. ERGODIC THEORY. CHAOS THEORY. TURBULENCE. STATISTICAL MECHANICS. PORTRAIT The preface says "The papers are organized by coherence of subject matter rather than by chronology, so that Wiener's intellectual evolution may stand out." It would seem to this abstracter tnat destruction of the chronological order is an excellent way to hide this evolution! BIBLIOGRAPHY. #519

EDWARDS HAROLD M 1977 Fermat's Last Theorem. A Genetic Introduction to ALGEBRAIC NUMBER THEORY. New York (Springer-Verlag). 424 p. FERMAT LAST THEOREM. GENETIC EXPOSITION. Although there is a good deal of historical information and conjecture,

492 Abstracts $520-531

the author distinguishes very clearly his genetic method (“explanation . . . in terms of its origin and development”) and history. “In a history there is no place for detailed descriptions of the theory unless it is essential to an understanding of the events. In the genetic method tnere is no place for a careful study of the events unless it contributes to the appreciation of the subject."(p. iv) A second volume is planned to follow these chapters: Fermat, Euler, From Euler to Kuuner, kummerts theory of ideal factors, Fermat’s Last Theorem for regular primes, Determination of the class number, Divisor theory for quadratic integers, Gauss’s theory of binary quadratic forms, Dirichlet’s class number formula. 1520 L

HEIBERG I L & STAMATIS E S editors 1977 Euclidis Elementa. Vol. V Pars 1. Prolegomena Critica, Libri XIV-XV, Scholia in Libros I-V. Leipzig (Teubner). 243 p. Text in Greek with Latin preface & notes. #521.

PRICE G BALEY 1976 History of the Department of Mathematics of the University of Kansas 1866-1970. Lawrence, Kansas (Kansas Univ Endowment Assoc). 800 p. KANSAS UNIV. USA. The 555 p history is followed by many documents and BIOGRAPHICAL REFERENCE materials. A valuable type of historical work, unfortunately rare. #522.

RAYMOND PIERRE 1973 Le passage au materialisme. Idealisme et materialisme dans l’histoire de la philosophie. Mathematique et materialisme. Paris (Francois Maspero) . 413 p. PHILOSOPHY OF MATHE;MATICS. MATERIALISM. MARXISM. #523 -*

WINTER HEINRICH 8 WIT’IMANN ERICH editors & PALZKILL LEONARD 1976 Beitr’dge zur Mathematikdidaktik. Festschrift flir Wilhelm Oehl. Hannover (Hermann Schroedel) , 220 p. OE& WILHELM. EDUCATION. Biography (4 pp. including a chronology and bibliography). PORTRAIT. #524.

CHAPPERT ANDRE 1977 Etienne Louis Malus (1775-1812) et la theorie corpusculaire de la lumiere. Paris (J. Vrin). 283 p. MALUS E L. OPTICS. Many mathematicians mentioned in the index. #525 -’

SCHACHER SUSAN ed 1976 Hypatia’s Sisters. Biographies of Women Scientists Past and Present. Seattle, Washington (Feminists Northwest). 72 p. $2 from Feminists Northwest, 5038 Nicklas Place NE, Seattle, WA 98105. WOMEN. POPULARIZATIONS. 17 biographies including: HYPATIA. WTELET EMILIE DE. SOMERVILLE MARY. 4 pages of oriefer biographies including AGNES1 M. NOETHER E. #526. .-

KOHLSTEDT SALLY GREGORY 1976 The Formation of the Arrlerican Scientific Community. The AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE 1848-60. Urbana (Univ of Illinois Press). 341 p. USA. "Mathematics" does not appear in the index, but many mathematicians do. The alphabetical list of active members of the AAAS with brief biographies in the unpaginated appendix is a good BIOGRAPHICAL REFERENCE source, including 25 in whose biographies mathematics is mentioned (out of 337 total). BIBLIOGRAPHY. #527.

JAY JAMES M 1971 NEGROES in Science: Natural Science hctorates 1876-1969. Detroit, Michigan (Balamp Publishing, Box 7390, 48202). 96 p. BLACK MATHBMArICIANS numbered 41 out of 94 in the physical sciences other than chemistry. Of 587 doctors, 10 % were female, of which 6 were in mathematics (10 % of the total and 15 % of the mathematicians). #528.

FINKBEINEK DANIEL T and others editors 1977 Basic Library List for Four-Year Colleges. Second Edition 1976. A classified BIBLIOGRAPHY with author list, including a few historical items. Iv.529 -*

T~ICH MIKULAS & YOUNG ROBERT editors 1973 Changing Perspectives in the History Of Science. Essays in Honour of Joseph Needham. ilortrecht (D Reidel) . 511 p. NEEDHAM JOSEPH biography ("Tine making of an honorary Taoist”) and BIBLIOGRAPHY. PORTRAIT. 20 essays. #530.

PRICE, DEREK J DE SOLLA 1973 The (symbols for three star-like polygons) and other geometrical and scientific talismans and symbolisms. In ff.530, 250-264. SYMBOLS. STAR POLYGONS. X531.

HM4 Abstracts #532-544 493

GARDNER MARTIN 1976 Tne Incrediole Dr. Matrix. New York (Scribner's). 256 p. NUMEROLOGY. REPRINTS. #532.

WEISSKOPF VICTOR F 1969 Catalogue of Reprints of Scientific Papers in the Pauli Collection. Geneva (European Organization for Nuclear Research). 475 p. (CERN Bibl. 8). PAUL1 W. PHYSICS. BIBLIOGRAPHY. Over 10,000 reprints Pauli wished to keep, including mathematics. $533 --

HOYLE FRED 1977 Un STONEHENGE. San Francisco (W H Freeman). 167 p. PREHISTORIC. CALCULATING INSTRUMENTS. A survey POPULARIZATION of the arguments for its use as an eclipse predictor and astronomical calculator, beginning in the third millenium BC. #534.

MONCEL CHRISTIAN 1977 Expose de Poetique. (Autopublication; 131 rue de Marechal Foch, 42300 Riorges, France). 110 p. Part 2 (pp. 81-107) discusses the classic work of POINCARE H on HEURISTIC in relation to the author's ideas on creativity in POETRY. #535.

SAlTZER WALTER G 1976 Theorien und AnsRtse in der griechischen Astronomie-- im Kontext benachbarter Wissenschaften betrachtet. (Collection des travaux de 1'Academie internationale d'histoire des sciences 23). Wiesbaden (Franz Steiner). 170 p. GREEK. ASTRONOMY. ff536.

RENYI ALFRED 8 editor TURAN PAL 1976 Selected Papers of Alfred Renyi. Budapest (Akademiai Kiado). 3 ~01s. 627, 646, 667 p. SELECTED PAPERS. The editor is to be congratulated on presenting the papers in the order of publication. #537.

Dt MORGAN AUGUSTUS 1974 The Encyclopedia of Eccentrics. La Salle, Illinois (Open Court). 421 p. REPRINT of the 1915 Open Court reprint of the 1872 A Budget of Paradoxes. #538.

THOMAS-STANFORD CHARLES 1977 Early Editions of Euclid's Elements. San Francisco (Alan Wofsy Fine Arts). 76 p + 26 plates. EUCLID. BIBLIOGRAPHY. An elegant REPRINT of the first edition of 1926. 13 plates are new. A standard reference. #539. --

NASHED M ZUHAIR editor 1976 Generalized Inverses and Applications. Proceedings of an Advanced Seminar. New York (Academic Press). 1054 p. GENERALIZED INVERSES. Annotated BIBLIOGRAPHY OF 270 pages! #540.

STEINITZ E & R4DEMACHER H 1976 Vorlesungen Uber die Theorie der Polyeder unter Einschluss der Elemente der Topologie. Berlin (Springer-Verlag). 359 p. (Grundlehren der math Wiss 41). REPRINT of first 1934 edition. POLYHEDRONS. TOPOLOGY. Tne first chapter of 91 p. is a historical overview. lt541. --

SIVIN NATHAN editor 1977 Science and Technology in EAST ASIA. New York (Science History Publications). 294 p. REPRINTS from ISIS, one of four. Included are MIKAMI Y 1914 (JAPANESE. DETERMINANTS.), HARTNER WILLY 1938 (CHINESE. MUSIC.), LAM LAY YONG 1970 (CHINESE. SQUARE ROOTS.), LAM LAY YGNG 1972 (CHINESE. ARITHMETIC.). #542 -*

GARDING LARS 1977 Encounter with Mathematics. New York (Springer-Verlag). 279 p. A historically oriented mathematics TEXT suitable as a supplement for the first two Universit years. "Its purpose is to provide a historical, scientific, and cultural frame..." Some passages from original sources. X543.

GLAVAS C B 1973 Introduction to the History of Mathematics. (In modern Greek). Athens (No publisher indicated). 344 p. BIBLIOGRAPHY of secondary sources in English plus works in modern Greek by the author and STAMATIS E S. t544.

POLYA GEORGE 8 editor BOWDEN LEON 1977 Mathematical Methods in Science. (New Mathematical Library 26) Washington, D.C. (Mathematical Association of America). 246 P. REPRINI slightly revised of the 1963 publication as Vol XI of Studies in Mathematics sponsored by the School Mathematics Study Group. TEXT for TEACHER

494 Abstracts #545-561 HM4

TRAINING. "One of tne essential tendencies of the course is to point to the history of certain elementary parts of science as a source of efficient teaching..." #545.

\" MAR& W & SREBRNY M & ZARACH A editors 1976 Set Theory and Hierarchy Theory. A Memorial Tribute to Andrzej Mostowski. Bierutowice, Poland 1975. Berlin (Springer- Verlag). 353 p. MOSTOWSKI A. Brief curriculum vitae, PORTRAIT, BIBLIOGRAPHY (116 titles of which the last is first published here). ff546.

THUE &hL & SIiGEL C L & BRIJN'VIGGO & editors NAGELL T & SELBERG A & SELBERG S & THALBERG K 1977 Selected Mathematical Papers of Alex Thue with an Introduction by Carl Ludwig Siegel. Oslo (Universitetsforlaget). 650 p. REPRINT OF Siegel 1970 on Thue's work. Biography (11 p) by Brun. BIBLIOGRAPHY of 12 papers not included. PORTRAIT. FACSIMILE. #547 --

GARDNER MARTIN 1977 Mathematical Carnival. A New Round-up of Tantalizers and Puzzles 'from Scientific American. New York (Vintage Books). 286 p. RECREATIONS. BIBLIOGRAPHY. The 7th such collection. #548.

‘ CAMPAN 'FLORICA T 1976 A Rhind-Papirusztol az Elektronikus Szamologepig. Bucharest (Ion Creanga Konyvkiado). 155 p. (In Hungarian), NUMERATION. COMPUTATION, COMPUTERS. POPULARIZATION for juveniles. #549. --

CAMPA FLORICA T 1976 Wie die Zahlen entstanden sind. Bucharest (Ion Creanga Verlag). 104 p. POPULARIZATION for juveniles. NUMERATION. ANCIENT. #550 -*

CAMPAij FLORICA T 1977 Povestea numarului pi. 2nd revised edition. Iasi (Editura Albatros). 263 p. (In Rumanian). General history of PI. #551.

GILLON' BRENDAN S 1977 Introduction, translation, and discussion of Chao Chlln- Ch'ing's "Notes to the Diagrams of Short Legs and Long Legs and of Squares and Circles" HM 4, 253-293. CHINESE. CHAO CHUN-CH'ING. RIGHT TRIANGLES. #552.

DUBBEY 4

J M 1977 Babbage, Peacock and modern ALGEBRA. HM 4, 295-302. BABBAGE C. PEACOCK G. Shows the dependence of Peacock on Babbage. #553.

KENNEDYYHUBERT C 1977 Karl Marx and the foundations of differential calculus. HM 4, 303-318. MARX K. CALCULUS FOUNDATIONS. #554.

LEIGHTON ALBERT C 1977 Some examples of historical CRYPTANALYSIS. HM 4, 319-337. HISTORIOGRAPHY. MATHEMATICAL METHODS IN HISTORY. ff555.

ALBIS-GONZALEZ VICTOR S 1977 LATIN-AMERICAN translations of Legendre's "Elements de Geometric". HM 4, 339-340. LEGENDRE AM. #556.

GRATTAN-GUINNESS I 1977 A history of mathematics course for teachers. HM 4, 341- 343. HISTORY OF MATHEMATICS IN TEACHER TRAINING. #557.

4 BABINI J 1977 La labor de1 Comite International pour la metrologie historique. HM 4, 344-345. METROLOGY. #558.

BIEdN K-R 1977 Gauss bicentennial activities in the GDR. HM 4, 346-347. GAUSS C F. #559.

TANNER R C H 1977 Nathaniel Torporley's 'Congestor analyticus' and Thomas Harriet's 'De triangulis laterum rationalium'. Annals of Sci 34, 393-428. TORPORLEY N.

HARRIOT T. An analysis and comparison of Torporley's 1627 transcription of Harriet's work on a NUMBER THEORY problem and Harriet's original manuscript. (A C Lewis). #560.

J GIORELLO GIULIO 1975 ARCHIMEDES and the METHODOLOGY of research probrams. Scientia (Milan) 110, 111-135. (English and Italian). The author suggests an interpretation of two aspects of Archimedes' work based on the LAKATOS I theory of research programs. (S Termini). #561.

HM4 Abstracts #562-572 495

G%YI,UIIAT LUDOVICC 1975 On tne conceut of 'Crisis' of scientific RATIONALITY. Scientia (Milan) 110, 325-355. (English and Italian). An analysis of the "scientific rationality" that can be applied to the role played by mathematics in the development of science. HISTOKlCAL THEORY. #562.

UBALDCI SAN20 1975 hpistemological significance of the Poincare-Couturat controversy. Scientia (Milan) 110, 369-418. (English and Italian). PHIlOSOPHY OF MATHEMATICS. Suggests that the decline of LOGIC studies in France until recent times was caused by the predominant role of POINCARE H. A motivated appreciation of the work of COUTURAT L. #563.

GALGANI LUIGI 1975 Classical MECHANICS and QUANTUM MECHANICS. Scientia (Milan) 110, 469-491. (English and Italian). New mathematical results show that the relation between classical and quantum mechanics is closer than generally presumed. Implicit in the paper is the interesting thesis that new mathematical results deeply influence conceptual controversies. HISTORICAL THEORY. #564.

DE FINETTI BRUNO 1976 PROBABILITY: beware of falsifications! Scientia (Milan) 111. 255-303. (English and Italian). A brillian and lucid presentaion of‘ SUBJECTIVE PROBABILITY, with many historical items and personal recollections. (S Termini) #565.

LO1 MAURICE 1976 Couturat unknown. Scientia (Milan) 111, 683-699. (English, French, Italian). A detailed analysis of the work of COUTURAT L in LOGIC and the reason for its misunderstanding. (S Termini). #566.

NORTON B J 1976 The biometric-Mendelian debate from Galton to Fisher. A reappraisal. Proceedings of the 9th. Intl Biometric Conf, Raleigh, NC -(The Biometric Sot), vol. 1, 357-376 Early development of statistical GENETICS. Seeks to explain and elucidate the famous controversy between the biometric (Pearson, Weldon) and Mendelian (Bateson) schools. CORRELATION. REGRESSION. ANCESTRAL HEREDITY LAW. MENDELIAN HEREDITY. STATISTICAL GENETICS. EVOLUTION. GALTON F. PEARSON K. FISHER R A. WELWN W F R. BATESON W. (C Eisenhart) #567.

DAVID F N 1976 Karl Pearson and correlation. Proc of the 9th Intl Biometric Conf, Raleigh NC (The Biometric Sot), vol. 1, 339-356. Univariate and multivatiate CORRELATION and REGRESSION from their discovery by GALTON F in the 1880's to the "Cooperative Study" (191~&pp~DI~F~IKEE~WGf). Si!‘;SCfiEK. WELDON W F R. BRAVAIS A. EDGEWORTH F Y. . GOSSET W S ("Student"). FISHER R A. (C. Eisenhart) #568.

HANKINS THOMAS L 1976 ALGEBRA as pure TIME; William Rowan Hamilton and the foundations of algebra. In Machamer Peter K + editors Motion and Time, Space and Matter, Columbus (Ohio State Univ Press), Ch. 12. Analysis and commentary on Hamilton's 1837 attempt to construct the real numbers and so make analysis as scientific as geometry. Presents the metaphysical and mathematical background based on a detailed examination of the manuscripts at Dublin. HAMILTON W R. SYMBOLICAL ALGEBRA. KANT. COLERIDGE. PEACOCK G. DEMORGAN A. ANALYSIS FOUNDATIONS. REAL NUMBERS. COMPLEX NUMBERS. ORDERED PAIRS. XIX. (J Mathews) #569.

GAUSS C F & BIERMANN KURT-R introduction & SCHUHMANN ELISABETH translator & WUSSING HANS commentator 1976 Mathematisches Tagebuch 1796-1814 von Carl Friedrich Gauss. Leipzig (Akademische Verlagsges). 9s p. (Ostwalds Klassiker 256). Historical introduction #il.. p), 19 FACSIMILES, original Latin text, German translation, commentary. -*

SEGRE BENIAMINO 1976 Enrico Bompiani (1889-1975). Rendic di Mat 9(3), l-32. BOMPIANI E. Biography and analysis of major work. GEOMETRY OF DIFFERENTIAL EQUATIONS. SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS. RIEMANNIAN GEOMETRY. PROJECTIVE GEOMnTRY. ALGEBRA. 296 item BIBLIOGRAPHY. (H S Tropp). Y571.

COMBRIDGE J T 1975 Obituary: Warin Foster Bushell. Math Gaz 59(408), 109-110. BUSHELL W F. Former president of the MATHEMATICAL ASSOCIATION (GB), of uhich his father, BUSHELL W D, was a founder. (L F Meyers). #572.

496 Abstracts #573-584 HM4

AITON ERIC J 1975 How KEPLER discovered the elliptical orbit. Math Gas 59(410), 250-260. Claims error in KOYRE remarks about Kepler derivation. Shows various stages in Kepler's orbit-fitting. PLANETARY MOTION. MARS. LAWS OF AREAS. EUCMJS. PTOLEMY. (L F Meyers). #573.

CASSELIS J W S 1976 Is this a Recorde? Math Gaz 60(411), 59-61. PORTRAIT bought by BUSHELL W D for HARROW PORTRAIT. and now at CAMBRIDGE, thought to be of RECORDE ROBERT and used as basis for monument, etc., is now thought to be misidentified, (L F+Meyers). #574.

MAXWELL A E 1976 Obituary: William Valiance Douglas Hodge. Math Gas 60(411), 61- 62. Biography of HODGE W D. CAMBRIDGE. (L F Meyers). ff575.

GREEN D R 1976 The historical development of COMPLEX NUMBERS. Math Gas 60(411), 99- 107. Early references to: HERON. DIOPHANTUS. MAHAVIRA. BHASCARA. BAR CHIIA ABRAHAM. PACIOLI L. CHUQUET. Later: CARDANO. BEMBELLI. DESCARTES. LEIBNIZ. HARRIOT T. COTBS R. DE MOIVRE. EULER. WALLIS. ARGAND. WESSEL. GAUSS. D'ALEMBERT. CAUCHY. (L. F. Meyers). #576.

BRUNTON JAMES 1976 The envelope of an ellipse. Math Gaz 60(412), 118-123. Discussion with FACSIMILES of "A sure guide to builders" by LANGLEY BATTY (1729). CONSTRUCTION of OVAL CURVE inscribed in a rectangle, thought erroneously by Langley to be an ELLIPSE. ARCHITECTURE. (L F Meyers). #577.

RIESEL HANS 1975 Vad nytt pa primtalsfronten? (What news from the prime number front?). Nord Mat Tids 23(l), 5-14, 48. Swedish with English summary. cuRREm HISTORY. PRIME NUMBERS. (L F Meyers). X578.

HANSEN H H 1975 H. C. Andersen og Pythagoras. Nord Mat Tids 23(3-4), 135-138, 147. Danish with English summary. A proof of the PYTHAGOREAN THEOREM is the subject of a POEM, Formens evige Magie (Form's eternal magic) by ANDERSON HANS CHRISTIAN while tutoring other students and reprinted here in FACSIMILE with short biography. CL F Meyers). $579.

ALBERTSEN K 1976 Slaegternes uddben (Extinction of families). Nord Mat Tids 24(l). S-13, 43. Danish with English summary, POPULATION GENETICS. PROBABILITY that a family will die out. Summary of contributions of: BIENAYME I J. DE CANDOLLE ALPHONSE. GALTON F. WATSON H W. FAHLBECK P E. WESTERGAARD H. WEINBERG. FISHER R A. HALDANE J B S. ERLANG A K. STEFFENSEN J F. BHRISTENSEN C M. KOLMOGOROV. VON SCHELLING. LOTKA. (L F Meyers). USSO.

ALBERTSEN K & KRISTENSEN E 1976 En hidtil utrykt l&ning pa Erlangs problem om slaegternes uddden af Carl Marius Christensen (A previously unpublished solution to Erlang's problem of the extinction of families by Carl Marius Christensen). Nord Mat Tids 24(l), 14-18, 43. Danish with English summary. CHRISTENSEN CARL MARIUS. Biography. REPRINT of the solution with letter of rejection from BOHR HARALD because a solution by STEFFENSEN J F to this problem of ERLANG A K was in press. POPULATION GENETICS. PRIORITY. PROBABILITY. (L F Meyers). #581.

ANON 1975 25 lat dzidalnosci Komisji Matematycznej Glownego Urzedu Statystycznego (25 years of activigy of the Mathematical Committee of the Central Statistical Office). Frzeglad Statystyczny 22(l), 171-174. Polish. Summary of activities 1949- 1971/ CURRENT HISTORY. POLAND, STATISTICS. (L F Meyers). U582.

WIERZCHOS&AWSKI STANISKAW 1976 Wspomnienie 0 Profesorze StanisLawie Waszaku (Reminiscence of Professor Stanis~aw WaSZSk). Przeglad Statystyczny 23(2), 191-195. Polish. WASZAK STANISKAW. POZNAN. POPULATION STATISTICS. PORTRAIT. CL p Meyers). X583.

BUKIETYNSKI WJXDYS.&tW 4 CIESLAK MARIA & SMOLUK ANTON1 1976 Profesor Zdzis~aw Hellwig. Przeglad Statystyczny 23(4), 379-387. Polish with Russian and English summaries. Preface to special issue dedicated to HELLWIG ZDZISgAW on his 50th birthday. Chronological BIBLIOGRAPHY OF 85 ITEMS. ECONaMIC STATISTICS, WROC1;AHI. (L F Meyers). #584.

ml 4 Abstracts #585-599 497

DUBIKAJTIS LFXH 1975 The life and works of Stanislaw Jaskowski, Studia Logica 34(Z). 109-116. JASKOWSKI STANISM. LOGIC. BIBLIOGRAPHY of 48 items. This ussue contains papers from the KX Conference on History of Logic (Cracow 1974) devoted to his work and its consequences. (L F Meyers). #585.

KOPIECKI RYSZARD & SABALSKI BOGDAN & WALIGORA GERALD 1975 The research of Jaskowski on DECIDABILITY theory of first order sentences (I). Studia Logica 34(2), 201-214. LOGIC. PREDICATE CALCULUS. GODEL. PEPIS JAN. JASKOWSKI STANISCAW. (L F Meyers). #586.

DE BRUIJN N G 1977 Johannes G. van der Corput (1890-1975). A biographical note. Acta Arithmetica 32(3), 207-208. VAN DER CORPUT J G. ANALYTIC NUMBER THEORY. (L F Meyers). #587.

REID WILLIAM T 1976 A historical note on STURMIAN THEORY. J Diff Eq 20(2), 316-320. STURM J C F had been led to his work on DIFFERENTIAL EQUATIONS ORDER TWO by working first with DIFFERENCE EQUATIONS. The author develops Sturm's unpubublished results in a modern way. (L F Meyers). #588.

ATIYAH M F 1977 William Valiance Douglas Hodge Bull Lon Math Sot 9, 99-118. Biography (revised from the author's publication in the Biog. Notices of the Royal Sot.), including a mathematical assessment and a 5.5-item BIBLIOGWHY. HODGE W V D. HARMONIC INTEGRALS. ALGEBRAIC GhOMETRY. HODGE CONJECTURE. (H S Tropp). ff5.89.

KAWAGUCHI A 1976 Professor Enrico Bompiani. Tensor 30, 211-212. BOMPIANI E. PORTRAIT. Obituary. (H S Tropp). #590.

ROSELLE D 1977 Award of the 1977 ChAUVENET PRIZE to Professor Gilbert Strang. Amer Math MO 84, 417. STP.ANG G. (Ii S Tropp). #591.

STEWART IAN 1977 Gauss. Scientific American 237(l), 122-131. Brief biography and sketches of better known accomplishments. PORTRAIT and ILLUSTRATIONS. (H S Tropp). x592.

D S 1977 Game theorist Morgenstern dies, Science 197, 649. MORGENSTERN 0. (H S Tropp). #593.

KOLATA GIN1 BAR1 1977 Mathematical games: are they bona fide research7 Science 197, 546. Commentary on the sources of the distinction between GAMES and serious mathematics by: CONWAY T H. GLEASON A. GRAHAM R. (H S Tropp). #594.

WADE NICHOLAS 1977 Thomas S. Kuhn: revolutionary theorist of science. Science 197, 143-145. Some influence of and reactions to Kuhn's work fifteen years after publication. KUHN T. HISTORICAL THEORY. PARADIGNMS. SCIENTIFIC REVOLUTIONS. PORTRAIT. (H S Tropp). #595.

SRIVATSA S K & BISWAS N N 1977 An annotated BIBLIOGRAPHY on THRESHHOLD LOGIC. J Indian Inst of Sci 59(l), l-28. 26 items covering 1959-1976. ARTIFICIAL INTELLIGENCE. LINEAR PROGRAMMING. PATTERN RECOGNITION. (H S Tropp). 11596.

DE M)NCKER E & PIESSENS R 1976 A BIBLIOGRAPHY on AUTOMATIC INTEGRATION. J of Computational and Appl Math 2(4), 273-280. 204 items plus chronological author index 1954-1976. NUMERICAL INTEGRATION. (H S Tropp). ff597.

GAINES B R & KOHOUT L J 1977 The fuzzy decade: a bibliography of fuzzy systems and closely related topics. Intl 3 of Man-Machine Studies 9, l-68. Brief exposition, but primarily an 1150-item keyword-indexed BIBLIOGRAPHY of FUZZY SYSTEMS and applications. NONSTANDARD LOGIC. SET THEORY FOUNDATIONS. PROBABILITY. LINGUISTICS. (H S Tropp). #598.

SEGAL L A 1977 WEIZAC to the present. Siam News 10(4), 1.3. Brief chronology of the APPLIED MATHEMATICS activities at the WEIZMANN INSTITUTE from founding in 1945 to the present. ISRAEL. COMPUTERS. PEKERIS C L. GOLEM. (H S Tropp). #599.

498 Abstracts #600-613 HM4

APPEL KENNETH & HAKEN WOLFGANG 1976 Everv ulanar mar, is four colorable. Bull Amer Math Sot 82, 711-712. The official announcement of a-computer assisted proof of the FOUR COLOR THEOREM. (The historical introduction and bibliography appear in J Recreational Math 9(3), (1977). 161-169.) (D E Kullman). #600.

WEIL ANDRE 1976 Review of Mathematische Werke by Gotthold Eisenstein. Bull Amer Math Sot 82, 658-663. EISENSTEIN G. A cleverly written biographical sketch and survey of his work. (D E Kullman). #601.

KRBISEL G 1977 Review of L E J Brouwer Collected Works Vol 1. Bull Amer Math Sot 83, 86-93. BROUWER L E J. PHIIOSOPHY OF MATHEMATICS. FOUNDATIONS. Includes a critical analysis of Brouwer's brand of CONSTRUCTIVISM and his dispute with HILBERT D. INTUITIONISM. (D E Kullman). #602.

MACINTYRE ANGUS J 1977 Abraham Robinson 1918-1974. Bull Amer Math Sot 83, 646-666. ROBINSON ABRAHAM. BIBLIOGRAPHY. PORTRAIT. WDEL THEORY. NONSTANDARD ANALYSIS. ROBINSON'S TEST. A survey of his work in mathematical LOGIC. (D E Kullman). #603.

STOLL WILHELM 1977 Aspects of VALUE DISTRIBUTION THEORY in SEVERAL COMPLEX VARIABLES. Bull Amer Math Sot 83, 166-183. ANALYTIC MAPPINGS. A survey including historical remarks and a BIBLIOGRAPHY. (D E Kullman). #604.

MURWCK PHOEBE J 1977 New alphabets and symbols for typesetting mathematics. Notices of the Amer Math Sot 24, 63-67. SYMBOLS. PRINTING. Evolution of a unified type style to make mathematics more legible dand beautiful in print. published in &holarly Publishing 8). (D E Kullman). #605.

(Originally

ANON 1976 To Mikhail Alexseevich Lavrentev on his 75th birthday. Russian Math Surveys 31(l), 3-4. LAVRENIEV M A. PORTRAIT. (D E Kullman). #606.

ALEKSANDROV P S + 1976 Georgeii Evgenevich Shilov. Russian Math Surveys 31(l), 233- 249. SHILOV G E. Obituary, BIBLIOGRAPHY, PORTRAIT. BANACH ALGEBRAS. PARTIAL DIFFERBNTIAL EQUATIONS. (D E Kullman). #607.

NORDEN A P & SHAPUKOV B N 1976 Boris Lukich Laptev (on his 70th birthday). Russian Math Surveys 3191), 259-263. LAPTEV B L. BIBLIOGRAPHY. DIFFERENTIAL GEOMETRY. HISTORIANS OF MATHBMATICS. (D E Kullman). #608.

KALUZHNIN L A + 1976 Vladimir Petrovich Velmin. Russ Math Surveys 31(l), 251-258. VEIMIN V P. Obituary, BIBLIOGRAPHY. ALGEBRAIC NUMBER THEORY. RECIPROCITY. CD E Kullman). ff609.

KOSTOVSKII A N + 1976 Aleksandr Sergeevich Kovanko. Russ Math Surveys 31(2), 209- 213. KOVANKO A S. Obituary. BIBLIOGRAPHY. ALMOST PERIODIC FUNCTIONS. CD E Kullman). #610.

ALEKSANDRCV P S + 2976 Tshmukhamed Alievich Sarymsakov (on his sixtieth birthday). Russ Math Surveys 31(2), 215-221. SARYMSAKOV T A. Biography. BIBLIOGRAPHY. DIFFERENTIAL EQUATIONS. PROBABILITY. MARKOV CHAINS. TOPOMGICAL SEMIFIELDS. (D E Kullman). #611.

KOZLOV V YA & MARDZHANISHVILI K K 1976 Andrei Borisovich Shidlovskii (on his sixtieth birthday). Russ Math Surveys 31(3), 199-206. SHIDLOVSKII A D. Biography. BIBLIOGRAPHY. ANALYTIC NUMBER THEORY. TRANSCENDENTAL NUMBERS. (D E Kullman). #612.

GALLIAN JOSEPH A 1976 The search for FINITE SIMPLE GROUPS. Math Mag 49(4), 163-179. Historical survey of the IO-year quest for building blocks of GROUP THEORY. Main themes are the RANGE PROBLEM and special classes of groups. Includes a comurehensive list with discoverers, dates, notations, orders, and BIBLIOGRAPHY of 79 items. (D E Kullman). #613.