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Studies in Mathematics, Volume 22. Studies in Computer Science PP7 TITLE Studiei in ' Mathematics, ;lope 22. StudiOsin. SompuXerl Sciehce. INSTITUTION matheM4ical Association of(America Washington, / REPORT' NO L$BN-0-88385-12*-5 / , PUB DATE 82 NOTE 404p. / 4kVAI,LABLE FROMMathematical Association of Ame'riCi, 1529 18th St., ° 'F.' N.W.*, Washidgton, DC/20036 ($29.00). PUB TYPE'H Collected Works -_General 020 -- Viewpoin)t's 0.20) --5- Reference-Ma erials General (130) , ; EDRSPRICE.. MF01 Plus Posta el:t PC'NotAvailable from oiDRS. DESCRIPTORS ArtifiCial Intelligence; College Mathematics; *Computation; *cbmputer.Pr9grams; Computer Science; *Ccimputer Science Education; Computer Sismaation; *Data AnalysisLHighereEducation; Mathematicians; *Mathematics ducation; *Programing Languages; ' Statistics / IDENTIFIERS Mathematical/Associatlon of'America; *Numerit'al Analysis . .% ABSTRACT The nine iirticies in this collection were selected because-they represent crcerns central to computer science, emphaSize ,topics of partilculartintereSt to mathematicians, MI6 tnderscore the wide range bf areas deeply and continually. affected by computer 'science-The 5A:intents consist of: "Intioduction" (S- V. Pollack), ".The Development of Computer Science", (S. V.,Pollack), "ProgramMing Languages and Systems", (W. E. Ball), "Specifying Formal Languages" (R. V. Book), "Formal Amalysis of Computer Programs" (T., W. Pratt), "Computational Complexity" (F. P.- Preparata), "Computer Science and ArtificAal Intelligence" (a°. R. Slagle),, "The Impact of Computprs on Numerycal Analysis" (E. R. Buley and R. H. Pennington), "Compass.eSimulatipn" (M. Franklin), and "Cdmputational Tools for Statistical. Data Analysis' (C. F. .Starmer). (MRS) ****t**L************************************************************* * Reproductions supplied by EDRS are the best tha-t can be made .0. '* / . from the original document. '* **r****************************************************************** 14.S. DEPARTMENTOF EDUCATION NATIONAL INSTITUTE OF EDUCATION EDUCATIONAL RESOURCES INFORMATIO 1, CENTER (ERIC/ id This' docurrSnt has been reproducedas received from the person or organization, originating It Minor chahges have been da to improve reproductiop, quality. Points of iimiv or opiniohs stated in'thisdocu- ment do,not necessarily represent officialNIE,, position or policy?' j'PERMISSION REPRODUCE YHI MATERIAL IN MICROF CHE-1NLY- HAS BEEN GRANTE BY - d 43. 10,1111641 TO THE EDUCATIONAL L IRESOLIRCES _INFORMATION CE TEP(ERICV: _ y MAOA' ST:UDI,ES IN. 'MATHEMATICS b . Publi;lit4 by THEMATHEMATICAL ASSOCIATION OF AMERICA Coinmitiee.on Publications E. F. BECKENBACH, Chairman - 7 Subcommittei.'-op M AA Softiies-in MpthematG G. 'L.. WEISS; Chairman D.' W.. ANDERSON A. C. TUCKER _ ; Studies in Mathematics TheMathematical Association Of America VOIURIC 1: STUDIES IN MODERN ANALYSIS edited by R. C. Buck Volume 2:STUDIES IN MODERN ALGEBRA edited by A. A. Albert Volume 3:STUDIES IN REAL 4D COMPLEX ANALYSIS edited by I. I. Hirschtnah, Jr. Volume 4:STUDIES IN GLOBAL GEOMETRY AND ANALYSIS edited by S. S. Chern 'Volume 5: STUDIES IN MODERN TOPOLOGY ediled by P.J. Hilton Volume -6:STUDIES IN N'CIMBFIR THEORY edited by W. J. LeVegue Volume 7:STUDIES IN APPLIED MATHEMATICS edited by A. H. Taub ,,Q. vumeol 8:STUDIES IN MODEL THEORY edited by M. D.Aforley V dlunie9: STUDIES IN ALGEBRAIC.' LOGIC Wiled by Aubert Daigneault Volume 10:STUDIES IN OPTIMIZATION edited by G. B. Dantzig and B: G. Eaves Volume 11:STUDIES IN GRAPH THEORY, PART I ° edited by D.. R.(Fulkerson Volume 12:STUDIES IN GRAPH THEORY,,PART 11 edited -D.R.Ettficerson Volume 13: sTuplEs INHARMONIC ANALYSIS edited by J. M. Ash Volume14:STUDIES,,IN ORDINARY DIFFERENTIAL EQUATIONS,_ edited by Jack !foie Volume 15;STUDIES IN MATHEMATICAL BIOLOGY, PART I edited by S. A. Levin Volume 16;STUDIES IN MATHEMATICAL BIOLOGY, PART II , edited by S.(A: Levin Voldne 17: STUDIES IN COMBINATORICS 0, edited by G.-C. Rota Voliime`0:STUDIES IN PROBABILITY THEORY edited by Murray, Rose Volume .19:STUDIES IN STATISTICS edited by R. V. Hogg Volume 20:-STUDIES IN ALGEBRAIC GEOMETRY edited by A. Seidenberg Voluble21:STUDIES IN FUNCTIONAL ANALYST edited by R. G. Bartle? "' Volume 22:STUDIES IN COMPUTER SCIENCE edited by S. V. Pollack v; William E. Ball , Washington University in St. Louis Ronald V. Rook' Univevityof California at SantaBarbartet,. ;E. R. Bulfr, General Research Corporation, Santa Barbara Mark, Franklin Washington. University in St. Louis R. if. Pennington General Research Vorporation, Santa Barbara r. Seyittour.V. Pollack ifaShingtonijniver.sitY in- St. Louis Terence W. Pratt Unityrsity of Virginiit Franco P. Preparata University of Illinois,rban*hatupaigti.- James R. Slagle Navel Research llabor ry, Washington, D.C: sA C. F. Stariner Duke University -.7.- Washington: ljniuer'S'ityirt.$(.:i.VOui; :* to- Published and distributeddistributed by The MathematicalAsociati6jnof America CO 1982 by , TheMathematicallissociation of America (incorporated) Library of Congress Catttiog CardNumber82-062390 - - - _ _ _ CornpleteSet ISBN 0-88385-1004 Vol, 22 ISBN 0- 88385 -1244 Printed in the Unita Sttes-of America Current printing(last digit): 109.8 7 6 5.4 3 2 I 4NTRODUCT1011 The AssOciation of Computing Michindy'S Administrative Di- rectory for 1979 lists 207 American computer science departments granting bachelor's degrees, 127 granting master's degrees, and ,73 offering Ph.D. oi D.Sc. degrees. In addition, the,directqrr includes computer science programs at all levels embedded in 163 math- ematics departments, 56 busines3 schools, 29 electrical engineering departments, and 40 other schools_or departments, including such diverse, areas as physics, industrial kengineering, and economics. What makes these figures remarkable is the fact that the first coin- piiter science departMent appeared less than-two decades-earlier: To me, this rapid grpwth is but one of several, factors that combine, to place computer science in an exceptional position vii-a,vis other areas of inquiry:A-brief exploration of these points will be helpful 'in providing some general perspectiv4 within which the articles in this study can be considered( important to, note that_ the burgeoning of coinp,uter First, it _ science programs cannot be equaiedwiththif inatbFatioircif-coni= puler .science..There Aill is no "sraildard" (i.e., universally inoffen- sive) definition al computer science, In fact, the existence of such a The cyclopedia of Computer Science (A.Ralston and C Meek, eds., Pet- rocelli/Charter, 1976) defines computer science as follows: "Computer science is \viii Seymour V. Pollack \ ., discipline continues to, be a debatable point for a substantillo nuMber 4, people. (A prominent educator, though himself it cl)airman of a computer science department, cautions his audiences to, regard with suspicion any discipline with "science" in its name urban \$tibnce, consumer scicncc, economic science, social science, .-- computer Sortie people think of computer science's "uni- verse" as\a relatively restricted one, limited by definition to elm= tronic .digital information processing ,,systcms. Definitions at the othcr end o4 the spectrum perceive an arena consisting of an arbi- trarily wide range of information processing systems, ineluding..bio. logical ones. .Despite this diversity, thc digital cOmputer system is clearly the dom'nant vehicle for study. Mildly staked, this is a very unusual gituatio :Instead of. exploring the behavior of a cell,' a fluid,ean Organis or a galaxy, the computer scientist seeks basic observable phenomena from an artifact (i.e., the cornputcr itself or' the program procesAtherein). Thus*,the quest cor"`natural rayvs7 carries little meaning\ here. There is no ultimate and final reality against which e natory structures are to be assessed. The \ "reality," .represente ardwarc, Software, and informations is arbitrarilX alterable.hough it may sound almost facetiojis, the fact remains that, if an attempt (regardless of its degree of formalism) falls ihRrt of explaining observed events, those events (i.e., reality) can be c anged'to meet the explanationalf- way. Inevitably, this has a pr ound effect on the phenomena com- puter scientists seek to descriNand the ways in which such de- scriptions are voiced. A second major peculiarity lies in-computer science's-inherent, invisibility. End products Of comp terscienCe,4:e., information pro- cessing systerns, generally are used and mbtivated) by people with -little° interegt in computer. science. \A major objective in the im- plementation of such produ s', is to obscure their inner workings so .,.. , i ..t that the user's attention r mains focUsed on the externally per ceived behavior. For instance, a well-designed translating system ford high=level -programming language (su\ ch at-FORTRAN) sue . ' i` 4 .. \ concerned' with information processes, with the informatio4 structures and pro- o. cedures that enter into representations of such processes\and with their implemen- tation and ihform tion proce&sing systems. It is also concerned with relationships between informatioi processes and classes oftasks that givefse'io them." .,. ......_./ 1" \ 1. INTRODUCTION .IX cesifully promotes the illusion that 'the user's prbgrams execute directly on a FORTRAN computer, with no apparent 'intervention bctwccn the program (as .written) and the machinery. (This is cm- ,. phasized by the jargon, which terms such a'system "transparent" to its users.) -Conversely, implementors of such systems generhily are less concerned with the ultimate uses than they are with the tcchni- cal issues
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