.A UNIVERSITY'S EDUCATIONAL PROGRAM IN COMPUTER SCIENCE BY GEORGE E. FORSYTHE TECHNICAL REPORT NO. CS39 MAY 18, 1966

Transcription

1 cs39...a UNVERSTY'S EDUCATONA PROGRAM N COMPUTER SCENCE BY GEORGE E. FORSYTHE TECHNCA REPORT NO. CS39 MAY 8, 966 COMPUTER SCENCE DEPARTMENT School of Humanes and Scences STANFORD UNVERSTY

2 A UNVERSTY'S EDUCATONA PROGRAM N COMPUTER SCENCE by George E. Forsyhe* ) f Absrac - 4- Afer a revew of he power of conemporary compuers, compuer scence s defned n several ways. The objecves of compuer scence educaon are saed, and s assered ha n a U. S. unversy hese wll be acheved only hrough a compuer scence deparmen. The program a Sanford Unversy s revewed as an example. The appendx ncludes syllab of Ph. D. qualfyng examnaons for Sanford's Compuer Scence Deparmen. c.. The power of compuers Wh enough money) one could oban delvery n 967 of auomac dgal compuers effecvely capable of makng decsons n less han 50 nanoseconds and mulplyng n less han one mcrosecond. Such machnes can rereve each of a quarer mllon words n less han 00 nanoseconds, and each of some 3 X 0 9 characers n somehng lke 0,5 second. Snce a 500-page book holds approxmaely.5 X 0 6 characers, he above large sore holds he equvalen of 2000 monographs--a subsanal lle lbraky. Unl he frs auomac dgal compuers were avalable for delvery approxmaely 5 years ago, we were lmed o makng decsons, mulplyng, and accessng a fas sore n somehng lke 0 seconds, whle access o each characer of a 2000-book lbrary could hardly ake *Ths s a revson of prevous Sanford repor CS 26. The auhor acknowledges nnumerable conversaon wh Rchard Hammng, Wllam Mller, and many oher compuer scenss.

3 4.,,! & F.. less han 00 seconds. Thus he pas 5 years has seen acceleraons of 200 (access o slow sore), 0 7 (mulplcaons), and even 0 8 (access o fas sore). n comparson, he speed-up n ravel beween walkng and gong by je s abou lo*, ha n he dssemnaon of nformaon beween manu- 6 scrp and a large newspaper machne s abou 0, and ha n communcaon speed beween usng sound and rado waves s also abou 0 6. changes n raes of ransporaon and communcaon have compleely remade he world of earler mes. These s evden ha he even greaer speed-ups n nformaon processng are remakng our world. s. furhermore clear ha wll be many years before our capacy o explo he new compuers wll cach up wh even her presen capables. By s speed of processng nformaon and makng decsons, he elecronc dgal compuer s an exenson of he human mnd wh capaces ncomparably greaer han hose of any oher menal proshess hereofore avalable o man. n descrbng he compuer as a menal proshess (a erm used by Gerard [4]), am assumng ha s beng used n nmae conjuncon wh a human mnd. Whle here s a grea debae as o how far an unasssed compuer can smulae human cognve processes, s a pror evden ha a compuer lnked wh a human mnd s a more powerful ool han an unasssed human mnd. One ask of compuer scence s o demonsrae n ncreasngly broad areas ha he compuer-human eam s vasly more powerful han a human alone0 hem, The exponenal growh n numbers of human bengs and daa abou and he ncreasng pace and complexy of our echnologcal cvlzaon creae problems of nformaon processng for whch he elecronc compuer holds he only vsble means of sollnon. Examples: arraffc conrol navgaon, over meropolan areas, ar-defense problems, space-vehcle nfrmaon rereval problems, naonal ax records. n such areas comp>jng can drecly smulae applcaons for whch mahemacal echnques are as ye unavalable. forecasng, n oher areas, lke weaher he compuer s he agen for carryng ou mahemacal echnques of grea complexy. 2

4 / r,,, c.. c 2. Wha s compuer scence? consder compuer scence n general o be he ar and scence of represenng and processng nformaon and, n parcular, processng nformaon wh he logcal engnes called auomac dgal compuers. Compuer scence deals wh such relaed problems as desgnng auomac dgal compuers and sysems, he desgn and descrpon of suable languages for represenng boh processors and algorhms, he desgn and analyss of mehods of represenng nformaon by absrac symbols, and of complex processes for manpulang ' hese symbols. Thus he cenral heme of compuer scence s lke he cenral heme of engneerng-- namely, he desgn of complex sysems o opmze he value of resources. Perhaps he man dfference s ha compuer scenss work wh a very absrac medum (nformaon), and desgn sysems ypcally far more complex n deal han mos elaborae engneerng sysems. Compuer scence mus also concern self wh such heorecal subjecs supporng s echnology as codng and nformaon heory, he logc of he fnely consrucable, numercal mahemacal analyss, conrol heory, swchng heory, auomaa heory, mahemacal lnguscs, graph heory, and he psychology of problem solvng. Naurally hese heorecal subjecs are shared by compuer scence wh such dscplnes as phlosophy, mahemacs, engneerng, operaons research, and psychology. To a modern mahemacan, desgn seems o be a second-rae nellecual acvy.. Bu n he mos mahemacal of he scences, physcs, he role of desgn s hghly apprecaed, and Nobel przes are awarded more or less equally o heorecal and expermenal physcss. s sad ha Donald Glazer was awarded a Nobel prze solely for he desgn of a bubble chamber, snce hs opened up new felds of physcs, The ulmae purpose of physcs s he nellecual one of undersandng he physcal world, and he role of expermen s he secondary one of asssng n he undersandng. n compuer scence, on he oher hand, he prmary purpose s o desgn opmal processes 3

5 and processors of nformaon, and heory#serves he secondary role of \, c. - -.!, &.- suggesng echnques, mehods of analyss, and proofs of opmaly. We conclude ha, f expermenal work can wn half he laurels n physcs, hen good expermenal work n compuer scence mus be raed very hgh ndeed. Because he represenaon and processng of nformaon are he core of compuer scence, scence of nformaon processng, for nformaon Processng bears such a name. dscplne s bul up, ' reanng he word "compuer" n our name. and nformaon scences" P, ha on Ths many persons refer o our subjec as he and ndeed he nernaonal Federaon Unl a raher subsanal prefer o keep explc our pragmac goal by Perhaps he name "compuer s a proper compromse a presen. A very concse bu general defnon of our subjec s gven n page -75: "The nformaon scences deal wh he body of knowledge relaes o he srucure, orgnaon, ransmsson, and ransformaof nformaon --n boh naurally exsng and arfcal sysems. ncludes he nvesgaon of nformaon represenaon, as n he genec code or n codes for effcen message ransmsson, and he sudy of nformaon --processng devces and echnques, such as compuers and her programmng sysems." An neresng comparson of compuer scence wh boh pure and appled mahemacs has been made by Gorn [5]. Whle Gorn s hnkng only of he scenfc applcaons of compuers, he dsncons presened could ceranly be ranslaed o cover oher areas of compung. To Gorn, he pure mahemacan s neresed n he synaccal rela,ons among symbols, que apar from her meanng n he physcal world or her compuably. deal wh he srucures of heores, Thus he all-mporan quesons of pure mahemacs and no wh her meanng or her use. For example, mos pure mahemacans are unconcerned wh wha numbers acually are, and ndeed he queson s unseled; hey are nsead concerned (among oher hngs) wh wha relaons exs among numbers and among objecs bul up from numbers. The appled mahemacan s prmarly concerned wh he semancs of symbols --wha do mahemacal heorems mean as appled o he phys 4 c

6 c. 4. cal world? For example, economcs or elecroncs? how can mahemacal analyss help us undersand Fnally, he compuer scens s concerned wh he pragmacs of he applcaons of mahemacs o problems. Wha algorhms can acually be used o calculae he roos of an equaon? Wha does cos n sorage or me or human effor o perform a ceran algorhm? Wha guaraneed or probablsc or merely plausble error bounds can be consruced for he answers? Wha languages can he soluon be descrbed n? Wha hardware do hey requre% Are he languages well sued o he curren mode of neracon of he programmer wh he * compuer? How can foolproof algorhms be found? (Ths s no a rval queson. Hardly any one knows how o solve even a quadrac equaon on a compuer whou unnecessarly rskng loss of precson or overflow or underflow!) One hng compuer scence s no: s no merely he unon of he applcaons of a compuer o dverse problems. Raher, he core of he feld s applcaon-ndependen and raher absrac, beng concerned wh languages and echnques ha are relevan o a varey of dfferen applcaons of compung, n much he same way ha mahemacs s an absrac ool ha s relevan n many dfferen applcaons. However, because of he newness of he feld, compuer scenss mus now be concerned wh applcaons of compuer mehods n many dfferen areas of echnology and learnng, wll laer ener he core of compuer scence. n order o gan he nsghs whch And so compuer scenss engage n a very broad specrum of acvy, rangng, for example, from pure logc o communcaons engneerng, o busness admnsraon, documens o medcal daa processng, from he psychology of learnng from compuer analyss of he conen of and from pure mahemacal analyss o mehods of plausble nference abou he accuracy of expermenal algorhms. Thus compuer scence s n par a young deducve scence, n par a young expermenal scence, and n par a new feld of engneerng desgn. Because of hs broad sweep of acvy, compuer scence s usually msundersood by hose wh an acquanance, however close, wh only one aspec of compung. 5

7 , 30 The objecves of compuer scence educaon. There are a leas hree dfferen groups of sudens o whom compuer scence educaon should be dreced, and he objecves are dfferen for each. a. Nonechncal sudens Almos all czens of he developed naons wll be grealy affeced by compuers. Hence a general educaon should nclude enough background for he czen o comprehend somehng abou compuer scence. Snce a unversy educaes he fuure leaders of he communy, he sudens need a background for makng decsons n a compuerzed world. They need 'o learn wha compuers are, wha hey can do, wha hey canno do. Sudens frequenly have a myscal awe of compuers as robos wh gan brans whch wll overwhelm he world. Sudens need o realze ha compuers are merely obeden slaves wh unendng capacy o make decsons. Sudens need o realze he large role of human bengs n creang compuer sysems, by human plannng n he large and n deal. o grps wh he queson, All hese hngs and-laboraory course language, Sanford. and we have and ha every b of auomaon s acheved "Can machnes hnk?" Sudens need also o come are reasonable objecves of a one-semeser lecuren whch sudens acually program n an approprae consderable experence wh such courses a b. Specalss n oher echncal felds The auomac compuer s one of he mos mporan ools o have been devsed n he hsory of man. ndeed, Gerard [4] has classed afer he nvenon of speech and sysemac scence as he hrd gan sep n man's nellecual hsory. s already recognzed by many knds of naural scenss ha hey mus know compung farly well. Curren sudes of engneerng educaon emphasze acqurng general purpose ools wh long expeced lfemes of uly--lke mahemacs, Englsh, sascs --a he expense of specal nformaon avalable n handbooks. hese lasng ools, Zadeh [6], Auomac compung s ndeed becomng recognzed as one of because of he wde doman of s applcaons. charman of he Deparmen of Elecrcal Engneerng, 6

8 c \ - \ f ( Unversy of Calforna, Berkeley, makes a parcularly srong clam abou he mporance of compuer scence n echncal educaon: he saes ha elecrcal engneerng wll suffer a serous declne n mporance as a dscplne unless can absorb a subsanal amoun of acvy n compuer scence. s now clear ha sudens of socal scence mus also acqure a famlary wh compung mehods. And he serous suden of he humanes wll soon fnd compuers ndspensable, on any subsanal volume of daa. f he s o carry ou research Moreover, he compuer producon of musc has opened a brand new feld of creave acvy. should be undersood ha one of he reasons auomac compung s such a valuable ool s he absracness of he nformaon represened n a compuer. s possble o represen no only numbers, bu also leers, puncuaon, cars on a freeway, muscal noes, parcles of a flud, chess peces, Moreover, or praccally anyhng else ha s dscrezable. we are no lmed o convenonal operaons on hese symbols, for a compuer s able o carry ou arbrarly defned operaons. nonlnear mahemacal models, processes, Thus hree-valued logcs, sochascally defned and many oher maers dffcul for humans o mplemen can be modeled or smulaed wh an auomac compuer wh no nrnsc dffculy. Even when operaons are exraordnarly complex, frequenly he mcrosecond speed of a compuer wll enable a reasonably large process o be compleed whn olerable mes. Thus he compuer no only perms hereofore unmanageable mahemacal processes o be carred ou for he frs me, bu also somemes perms he expermener o be freed from any mahemacal model whaever! Tha s, he compuer model can somemes smulae he physcal suaon drecly, whou he nermedary sep of mahemazaon of he suaon. of compuer models s manly wang o be exploed. c. n educaon of compuer scence specalss Ths enormous poenal The mos mporan group o be educaed n compuer scence are he fuure specalss n he feld, for hey are he seed who wll become he creaors and he eachers of he fuure. They mus receve enough background o be able o follow and preferably lead he fuure 7

9 ( ~. - developmen of he subjec. For he graduae suden of compuer scence he faculy mus creae a currculum and nculcae sandards of performance n. The suden mus learn o read and o wre he approprae leraure. A background mus be bul for years o come. Compuer scence educaon, lke all educaon, mus am o lgh a lamp for he suden, raher han ry o fll he suden's bucke of knowledge. Ths educaon mus creae he feld's leaders, full of ambon and fre o aack he all-pervasve unsolved problems of compuer scence. Even he average suden mus realze hs dependence on connung educaon, ha he wll have o learn and relearn almos everyhng he knows every few years of hs revoluonary epoch n echnology. 4. How can a U. S. unversy realze he above objecves? The frs major sep by whch a U. S. unversy can realze he objecves saed above s o creae a deparmen of compuer scence, or he same hng under a dfferen name. The reason for formng a deparmen s o enable compuer scenss o acqure a faculy of her own choosng, and exercse conrol over he currculum of sudens wshng o specalze n compung. There s abundan experence o show ha whou such an admnsrave sep compuer educaon wll no even keep up wh he feld. Whou a deparmen a unversy may well acqure a number of compuer scenss, bu hey wll be scaered and relavely neffecve n dealng wh compuer scence as a whole. For example, numercal analyss locaed solelywhn a mahemacs deparmen may be oo rnldcl': concerned wh analyss, and oo lle wh compung. Whou acually sudyng he soluon of problems on compuers no analys s llsely o learn wha are he acually pressng problems of scenfc compung. And whou hs knowledge one can hardly serve as a compuer scens. (A he same me, we sress ha compuer scenss owe a grea deb o all mahemacans, pas and presen, who do research n numercal or consrucve mahemacs.) Naurally a compuer scence deparmen canno be sared unl here are wo or hree compuer scenss on he faculy. One may herefore expec, ha he deparmen-o-be wll be n a probaonary 8

10 , r! f f 9 : saus for wo or hree years, as Sanford's was. - Compuer scence deparmens are known o he auhor a he followng unverses, and ceranly he ls s ncomplee: Carnege Tech, Cornell, llnos, Mchgan, Norh Carolna, Nore Dame, Pennsylvana, Penn Sae, Purdue, Sanford, Texas, Torono, Wsconsn. Sanford's was he frs or nearly frs of hese. There are srong compuer scence programs whou deparmens a he followng unverses (and ohers): Brown, Calforna, Cal Tech, Chcago, Harvard, M.. T., Maryland, New York Unversy, Prnceon, Vrgna. Several of hese programs wll become deparmens n he near. fuure. Probably a deparmen of compuer scence belongs n he school of leers and scences, because of s close es wh deparmens of mahemacs, phlosophy, and psychology. Bu s relaons wh engneerng deparmens concerned wh sysems analyss and compuer hardware echnology should be close. n years o come we may expec a deparmen of compuer scence o come ogeher wh deparmens of pure mahemacs, operaons research, sascs, appled mahemacs, and so on, nsde a school of mahemacal scences. We can hope for some weakenng of he auonomy of ndvdual deparmens, and a concoman srenghenng of he ably of a unversy o found and carry ou nerdscplnary programs. The Dvson of Mahemacal Scences a Purdue appears o be a leader n hs respec. A deparmen of compuer scence has he responsbly of creang currcula for each of he groups menoned n secon 3 above. Thus here wll be degree program for s own majors. There wll be servce courses for majors n oher deparmens n whch compung s recognzed o be cenral. There wll be "compuer apprecaon" courses or more subsanal courses as par of a general lberal educaon program. n a unversy wh an adul educaon program some or all of hese wll be offered a ngh for he "rereadng" of graduaes of pas years. n all hese courses he compuer scence deparmen mus srve 9

11 o exrac and each he essence of compuer scence, and avod s - * c! c C c ransen and accdenal aspecs. For example, general nroducons o compung need no longer spend much me comparng base 2 and base 0 arhmec, alhough sudens of numercal mahemacs mus be perfecly aware of he arhmec peculares of any number sysem n use. he dealed sudy of a machne language seems beer relegaed o specalzed compuer scence courses han augh n a frs course. Whereas a one me performng arhmec on machne-language commands seemed o be he essence of programmng, s no longer so mporan. n fac, where several programs use he same sysems one canno nerm he leer 'o be modfed a all. And Fnally, he deparmen should nss ha s majors devoe subsanal me o sudes n oher deparmens (mahemacs, logc, psychology, elecroncs, ec.). For havng conrol of he compuer scence currculum does no mply acually eachng he enre currculum! n addon o a compuer scence deparmen, a unversy needs a srong compuaon cener n order o aan s educaonal goals n compuer scence. Such a cener mus be organzed wh machnes, languages, and sofware capable of recevng a large number of programs from dfferen classes of sudens. n a bach-processng compuaon cener we expec ha each suden of nroducory programmng should have one shor pass per calendar day on a compuer. ofen, bu wh longer runs.' More advanced sudens wll come les's Thus he cener mus be well endowed o receve a very large volume of suden programs n addon o s radonal and beer rewarded goal of servng faculy research work. you have had experence wh hs job-shop ype of compung, you canno recognze how poorly adaped ypcal machne sysems are o dealng wh. Even wh good machne sysems s a large problem n logscs and human relaons o run more han 000 jobs a day for a varey of users. Unless As we look ahead, s commonly beleved ha unversy compuaon servces wll generally ake he form of a cenral processor, me-shared as a unversy uly from many consoles around he campus. workng well, When acually such sysems should cure many of he dsadvanages of bachprocessng sysems appled o suden work. We may expec a consderable 0

12 shake-down perod before he sysems work well, dffcules as ye no dream of. and we may also fnd some The opmzaon of such me-shared servces should provde many research problems for sudens of compuer scence and operaons research. 5. Sanford Unversy's educaonal program n compuer scence. Snce January 965 Sanford Unversy has had a Compuer Scence Deparmen whn s School of Humanes and Scences. The new deparmen had been gesang for approxmaely hree years whn he Mahemacs Deparmen. n Sepember 966 he Compuer Scence Deparmen wll have postons for approxmaely welve faculy members a levels of asssan ' professor and above. wl: be roughly as follows: The prncpal felds of neres of he faculy numercal analyss (3)) arfcal nellgence (3), programmng languages and sysems (3), machne organzaon (l), compuer conrol of physcal daa (l), logc and lnguscs (). One measure of he dversy of compuer scence s he varey of.backgrounds of s praconers. as follows: n our faculy have Ph. D.'s mahemacs (4), appled scence (), elecrcal engneerng (2), ndusral admnsraon (l), physcs (2). We have no undergraduae degree program n compuer scence, and no presen nenon of sarng one. regard a B. S. A he presen me we would n Compuer Scence as oo lkely o be a ermnal degree, alhough mgh be excellen preparaon for graduae work n felds lke busness admnsraon or medcne. Our recommendaon for Sanford undergraduaes neresed n compung s ha hey major n mahemacs and ake our senor-graduae courses. n our opnon he undergraduae compuer scence currculum gven n [l] s nearly a maser's currculum. We have approxmaely 5 graduae majors, of whom approxmaely 80 are full me sudens. We offer a Maser of Scence n Compuer Scence, and by June 966 wll have awarded approxmaely 67 of hem snce 96. We offer a Ph. D. n Compuer Scence. The frs wo wll probably be awarded n 966, and approxmaely en more sudens have passed he wren qualfyng examnaons for he Ph. D. Two sudens have aken nerdeparmenal Ph. D. degrees nvolvng subsanal sudy n compuer scence. Over he pas egh years he auhor has been he prncpal

13 hess advsor of some seven sudens who have wren dsseraons n numercal analyss for her Ph. D. n mahemacs. The Bullen [7] be offered n n our deparmen, gves our caalog descrpon of he courses o he requremens for he M. S. and Ph. D. degrees. course normally consss of 30 lecures.) for our qualfyng examnaon, ogeher wh an ndcaon of (A one-quarer 3-un n he wendx are gven syllab whch ncludes hree papers: ( > numercal analyss and compuaonal mahemacs; 2) compuer and programmng sysems; (3) advanced nonnumerc applcaons, arfcal nellgence, and he mahemacal heory of compuaon. Experence has already augh-us ha many of our graduae sudens are no neresed n all hree of he syllabus subjecs above. We frs saw he need for hs flexbly n sudens who were srongly neresed n numercal analyss, bu who lacked he nclnaon o learn eher he subjecs of our examnaon (3) or he exensve real and complex analyss requred for a Ph. D. n mahemacs. As a resul, we now perm he subsuon of equvalen work from anoher deparmen for eher examnaon () or (3)* cenral o our subjec as o reman compulsory. We regard examnaon (2) as so We have found ha several of our sudens mos neresed n numercal analyss are happy o wre examnaons () and (2), and also one of he qualfyng examnaons for he mahemacs Ph. D. (real analyss, complex analyss, algebra, or appl.ed analyss). Cn he oher hand, some sudens mos neresed n ncnnumerc compuaon are happy o wre examnaons (2) and (3), and also ake an examnaon n logc or perhaps psychology. We expec oher subsuons o be proposed laer. Snce compuer scence s young and n a formave sae, and snce our examnaons cover such a broad sweep, descrbed above s a wse one. we feel ha he flexbly Our man servce courses are dreced o sudens who have already had calculus. Our one-quarer nroducon o compung (course 36) ranks as one of he mos popular elecve courses a Sanford. We have wo quarers of nroducory numercal analyss (courses 37, 38) pre- 2

14 4- c a-.! supposng course 36, lnear algebra, and ordnary dfferenal equaons. We have a specal form of course 36 (courses 5, 6) dreced o younger engneerng undergraduaes. We have nsued one course (26) for general sudens, presupposng only hgh-school mahemacs and dreced o sudens of humanes and he socal scences. Praccally all our courses nvolve subsanal amouns of compuer use by he sudens as ndvduals. They are effecvely laboraory courses. As me goes on, we ancpae he creaon of more secons of course 36, dreced o majors n specal areas and presupposng dfferen backgrounds and neress. Several oher deparmens a Sanford each compung n one form or anoher. Mos of hese are applcaons courses presupposng our course 36. Our graduae offerngs nclude a wo-quarer sequence on programmng sysems; a one-quarer course on he logcal srucure of compuers; a hree-quarer sequence on numercal analyss; a wo-quarer sequence on elemenary arfcal nellgence; a hree-quarer sequence coverng ls-processng, logc of compung, and advanced arfcal nellgence; a specal numercal analyss course; a one-quarer course on conrol programmng; a programmng laboraory course; a one-quarer course nex sprng on mahemacal lnguscs; a one-quarer course on graphc daa processng; and some courses n mahemacal programmng. As we each compung o specalss of oher felds, s essenal ha her own faculy-be able-o follow up wh mporan applcaons. n he ranson perod, was desrable o each he faculy drecly. Earler n he decade he Compuaon Cener held hree specal one-week sessons, wo for engneerng faculy and one for bomedcal faculy. These courses ake very careful plannng, bu pay off very well n knowledge and good wll. The Sanford Compuaon Cener s well organzed o receve large numbers of suden jobs, manly n Exended Algol for he Burroughs B5500. However, he oal cos for handlng suden jobs n compuer scence 3

15 ; c l. courses has now reached $84,000 per year, specal fundng for hs work. and s essenal o receve The Compuer Scence Deparmen s no responsble for he Compuaon Cener's servce work, bu does provde leadershp for sysem selecon and organzaon. However, he Compuer Scence Deparmen wll self soon have some large compuer sysems acqured n connecon wh research conracs. 6. The research program of Sanford's deparmen. A unversy deparmen has he wn roles of educaon and research. Though hs repor has concenraed on educaon, should lke o ' summarze he research areas ha we happen o be acve n. course, s, of no concdence ha hese nclude he hree areas of our qualfyng examnaon lsed above. We also have compeence n heorem provng by compuer, mahemacal lnguscs, and compuer recognon and conrol of exernal evens. semnars gong on--n machne desgn, Durng sprng quarer 966 we have fve human values n a echnologcal socey, mahemacal heory of compuaon, programmng languages and sysems, and graphc daa processng. n oher quarers here have been semnars n such subjecs as numercal analyss, paern recognon, arfcal nellgence, me-sharng, ec. n The followng research projecs are or have recenly been acve he deparmen: Numercal analyss: algorhms for compuaonal problems of lnear algebra, wh error bounds; solvng lnear paral dfferenal equaons by dfference mehods, and by expansons n parcular soluons; algorhms; Compuer conrol: conrol of expermens; solvng nonlnear sysems; lbrares of sudyng eraon funcons. auomaon of daa reducon from expermens; porable compung. Auomaon: conrol of large lnear acceleraor; on-lne Can a general-purpose dgal compuer (PDP 6) use a TV ube mage npu o conrol he acon of a mechancal hand o carry ou useful work? Tme-sharng: How can one bes desgn a me-sharng sysem based - 4

16 on cahode-ray-ube dsplays nsead of ypewrers? Arfcal nellgence: speech recognon, pcure recognon; classfcaon of organc molecules; smulaon of human learnng. Programmng languages: represenaon of he semancs of a programmng language; desgn of approprae successors o AGO 60; nvenon of approprae languages for persons desgnng algorhms n a conversaonal mode a a console; languages for complers of compuers. Hardware sysems: Compuaonallnguscs : ransformaonal grammars; grammars. Theorem provng: modular arhmec. desgn of operang sysems; compuer procedures for manpulang he parsng problem for ransformaonal proof procedures and decson procedures n he frs order predcae calculus and her mplemenaon on compuers. Psychary: smulaon of psycharc reamen of menally dsurbed, wh paen a a eleype console ypng naural language. 70 Mscellaneous remarks. would be desrable o have crera of Sanford's progress owards our goals n compuer scence educaon. So far we are oo much nvolved n geng organzed, recrung, eachng, and so on, o have done much evaluaon. We do know ha Sanford sudens apprecae our program very much. Courses 5, 26, and 36 have a campus-wde repuaon for beng me-consumng, because akes begnners many hours o hnk ou algorhms, and ge hem correcly keypunched and run. Neverheless, he enrollmens are very hgh. Wh boh formal and nformal programmng courses, we esmae ha we reach abou 200 persons a year. f hese people average bu wo years a Sanford, hen abou 2400 persons know compung n an acve way. and eachng saff, Wh some 0,000 sudens and 000 faculy ha means ha over 20 per cen of he Sanford academc famly are well acquaned wh compung. n he wner quarer of 966, approxmaely 400 sudens n 66 courses used he Compuaon Cener o solve homework problems. We herefore feel ha compung s esablshed a Sanford, and 5

17 J(, fl a ;; s me o urn our aenon owards rasng he qualy of our work. For example, we need no only o each sudens o program--we need o each hem o program well. We mus gve many more of he scence and engneerng sudens who use he compuer an nroducon o good algorhms and a fear of bad algorhms. More mporan, we need o brng he advanages of symbol manpulaon o our sudens. Even for scence, s probable ha he ably of a compuer o auomae algebrac manpulaon wll n he end be more mporan han he ably o auomae arhmec compuaon. For hsorcal reasons and because of he lack of easly used ls-processng languages, he ' emphass ll now has been manly on arhmec compuaon alone. We have wondered abou he place of numercal analyss n a unversy wh a deparmen of mahemacs and anoher n compuer scence. Apparenly here wll be wo knds of numercal analyss Ph. D. degrees. One wll be a mahemacs degree, followng he regular requred mahemacs courses, wh some elecve courses n compuer scence and a hess n numercal analyss dreced by some one n he compuer scence faculy. Ths would be approprae, for example, for a suden whose hess developed asympoc error bounds for fne dfference mehods for solvng paral dfferenal equaons. There mgh or mgh no be expermenal compuaons. The oher wll be a compuer scence degree, wh a number of exra mahemacs courses and a hess n numercal analyssc Such a hess mgh emphasze he algorhmc aspecs of ru-mercal analyss, and would ceranly nvclve expermenal compuaons on a dgal ccmpuer. mgn, for example, explore he knds of languages apprcprae o solvng dffcul mahemacal problems wh compuer sysems nvolvng nrcae man-machne neracons. (Cf. Culler and Fred [3].) 0r mgh nvolve creang algorhms whch are ruly complee and foolproof n regard o error bounds, over- and underflow problems, and so on. n shor, such a hess would face up o he real dffcules of usng lmed-precson arhmec o solve mahemacal pro?;lems. s ofen more dffcul o decde when an erave prozess should be ermnaed on a compuer han s o prove s convergence, and hese heses should help solve such problems. 6

18 References [l] ACM Currculum Commee on Compuer Scence, AN UNDER- GRADUATE PROGRAM N COMPUTER SCENCE--PREMNARY RECOMMENDATONS, Comma ACM8 (969, pp [2] Unversy of Chcago, GRADUATE PROGRAMS N THE DVSONS, c f f ANNOUNCEMENTS , pp , descrbng Commee on nformaon Scences. [3] G. J. Culler and B. D. Fred, THE TRW TWO-STATON, ON-NE SCENTFC COMPUTER: GENERA DESCRPTON, pp of Margo A. Sass and Wllam D. Wlknson (edors), COMPUTER AUGMENTATON OF HUMAN REASONNG, Sparan Books, [4] Ralph W. Gerard, COMPUTERS AND THE FUTURE OF EDUCATON, alk o Fall Jon Compuer Conference of Amercan Federaon of nformaon- Processng Socees, as Vegas, Nevada, 2 December 965. [5] Saul Gorn, THE COMPUTER AND NFORMATON SCENCES: A NEW BASC DSCPNE, SAM Revew 2 (963), pp \ 63. A. Zadeh, EECTRCA ENGNEERNG AT THE CROSS-ROADS, paper presened o he nsue for Elecrcal and Elecronc Engneerng, March 965, Proceedngs, pp r [7] Sanford Unversy, COURSES AND DEGREES , Sanford Unversy Bullen, May 966 (obanable from Regsrar, Sanford Unversy, Sanford, Calforna 94305). Compuer Scence Deparmen Sanford Unversy Sanford, Calforna WY 966 7

19 . STANFORD UNVERSTY COMPUTER SCENCE DEPARTMENT Revsed December ls', 965 c c- e _ :. Syllabus for Ph.D. Examnaon n Numercal Analyss and Compuaonal Mahemacs. A general famlary wh he followng compuer problems: solvng one or more lnear or nonlnear equaons; smple problems nvolvng ordnary or paral dfferenal equaons; approxmaon of daa by polynomals; approxmang negrals and dervaves of funcons by lnear formulas; locang maxma of funcons; compung egenvalues of marces, The subjecs and he supporng Mahemacs or Sascs should be known a a deph lke ha of courses 37 and 38 and he followng books: Hammng, NUMBERCA METHODS FOR SCENTSTS AND ENGNEERS; Henrc, EEMENTS OF NUMERCA ANAYSS; Ralson, A FRST COURSE N NUMERCA ANAYSS; Sefel, EEMENTS OF NUMERCA ANAYSS. For compuaonal mehods of lnear algebra, see Forsyhe, NOTES ON COMPUTATONA METHODS OF NEAR AWEBRA (doed noes for course 38, 965, on reserve n Compuer Scence brary), or Faddeev and Faddeeva, COMPUTATONA METHODS OF NEAR AGEBRA, For solvng parabolc and ellpc paral dfferenal equaons, see D, Young's Chap. of John Todd (edor), SURVEY OF NUMERCA ANAYSS, or "A survey of numercal mehods for parabolc dfferenalequaons", by Jm Douglas Jr,, n ADVANCES N COMPUTERS, vol. 2 (96). ' 2. A reasonable undersandng of he pragmacs of scenfc compuaon wh, auomac dgal compuers: he mporance of fully auomac procedures for frequenly used compuaons; pfalls n usng sandard algorhms of mahemacs on compuers wh (necessarly) lmed precson: wha consues a good and well documened algorhm, and where such algorhms can be found for varous problems; he dfferen ypes of errors n compuaon, and ways o esmae and (where possble) reduce he errors;

20 Page 2 Syllabus for Ph.D. Examnaon n Revsed Numercal Analyss and Compuaonal Mahemacs December 5, 965 he nfluence of he logcal desgn of compuer hardware and sofware on he desgn of algorhms, and he accuracy and cos of compuaon n me, sorage, and human effor A deeper knowledge of some seleced area of numercal analyss and supporng mahemacs, wh a deph lke ha of courses 237a, b. Examples: dscrezaon error and sably n solvng ordnary dfferenal equaons (Henrc, DSCRETE VARABE METHODS N ORDNARY DFFERENTA EQUATONS), round-off error (Wlknson, ROUNDNG ERRORS N AGEBRAC PROCESSES), soluon of paral dfferenal equaons (Varga, MATRX TERATVE ANAYSS, or Forsyhe-Wasow, FNTE-DFFERENCE METHODS FOR PARTA DFFERENTA EQUATONS), approxmaon (Davs, NTERPOATON AND APPROXMATON, or J. R. Rce, THE APPROXMATON OF FUNCTONS), compuaon mehods n lnear algebra (Wlknson, THE AGEBRAC EGENVAUE PROBEM), numercal negraon (Krylov, APPROXMATE CACUATON OF NTEGRAS); Mone Carlo mehods, (Hammersley and Handscomb, MONTE CARO METHODS); combnaoral compuaon problems (B,eckenbach, APPED COMBNATORA MATHEMATCS); soluon of equaons (Osrowsk, SOUTON OF EQUATONS AND SYSTEMS OF EQUATONS; Traub, TERATVE METHODS FOR THE SOUTON OF EQUATONS). 4. Famlary wh he prncpal reference books for mahemacal compuaon --bblographes, ables, collecons, formulas and algorhms, specalzed monographs, ec. c

21 f STANFORD UNVERSTY COMPUTER SCENCE DEPARTMENT f, March 30, 965 Syllabus for Ph.D. Examnaon n Arfcal nellgence Research, Non -numerc Applcaons, and Mahemacal Theory of Compuaon :.! f The followng s a ls of opcs wh whch he suden should be famlar:. s Processng, Symbol-manpulang languages for non-numerc applcaons.. Thorough famlary wh SP or some oher ls processng language..2 Some famlary wh he oher languages of hs ype; smlares, dfferences, and ssues n he consrucon of ls processng languages. NOTE: 2. Arfcal nellgence The languages under dscusson here are SP, PV, SP, COMT, SNOBO, plus ohers you may dscover n your readng. 2. Heursc Programmng heavy. emphass. Chess and Checker Playng Programs(varous; Samuel) SANT (Slagle) ogc Theors (NSS) Geomery Theors (Gelerner) Assembly ne Balancng (Ton& General Problem Solver (NSS) Geomerc Analoges (Evans) Graph somorphsm Fnder Fndng Group Transformaon (Amoreo Theorem,Provng a la J. A. Robnson, H. Wong, ec. (s any of hs, or s hs no, heursc programmng?) STUDENT (Bobrow) Advce Taker Conceps (McCarhy) Musc Composon (Hller and ssacson) MH- Hand (Erns)

22 2.2 Smulaon. of Humczn Cogcon General Mehodologcal Consderaons Regardng nformaon Processng Models n Psychology EPAM (Fegenbaum) Bnary Choce Hypohess Former (Feldman) Concep Formaon (Hun) nvesmen Decsons (Clarkson) Belef Srucures, Personaly, Neuroc Behavor (Abelson, oehln, Colby) 2.3 earnng n Problem Solvers 2.4 earnng n Random and Srucured Nes, and The General Sae of neural models. 2.5 Paern Recognon Theory and Applcaons 2.6 Oher Adapve Sysems 3. Oher Non-numerc Applcaons. 3. Queson-Answerng Programs (BASEBA, SR, Black s Program) 3.2 nformaon Rereval Research, more generally consrued... broad oulnes of he curren. sae of ar. 3.3 Auomac ndexng and Absracng 3.4 Machne Translaon.., broad oulnes of curren sae of ar. k 4. Mahemacal Theory of Compuaon. 4. Formalsms for Descrbng Compuable Funcons - Turng Machnes, Pos Canoncal Sysems, General Re ursve Funcons. 4.2 Unversaly and Undecdably 4.3 Funcons Compaable n Terms of Base Funcons 4 4 Formal Properes of Condonal Expressons - Proofs of Equvalence of Compuaons. 4.5 Recurson nducon 2

23 4.6 Spaces Represenable n Terms of Base Spaces 4.7 Absrac Synax - Condons for Correcness of Complers 5. Mahemacal ogc 5. Proposonal Calculus - Canoncal Forms Rules of nference, Decson Procedures. 5.2 Predcae Calculus - Axomazaon of Theores n Predcae Calculus; Axoms and Rules of nference, Models, Compleeness, Proof Procedures. 5.3 Se Theory - Zermelo-Frankel or Von Neuman Axoms. References For Secon see he PV Manual, he SP.5 Manual, he SP Manual (Comm. of ACM, Sep. 963)) COMT Manual, SNOBO arcle (JACM, n 964). Also, Bobrow s and Raphael s survey arcle (Comm. of ACM, n 964). For Secon 2. and 2.3 he prme reference s Compuers and Though. Ths book wll lead, you o he orgnal sources (e.g.) Slagle s SANT was orgnally a Ph. D. hess, as were many ohers), and also o many andvarous references as you read hrough he arcles and scan hrough he ndex o he Bblography. Mnsky s survey arcle s no o be mssed! The hos of Newell - Shaw - Smon papers, n RAND repors, n publshed leraure, n he lbrary, should be read. See Fegenbaum s shor survey arcle n he EEE nformaon Theory Transacons, plus oher revew arcles n hese Transacons. See he volumes Self -Organzng Sysems (960 and 962). Also, he numerous JCC Proceedngs and ACM Conference Proceedngs, Bobrow papers s Projec Mac TR-. Hller and saacson wroe a book, Expermenal Musc. For Secon 2.2 prme reference agan s Compuers and Though. See also Newell and Smon n he Handbook of Mahemacal Psychology, chaper on Compuers n Psychology. EPAM papers wll be pu n he lbrary. Hun has a book, Concep Formaon:.An nformaon Processng Problem. See also Tompkns and Messck, Compuer Smulaon of Personaly. 3

24 c f c E f ec For Secon 2.4 leraure abounds. Mnsky s * Sq& arcle s a good sar. For Secon 2.5, do. See, also, Sebesyen,Decson Makng Processes n Paern Recognon. ook a Selfrdge s Pandemonum and Uhr s work ( cf. Compuers and Though). For Secon purposely vague. For example, see Ashby, Desgn for A Bran(secoad edon); Auomaa Sudes (Shannon and McCarhy). For Secon 3. see Compuers and Though. Raphael s SR s Projec Mac TR-2. Bac&% repor s n Fran Thomson s offce. For Secons 3.2 and 3.3, scan recen ssues of he NSF publcaon Curren Research and Developmen n Scenfc Documenaon as a means of asceranng sae of ar and dvng no leraure. For Secon 3.4, do, perhaps, for hs. ook a survey arcle by Dck See of NSF n he magazne, Scence, someme n Sprng of 964. Use as sprngboard o leraure. See also, Bar-Hllel s famous arcle, hghly crcal of MT work (Advances n Compuers, Vol. ) On pages of Compuers and Though here s a ls of collecons and specal pkoceedngs and symposa ha are relavely dense n arcles wh whch you should be somewha famlar. Try o ge a look a as many as you can. Wh respec o Secons 4 and 5, he followng references are recommended: Davs - Compuably and Unsolvably Suppes - nroducon o Mahemacal ogc; Axomac Se Theory McCaahy - A Bass for a Mahemacal Theory of Compuaon n Compubrs and Formal Sysems - Towards a Mahemacal Scence of Compuaon, CP, A Formal Descrpon of a Subse of ACO, A Memo. - Problems n he Theory of Compuaon, CP 965, A Memo. 4

25 .... ( S!l!ANFORDUNVERSTY COMPUTER SCENCE DEPARTMENT March 0, 965 Syllabus for he Ph.D Examnaon n Compuer Sysems, Programmng Sysems and Programmng anguages The suden akng he examnaon should have a background n he followng areas:. Compuer Componens and Memores, s F. A general famlary wh he elemenary physcal properes of he followng devces whch make hem useful n dgal crcury: ubes, ranssors, dodes, unnel dodes, negraed crcus, cryorons, #n flms, and*magnec cores..2 An undersandng of he prncples of operaon of mechancally scanned memores (ape, drum, dsc, card) and elecrcally scanned memores (core planes). 2.- ogcal Desgn and he Srucure of Dgal Compuers 2. Some famlary wh Boolean Algebra and he synhess of Boolean Expressons (hs assumes some knowledge of elemenary mnmzaon procedures; Karnaugh or Vech dagrams). 2.2 A knowledge of he properes of elemenary sequenal crcus (flp flops, shf regsers and couners). 2.3 An undersandng of he common number sysems used n presen machnes (sgn magnude, l's complemen, 2's complemen and bnary coded decmal). The suden should have some apprecaon and famlary wh he fac ha many algorhms exs for performng arhmec n varous number sysems. 2., Compuer Organzaon An undersandng of he basc organzaonal feaures of a Van Neuman Sequenal Processor (he 7090 as an example) a Sack Machne (he B-5000 as an example) and an undersandng of how daa flows hrough a machne; and how -O can be organzed. 39 Programmng anguages 3. A horough famlary wh AUO: 60 and B55ob AGO. 3.2 A general famlary wh some oher programmng languages such as FORTRAN, ' SP, ec. and a leas one machne code. 3*3 A knowledge of some of he more useful feaures of verson's noaon.

26 * \ f E C 4. Programmng Sysems 4. A general famlary wh he prncples and organzaon of assemblers, nerpreers and complers and he knowledge of he problems conneced wh he mplemenaon of varous compuer languages, n parcular AGO (he mechansms for complng expressons, procedures ec., and he problems of sorage allocaon) An undersandng of he general prncples and asks of supervsory~ syuems s.and he problems nvolved wh me-sharng a compuer and wh parallel processng. 4.3 A horough famlary wh a leas 2 compuers, and a general famlary wh he capables and organzaon of a machne of he new generaon. 5. Phrase Srucure angusges A knowledge of producon grammars, he specfcaon of a programmw langugs by a synax (BNF) parsng of senences of phrase srucure hmguwes, and synax dreced complng. BEFERENCES A paral ls of useful references s ncluded below. Oher reference8 of a smlar,naure can be found n he lbrary. Componens, Memores, ogcal Desgn and Compuer Srucure Braun, Dgal Compuer Desgn Phser, ogcal Desgn of Dgal Compuers Buchholz, Plannng a Compuer Sysem edley, Dgal Compuer and Cdnrol Engneernq ' Beckman,.... "Developmen n he ogcal Organzaon of Compuer Arhmec and Conrol Uns", Proceedngs of,he ST& January 96, pp 53. Rajchman, Compuer Memores : A Survey of he Sae of he Ar, Proceedngs of he RE, January 96, pp 04. Mac Sorely, Hgh Speed Arhmec n Bkry Compuers, Prooaednge of he RE, January 96, pp 67. Burks, A.W., Goldsne, H.H., and von Neumann, J. Prellmnar~ Dscusson of he ogcal Desgn of an Elecronc Compung nsrumen, Colleced Works of Von Neuman. 2

27 (R e f erences, con'd) Crchlow, A.J., "Generalzed Mulprocessng and Mulprogrammng Sysems", AFPS Conference Proceedngs (FJCC - 963), pp Amdahl,... "Archecure of he BM Sysem 360", BM Journal of Research and Developmen, Vol. 8, No. 2, Aprl 964, pp "The Srucure of Sysem 360", BM Sysems Journal, Vol. 3, Ncls 2,3, 964. Baron, "A Nev Approach o he Funconal Desgn of a Dgal Compuer", Proc. WJCC 9, (96) pp Programmng anguages and Sysems - Baron, R.S., "A Crcal Revew of he Sae of he Programmrg Ar", AFPg, Conference Proceedngs (SJCC - 963) pp Bobrow,,Danel and Raphael, Berram. A Comparson of s Process'ng Compuer anguages", Vol 7, No, 4, Aprl,-964, Comm ACM pp Floyd, 'R.W., "The Synax of Programmng anguages - A,Survey" EEE knsaclons on Elecronc Compuers, Vol, EC-&no. 4, Augus 964. verson, A Programmng anguage, Wley, 962 f, Rosen, Saul, "Programmng Sysems and anguages, A Hsorcal Survey", AFPS Conference Proceedngs (SJCC - lg&), pp l-5. Survey of Programmng anguages and Processors", Comm ACM 6,3 (March 963), PP Survey ssue on Programmng anguages: EEE Transacons on Elecroncs Compuers, Vol, EC+, No. 4, Augus 964. B. Randell and B. Russell; "AGO 60 mplemenaon; AP 964 3