0?J European Mathematical Society
NEWSLETTER No. 26
December 1997
Interview with Sir Ron Dearing 3
Meeting of the EMS Executive Committee, October 1997 4
EMS Agenda 7
Diderot Mathematical Forum 8
European Consortium for Mathematics in Industry 9
Meeting of the Council, August 1998 ...... 11
EULER - European Libraries and Electronic Resources ...... 14
Euro11ews ...... 16
Problem Corner ...... 22
Book Reviews ...... 28
Produced at the Department of Mathematics, Glasgow Caledonian University
Printed by Armstrong Press, Southampton, UK
/ .ISS:'\ iiJn 4..:..:x Secretary Peter W. Michor EDITORS lnsti1ut for '.\latl1e1n,,:.ik. l'ni1·er�iti;1 \\'icn. Strwllbof- Prof Roy Bradley 1;,1.�se -i. A-1090 \Vien. A0.1,;tria. Departrncn: of !\fath1'matirs e-n1a)l: rriicltor((1csi.hc.at Glasgo,v Calexloniall 1 :mn,rsity CLASCOW G4 OBA. SCOTLA:,m Treasurer A. Lahtinen Editorial Team. Glasgow: Departmertl of Mathematics, P.O.Box 4 H.. Bradley. I. Clark, J. Gonrntam, V . .Jha FfJ\.-00014 t'r,in·rsity of Helsinki G. Kennedy. :\L A. Spelkr. J. \Vilson Finland e-mail: lahtineu NOTICE FOR MATHEMATICAL SOCIETIES Please note labels are prepared during the second half of the month before the next issue. Would you please send your updated lists before this time. Many thanks. Ms T Miikelainen 2 J N 1•• H!dtT �:.l infltHJiCt:1:1 the deH lir;1 al.in11:--; t,f tJu,. Ftr,bbi1is fit llo·!l vvas sPt UJ>, in the Cnmn1ittcr'? elf,ctimi b11! \\ith : he agn:eu1.1"nt of ! he Al mr,mlwir of the Cmitmitt,,c had a copy to n'View •1ducaiioa in of the Robbin" 'flw CmrnniUt;t', paid the l!nit,,1.! Kingdom (UK). Its remit include..:! the pari,icula.r fl.ttent1on io the Hohbin.-. Comniit,.ee's making of n,tomimmdations into all a:c;pects of definition of the purposes of higher edueation. The higher f:ducation hidudiHg f.;npport for 1:,tudents. Committee folt 1 hat those purposes still ha.d much lt was obliged to take account of t:he incrnasing validity a.Jthough we reformulated them to mateh participation in higher education by young and the conditions of the modern world. mature students, of the standards to be maintained, of the need to maiutaiu international standards in Q2 1\fod1 of the increased demand for higher degrees and in research aud in the cost- effectivenf'...ss education is expected to be at the sub-degree level. of the proposals, bearing in mind the distinctive Is there any estimate of the expected percentage of features of higher education in different parts of the the relevant age-group in higher education? \Vithin UK: its report was scheduled for Summer 1997. To five years, how many stud(mts (full-time or part this end, its first que,,5tion in a written consultation time) do you envisage there will be in l!K higher exercise WEIS "\Vhat should be the aims and pnrpoSPB education? of higher education over the next twenty years?" A2 The Committee was clear that it did not want to set a specific target for participation in higher The last major review of UK higher education was by the Robbins Conunittee iu 1963. (It education. ]t noted, however, that participation rates of around 45% have alre..ady been achieved should here be remarked that committe<"S of inquiry in the UK are given formal titles but, by in Scotland and Northern Ireland and thought it custom, they arc referred to by the name of their reasonable to assume that a similar participation distinguished chairman - or chair as the case may rate might be achieved across the UK as a whole over the long-term. be). Arising out of the recommendations of the In Scotland, moi;i. of the Robbins Committee, many new l1niversities were participation in excessof levels in England is in sub created. In the case of the Dearing Committee, degree higher education. many institutions had suddenly been designated as Q3 The Committee is obviously concerned about universities; the Dearing Cornmitte,--e has had to potential students who are disadvantaged in some anticipate the subsequent future of theA'le and other parti<..11lar way and who, accordingly. need some longer established institutions. The final report special assistance. If it is believed that the pre.sent of the Comrnitte<, runs to some 467 A4-size page�5 system is failing such people, what active steps togcihff with weighty appendices. should be taken to help them? Sir Ron Dearing, a,.c, Chairman, was asked a number A:3 The Committee realised that many of the of quf'.Btions to which he freely gave answer;;. The disparities in participation in higher education questions and answers are reproduced verbatim among different group,,, in society are the result of below. The ntmost gratitude can only be t,xpressed factors beyond the influence of higher education. to Sir Ron Dearing for the promptness and fullnes:,; Nom,thdt'Ss, W(' fojj that higher edncation had n of the answers. responsibility to take what steps it could t.o ensure <->quity of access. The rnport r('(..:ommem!s u whoh· The questioning wit.bin ihc UK univer:-.ity scene range of measurf'.S to improve access. including: rnay be pa.rallded in similar <:rnrnidnat.ioHii in other countries. T'he d,�baf,e on higher educaiion and its - nx1niring all higher education instil utions to have costs i;; not lik;•]:,• to aud end in the [iK. part.icipa.tion policies "-hid1 ar<' regularly n·vi<·w,xl tlw f (! 1 J hi.' la.st r<·:vit,:�v <.1..f l.J�i)ttx1 edu1:J.i,if,u y:ra':,: h\,, d1t' Ilol)b}n:•3 (;(nnzpiil.t�t: n1 tn rhv:-:;e ;n:::titntirn1;-,; \:ii1h.it''h ;-sho,v,: �·, {\Hnn-.1ihnt;nt to. tltf' i9no.�·,, 0 \',1·hnt ('Ktf':JH \VtU:i 't'OJ;,f f \-),fJtlnlitt�:-;·i-:, Lion, �) to thr? fhr.an.c:inl for (lis.a,biefl I\. 7 I''.hr- (�\nr.un.i tt,.:;r· (lid IJf)t ::,,,f_,t otit to :·,t m.lc·i its; .in detail lH)tv thr� .Institute, sht?t1h:t ('·a:rr;;r ti.:.fUl. its a-.tt!± ta..�ks. 1"1.tis '�V(>u1d -re<�uirf.. (;.fHtsultotion \>'dU,in 1he beet-or nnd of stude11ts a better !J.alance bd,,\'f'('.!J in11n:E!diute breadth and prograrm.nes shi,ukl be achie1'1'd than Jn what wnys would you like to see tiw of this on A8 The ha.lance bet.',w,en breadth am! 4 f' re:ie,-1reii. -�:�p<.,,t1St)rs. (}ii' Thf' ConincitH'.f' is s a �hnlt-sd r:n.un.b·er uf �lt, pt:·t c.e.n1- of t.he· i�t\·-r�rti.J:'l"' cot J:s thi:s intenc(r:d. haition 1:;,houit:l bt::-. n1t._ft 4-'i',.'..l!Tet� sc.he;ne. · f'his Ctppr�DJ'fJ to rnen.n. tha,t 1� tuition fc·t: AI:J Those of some 1.000 per ammm v./ould hav,, to he n1et loan hJnd \}V()ukd IH?{:�d to a .student ov.f'r fl I.):f�riod irn:�pef:tive of thf\ t.be'i.:r df·<·-h,io.n.s. ;'fbe (>nTHT:t.i1.t-<�':- -'6 vif'\\'' actuo.l r·onn,:;(': or (ha.1: the fnnrls shotJd L•e tLSe(_; to snp}>ort a. Hn-1H,e(J Uow· does the ('ommiUee reconcile thi!i rf,.-:.rn,i.nwn rn. rnrlH!:r of W(li1ld t.1,lt!1(tSt dat:iori \viff� ll rue·an that. funth� ·vvr:�re fr)cUsf�d on "\�.f}.nt.rr,:s \\ ho arr� of ,.,:,.cdlencfr, thrit ::,ti 1d.e.nt�: 1 nay be in d. .:?l:i;f? Huw will tuition cost,.; in Ute UJ:i. cornparc •.vitb 'fhe ( ()Hnnit.t.t�e set-:n1s to l)f.� ver:f· ('o.nc·erru�d Lultioa cost.s in ,(Jt11er count-d.c�? l:?,htHJt a.,,11d h()\V Use:\-' arc A:l7 rl'he (''.o:nnnittet:·t� ititenrion iN8)-i 1 Lta.t t3tudents of an institmion. shonld n,eet around nf thc average cost of Is Lh i:< one· or l \:Vet ·instances <·ducation tnii ion each year This would of improper or l1ehtt\'·iour OH tbf� part of mean, in gew'ral, that total cont.ributions would sonw governrng bodit's? be proportional to the length of the prognun1ne :\ l 4 The Cornmittee was aware of certain specific studied. The CornmiUee's recommendation would iHstances of failings on the part of governing have increased the potential debt burden at bodies but also knew that others, for example the graduation of all stmlents regardless of background Nolan Committee and the Connnittee of University by 1.'.1,000 per year of study but would have Chairmen, had issued guidance to address these retained the means-tested student. maintenance problems. T}w Committee's concern was that grant. for stude11t.s from poorer families to curtail gtwerning bodies and their institntions should be the debt burden they faced on graduation. The able to respond effectively in an increasingly fast Government has adopted a somewhat different changing and challenging environment for higher approach involving the introduction of tuition education. Structures which have worked well in the fees (albeit not for those from the least well pa.'lt may not continue to be adequate in the future. off home;;) and replacing maintenance grants by QI5 The Committee devotes a fair a1nount of loans, the effect of which is t.o provide a greater attention to the w,e of the term 'university' and to contribution to the cost of higher educat.io11 than the growth of degree level qualifications in further in the Conunittee's preferred option. The es.,;;ential point is, however, that it is not students who are education colleges. Is there a feeling that. some irn,titutions were unwisely or prematurely granted expected to contribute to tuition costs for graduates the title of 'university'? in work. The Committee strongly recommemkd Al5 The Committee was concerned not so much income contingent. payment arrangements so that with those institutions already legitimately granted no-one is askedto paymore than they can affordand the Government has accepted that argument. The the title of university but. with the impact of the criteria which have been set down for further contribution costs in the UK would be higher than in ma11y other European countries but much lower institutions to acquire that. title. The effect of than in the US, Japan and more widely in Asia. Jt is numerical criteria is to encourage institutions to focus on achieving a t.arget size. Such criteria do relevant also t.o look at support for students' living not enable those taking decisions to take account of costs which has traditionally been more generous in the UI, than in other count;ries elsewhere in Europe. any wider consideration:,, such as whether additional universitit,5 are needed in specific parts of the (� 18 vVhat implications, if any, are there for inter count.r.v. national, and particularly European, programmes of study and research'? Ql6 Is t.here not some inconsistency in recormnend A 18 T'lie Corrm1iUee's report fiays that the CK ing that funding for teaching should be normally should aim to be the worid leader in the practice within modest marg11is and also reeommendiug that, of learning and teaching in higher education. Hs in certain unspecified circumstances, exceptional recommendations are also designe 5 the co-nsider in iL,; ifoliherations" ad 0 l Al 9 rh, : ConrmiUr..:· W:V.'l Ve!)' conscious of the but "international dimension'" in a.11 of its ,<'ork h ah.;;., f,olution to thE ET.I is" looked at: the poslt,mn of Enropean C nim1 students if - the relationship between a UK higher education tuition contribution,,; were (they would qualifications frarnework and for on tfo, sank as l ;K studentB elsewhere in '"'''·�'"' would reduce the extent to which the GK concludes t.hat a framework the raxpayer subsidises students from other of VK awards in Et: coun the di fficn!lie;-; faced t: K higher fxlucation insti Profl":.'isor D A R \Valia.!·e ( ntions which win l l nion eontrncts which Ivlathematical EUROPEAN MATHEMATICAL SOCIETY Meeting of the Executive Committee Capri (Italy) October 10-11, 1997 Afoin topics of the agenda a.nd decisions Summer Schools A detailed report will appear in the l\farch Issue of In 1998, there will be two Summer Schools, one the Newsletter. in France (Wavelets and their Applications) and another in Romania (Singularities in Algebraic Geometry). SCIENTIFIC ACTIVITIES For inforrnation : G. Monegato Third European Congress of Mathematics (e-mail: [email protected]). (3ECM) Zentralblatt fiir Mathematics July 10-14, 2000, Barcelona (Spain) The President will sign a Memorandum of The Scientific Committee is as follows : V. Arnold Understanding between the EMS, Heidelberg (Russia), M.F. Atiyah, chair (UK), R. Azencott Academy of Science, FIZ Karlsruhe and Springer (France), F. Catanese (Italy), J.I. Diaz (Italy), Verlag. A. Kupianen (Finland), C. Moeglin (France), J. Sjoestrand {France, Sweden), A. Smith (UK), S. INFORMATION SERVICES Domokos (Hungary), S. Woronowicz, D. Zagier Server (EMIS) (Germany). At the moment there are 27 mirrors operating (one in Japan will be added soon) and there are 22 Diderot Mathematical Forum journals in ElibEMS. On December 19-20, 1997, the Forum on ""tvlathe mat ics and Environment" will be held in Amster The Newsletter dam. ivladrid and Venice. It ,\ill concentrate on The new cover will appear in the first issue in 1998. problems related to water. The cover will be in full colour and the paper quality improved. Nev.r columns will also be created. In preparation : "'iVIathernatics as a force of cultural evolution'' (June 1998) in Berlin and WMY 2000 Florence. ''l\1athematicsand Music" (Auturnn 1999) The EI'vlS member Societies will be asked for details i11 Lisbonne and Paris. of their plans for the Year 2000. For information : Mireille Chaleyat,.fv1aurel (e-mail: For information: Mireille Cha1eyat-!Vlamel (e-1nail: mcm\&tccr,jussieu. fr). mcmtkcr.jussieu. fr). (, E�IS AGENDA 1997 EMS Summer School in OHSAY (France) "H1avdets aud j : A. Cohen (l Second Diderot 1\1athernatkal Forum (DI\IIF) Ol! iVfathemat.ics and EnvHon1nen1 ·A EMS Summer n w:in((�1n:r .1 u.-.,:,mu Pure ;\fat.hernatics . 20th try". Organiser: N.Te!enmn ( of the D!vIF Committee in Venice (Italy) A1J.ga;:;t,. 1 Sth Deadlirw for submission of iuforrnation or papers for 1998 the Sept ember issue of the E:VIS Newsletter ( Ccml.ad,: Martin Speller, [email protected]) Jannar:IJ. 1st A-ugw;f 18-27th Deadline forbi&, for EMS Lectures 1999 ( Contact.: Tuulikki Miikelainen, EMS booth at the International Congress (JCM98) [email protected]) in Berlin (Germany) Launching of JEMS (the Journal of EMS) at ICM98 Febmar:IJ, 15th August 28-2.9th Deadline forsubmission of information or papers for EMS Council in Berlin (Germany) hosted by the the March issue of the EMS Newslet.ter DMV ( Martin Speller, mspCQlgcal.ac.uk) Contact: Election of the President, a Vice-President, the Afarch. 21st-22nd Treasurer, the Secretary, EC members. Executive Committee Meeting in Helsinki (Finland) November, 15th May, 15th Deadline forsubmission of informationor papers for the December issue of the EMS Newsletter Deadline for sul:m1i88ion of infonnationor papers for ( Cont:act: Martin Speller, [email protected]. uk) the .Jmie issue of the EMS Newsletter ( Contact: �fartin Speller, n1.-;p(Q!geal.ac.uk) Atay. 31st 1999 Deadline for submission of proposals for the 1999 Autwnn EMS Summer Schools DMF "Mathematics and Music" in Lisbon ( Contact.: Giovanni .Mo11egato. mouegatol :20th - J11.!y. Oth1 I ECI\113 in Barcelona (Spain) 7 1 1 ca1ft-':(J the �l)irtir.:r�)t .\ta1'.11.ettrfr1.t:;c.aJ r··or1D�f�,, fcat1_iX'�',1t:: t,\.'1) {�t)r;Jel'f:. ,ncet� r,:·;J},t:\S, infr.. rr r:nat l�->�1. Lfr,f:<.:01.Tt�n1jnk,:. atio-ti f;,.nd �·,.,··tch·.:.·,;,;:·�-:. in thf:ir pro;?;ra.nu�rc,s � h:-r�f; diff�:rf>ut &spei:-.:t,ts:. t.Ldr reiation Lo December 1997 The second Diderot .\fathcmalical Forum will be '· 1vfathematica1 modelling and optimal contml rnethod8 in hdd in Arnsterdam, Madrid an � The European Consortium for 1\t!athernatics in Industry and The ECl\tll 98Conference ECf..f! its COiv1ET1', ERAS;'\1USand HC'.;V[ of EC :\H hrwt· n,'1i',ds t echuology aud the needfor mathematical in both H'.:-K·,u·ch and can A TO PHO\lOTE THE USE OF MA'fHE.\fA1T Too fow people rec{Jgnize that the high CAL ,\lODELS JN INDt'STHY so celebrated today is a mathematical technology. " Engineers, applied scientists and mathematicians working in industry ean greatly benefit from close 1'1iis staternent by Edward E. David, recent collaboration with university applied mathemati President of Exxoll R & D, is more true now cian:,; with relevant skills and knowledge. This than ever before; and more and more companies collaboration may also be extended t,o developing recognise that mathematical/computer simulations mathematical models forthe environment, earth sci may replace experiments in their product design ences, biology and finance. to give both reduced costs and flexibility. These simulations leading to the optimisation of the B. TO EDUCATE INDUSTRIAL MATHEMATI rna1mfacturing proc.ess itself, including possible CIANS TO MEET THE GROWING DEMAND safety and environmental constraints, require FOR SUCH EXPERTS mathematical skills if they are to be used effectively. They involve problem identification, a mathematical There is a shortage of industrial mathematicians formulation, and mathematical/numerical analysis within European industry and they net' 9 on ! Tdecon,:,rn.mic1,t1ous f'l::-i.r�11:ac-E�'tt U.ca.1s Scit�nt ifk q,,•r The confs,rence will t.ak,,, June 22 .,:,,.; 1 !998 at the Scliocil of T\'Ia.thernat.ic;al and one inv i trxl lr·ct.1.1n::, ScicnucB al Clrn.hncrn of as "'·"ell a.s ir1ird- dw of G sitnc.1tetl a.,t tl":a.· beriutifui S\ve�Jh;h 'Nf·�st t:o;;:i�t.. �r11e the session. I'here will ,iiso be a numb1;;r couferem:e ,\'i.11 cncon,pas.·, a 1n.m1ber of of irr,·iteil :1:·:pccu., of iml.1.rntrial m1:d.herm,tics. \'l'c trorn·' tfie ' r(''\e, ." .:.i'.u. H th(.l.: ,viU besides tb,· int,;i·e,,;ts Sorne of! he invHed or,;: E:CM!.-nien.d:;fl'S at soinc of the of the local. i.rnlustrml relations with ECMl 'f:raub 1..md indust.riul m1:1..thernatlcs. The purp0:,;e of t.he 1 M1..tzuHo ( conforenceis to a forum for the oresi,·nta1.w1 Langer of mathematics to Leest; ( industrial problems.. Such work is carried out by Hougaard (C.:openlrngen) academics working on industry-relat,xl problerns, Fasano (Firenr,e) by those based in industry who use mathematics Engqvist (Stockholm) to solve probk!ns or in a collaboration between Laporte (Montreal) universities and industry. The conference will Widman ·(Djurshoim) provide a fornrn for academics and industrialists to rneei.: and discus current problems of nmtual Invited mini-symposia topics include: Combustion interest.. It. should also serve to give advanced engines Airline scheduling Smart materials \Vood, students a first-hand impression of the challenges pulp and paper Molecular dynamics Molecular and opportunities for mathcmaticiaus in European modelling Elastic liquids Finance Cryptography industry. Industrialists can meet talented students Reservoir simulation educated in practial applications of mathematics Special student sessions will be arranged, as well as aud in a European spirit. the contributed mini-symposia. The scientific programme focuses on seven main Acknowledgements: The text forthis fileis partially topics: taken from from the ECMI brochure, which was Vehicles edited by Prof. V. Capasso (University of Milan) Vehicles - Logistics and Dr. A. Tayler (University of Oxford) in Materials collaboration with various members of the ECMI Finance Board and the ECMI Educational Committee. 10 ]''he ('.\r:H1.nci1 1Iie no laJer thn.n 27th 1 HH8 to the Secreta:dat. of _ 28 El\lS in I-ldslaki. after the fotematirnmi in the tSenH.tssaa1 dt::�r 6, D- 1nen1bers of the l<.:xecut.ive W099 Berlin. of the Executive Delega.t.Ps to the Council will be elecied by the with t.erms of office, is as follows. followingcategorie.s of rnembers. President 1995--1998 Prof. J.-P. Bourguignon (a) Full Members Vice-Presidents 19951998 Prof. D. Wallace 1997 2000 Prof. A. Pelczar Full Members are national mathematical societies Secretary 1995--1998 Prof. P. Michor which elect l, 2 or 3 delegates according to size and Treasurer 1991-1998 Prof. A. Lahtinen resources. A society is responsible for the elections Other members 1997 2000 Prof. B. Branner of its deregates. Each society should noti(y the 199.5--1998 Prof. A. Conte Secretariat of the EMS in Helsinki of the names and 1997-2000 Prof. R. Jeltsch addresses of its delegate(s) no later than 20th March 1997-2000 Prof. M. Sanz Sole 1998. As of lst July 97 there were 44 societies which 1997-2000 Prof. A. Vershik could designate a maximum of 66 delegates. (h) Associate Members Under Article 7 of the Statutes, members of the Executive Committee shall be elected for a period There are two associate members, namely the of 4 years. Committee members may be re-elected Cesellschaft fi.ir Mathernatische Forschung and the provided that consecutive service shall not exceed European Mathematical Trust. Their delegate is 8 years. The President may not serve as President elected till 1999. for more than one period, acc.ordingly Professor .J. (c) Institutional �lembers P. Bourguignon will demit office in December 1998. There are two institutional members, Institut By Rule 16 of the By-Laws, the incoming President Non Lincare de Nice and Moldovian Academy of must be elected from among the members of the Sciences. Their delegate is elected till 1999. Council. No such stipulations apply to the other members of the Executive Committee. Profossor A. (d) Individual Members Lahtinen is not eligible for another period. A person becomes an individual member either It would be convenient if potential nominations t.hrough a corporate member, by paying an extra for office in the Executive Committee, duly signed foe, or by direct membership. On November 1, 1997 and seconded, could reach the Secretariat by 27th there were 1745 individual rnembers and, according April 1998. It is strongly recommended that a to our statutes, these mernbers will be represented statement of intention or policy is enclosed with by 18 delegates. The mandates of 6 of the present 17 each nomination. If the nomination comes from the delegat.esend on December al, 1997, and soelections floor during the council meeting there must be a 1nust be held for their positions. Nomination written declaration of the willingness of the person papers for these elections appear in this issue of the to serve or his/her oral statement. must be secured Newsletter. 11 delegates WE're eiected for the term by the chair of the Nominating Cmnmittec if there 199fl 1999, so trwv will contimw unle.58 they inform is such or by the President. It is recornmended that t.h,· Seer!'taria1 t<; the contrary by :Jlst r>ecemher staternellt.s of policy of the candidates nominated 1997. from the floor should be a.vailable. The Executiw• Committee is responsible for The Couudl may, at it.s meeting, add to the preparing the matters to be discussed at Cmmcil nominations received and set up a Nominations meetings. Items for the agendn of this meeting of Conuuit.t.ee, disjoint from the Executive Committee, lhe Council should be sent. as soon as possible and to consider all canditlates. After hearing the report 11 ...... --·- - -·------·----=------�-----�- """''--""'"W ___ C.,, __ ,,., .... ,,,_,.,._#_0..,.<'N._,-,.,..,.,.,...... _,,._,...... ,._, , ...... __ ___• -··- rhc dm1n11.1n of the Nrnnim.ttion1'> CmmniUee .P .. S. 'I1in1r�1.,nb1e. for the (?(1rG1cU on·e hi11s bet'·:n sc�t the Coundl tA} f;le·ction.f. tc, tbc .E:xxx:TJfi'ivt� (\.1.:rnrrtit.tef; ;·\J 1998: 1)e2.;;Jb)1f.'· fr.)J norn.iniJ/,tor1"4 t'.nr flf tnd'ivid.:· .ia"l UH�1r1.her3� to the ('mmdi who an' to attend l99S: r.r!1e b·ailots for ..:ie!eg:}.tes of b:�t-.li,ticluei the JC�,,i, a.re advised t.hcr! their acconirnodatiun r:nt:rnbers :!:ffC sent Lo in!livi.du.a1 rra1::111L1en;, can he mad<-, the l():1vl. J'v!"an·:h (.\.ntdida.t'::>::f for to che C'.ounciL 1,1,ho are not ,.,.,,,,,.,,"'' T�ewsiet.t-cr; of iri.divid.ua.1 rnr·rn.l.-:-cr8 ar:r�, :t-Hlt,<)ur:cc Peter \·hdior A. ]fi;i-.te1 l;:1 3t�nt L Election of Council Delegates As announced in the previous issue of the Nominations are nowsought for7 delegates to serve Newsletter, nominations are required for Council for the years 1998-2001. Attached to this notice is delegates representing individual members of the a nomination form. Completed nomination forms Society. On 1 November 1997 there were must arrive at the Society's office in Helsinki by 31 174-5 individual members, and this means, by January 1998. If there are more nominations than the Statute.,s, that there should be 18 delegates the allowed number of delegates, a postal election representingthem. During the term ending with this will be held; members will receiveballot formsat the year the delegates representing individual members end of February 1998 and these must be returned by were: 10 April 1998. Nominated delegates must be individual members Term 1994-9'7: of the Society and they must be proposed and Castcllet, �fanuel Jaiani, George seconded by individual members. The Society will Kufner, Alois Langevin, Rerni pay sub8istencecosts forthem to attend the Council Michor, Peter \V. Sch·warz, Wolfgang meetings, if needed, but is not able to cover tr avd costsexcept perhaps in cases of particular hardskip. Term 1996-1999: Candidates for ek·'Ction are invited to submit with Anichini, Giuseppe Bolondi, Giorgio their nomination form a short biography (not. more Br armer. Bodi) Deshouillcrs, .Jean-Marc than 200 words) together ·with a. Statement. of not Habetha., Klaus I...:aroubi, Max more than 100 \Vordsin support of their c1u1didarure. h:unsalo, Ta.pani Lahtinen, Aatos These will he circulated to the members ·with i\larki, Liiszl6 Piccinini, Renzo the ballot forms. A copy of these can be sent Puppe, DieLer as a t<;xt. file by e-inail to the Secretariat to tuuhkki.rnakelainen<{}helsinki.fi. 'fhe tenn of the fin,, mentioned Ii delegates ends now. They are all eligible for re-f'led.ion. Peter l\lidmr, 12 ------·------· N orninatiou Form for Council Delegate NA�IE: TITLE: ADDRESS: PilOP()SEH.: ...... SECONDER: ...... · · · · · · · I certify that. I am an individual member of the EMS and that I am willing to stand forelection as a delegate of individual members to the Council. SIGNATURE OF CANDIDATE: ...... DATE: ...... Completed forms should be sent to: Ms T. Makeliiinen EMS Secretariat. Department of Mathematics P.O. Box 4 {Yliopistonkatu 5) FIN-00014 University of Helsinki Finland to arrive by January 31, 1998. A photocop,v of this form is acceptable. 13 E!JLER Lihrnri<:!8 and Electronic Rc- I'hcre are many diffkultiPi>in the Intenu•i,; sn;:rrl.·t:•,s 1n ��··i�.n-1.0,rn:: )_ is a, there an·' ;io aduuJ a.ud about br, r·o-fmided lJw ) sear.;j1 I,·lematic...; for L.ibn1xies .s;f: i,, to the dt··hvurk bnsed access to ma.thematical One of its usm will t.he Vi'chis very Uwre are uuwy he to improve t.lw Uh(\r interfoce of the of the services availabie iVlathematical Infornmt.iou Sr·rvice (EMIS). The - the different 1'I r will be used. Common resource descriptions of Main project partners are document-like objects will enable common access to heterogeneous re.sources. - FIZ Karlsruhe (Dept. Math. & Comput. Sci., Berlin) (Coordinator) EULER will develop the prototype of new electronic information services. Most relevant information of - The European Mathematical Society one subject area is integrated (one-stop-shopping). - Cellule de Coordination Documentaire EULER results will be portable to other subject Nationale pour Jes Mathimatiques domains. - NetLab, Lund University Library llsers will be enabled to make effective use of the - SUB Gvttingen mathematical library-related information resources offered through a single user interface. Time - Centrum voor Wiskunde en Informatica consuming tasks associated with the use of non - Universit' degli Studi di Firenze integrated services will be eliminated. The user will be enabled to search for and localise relevant The project is an initiative of the European documents. In many cases he/she will be able to Mathematical Society. The role of the EMS in the retrieve the full text electronically. project will be to representthe community of users interested in mathematics fromthe whole of Europe. Since EULER will combinedescriptions of resources The EMS will inaugurate its Electronic Library of (the bibliographical databases) with the full text of Mathematics, distributed through EMS's system of documents, free resourceswith commercial onesand Internet serve:-s, EMIS, http://www.emis.de/. This databases with very different structures, retrieval Electronic Library is today the most comprehensive systems and user interfaces, this integration must archive of freely available mathematical electronic be built upon common resource descriptions. This journals and conference proceedings. Some glue or intermediate level is accomplished by using improvements of this servicecan be expected during descriptions of all resources following the Dublin the project. Core (DC) metadata standard, recently developed and published as an Internet draft. Clo.seinteraction betweenthe informationspecialists and the mathematical community is very important. Technically, the integration of the differentresources Experiences in other projects - as for example the will be accomplished by producing DC metadata for all resources (by means of conversion, automatic project 'Specialised information' of the Deutsche generation or metadata creator software), and Mathematiker-Vereinigung - have clearly shown this need. This interaction has led to many collecting it into front-end databases for each individual EULER service. Retrieval and search improvements of special information systems; for example the database MATH. Accordingly, a broad software, the EULER Engine, will use these discussion with the mathematical community is rnetadata databases as sources for a distributed search service. The integration approach will be planned foreach phase of the project. The EULER serviceswill be installedat all participating libraries based on the Z39.50 standard or on HTML-form and at the central site of the EMIS system of the based data interchange. European Mathematical Society. At distributed servers, multilingual EULER service interfaces will be provided as entry points to the More, constantly updated, information about the EULER Engine, offering browsing, searching, some EULER project is available fromthe project's home document delivery and user support (help texts, page at http://www.emis.de/projects/EULER/. tutorial etc.). The interface will be based on common user friendly and widely used Web browsers (public domain or commercial). Michael Jost, November 1997 15 EVUONEl\tS EUROPEAN. NE\VS: Count.ry by Country BELGIUM K. Ckrnents, 08.02.98 22.02.98 { ;\fai.hanatical wum.<1,, An inkrnational confor,•nct, on Advaun'.d !vktz. 08.D2.t18 22.1)2.98 tional Met.hods in will be held in on 2nd - !Jth 19\l8. It will frxuson t.opics ive fiuiteekrnen! finik, differ· G. de l:'U)'2.ll8 ······ OLO:{ 98 enc,'.,.;, dornain arHl spei:- ical Education) tral methods and 1.heir applications in Solid Mechan R. Cantorn!, Colouia. del \'a1k, 15.02.98 01.mUJ8 ics. Heat and Mass Transfer, Einmonmental Engi (Matlwmatica! Education) rw,,ring and Fluid Dynarnics. F. Bosch en Duin, 15.02.98 15.0:HJ8 Tlw programme will include some seven invited lee (Mathematical Education) ! ures, mini-symposia on selected topics. contributed T. Dreyfus, Quebec, 17.02.98 27.02.98 (MaU1emat papers, a soft.ware exhibition and a poster session. ical Education) E. Si!v{'l'. Pittsburgh, 17 .02.98 -- H>.03.98 (Mathe Ghent is the historical and cultural capit.al of matical Education) Flanders and is only 55 kilornetres from Brussels which is well-served by airlirn� connections with P. Hilton, Binghamton, 08.03.98 22.03.98 Europe and the world. Accornmodation, with a wide (Mathemai.icalEducation) range of prices, will be available in nearby hotels and J. Pedersen, California, 08.03.98 - 22.03.98 possibly student residences also. (Mathemat.ical Education) B. Bolt, Exeter, 08.03.98 - 22.03.98 (Mathematical For more details contact !\,Is Martine BOTTE, Education) St·cretary ACOMEN 98, Department of Applied Mechanics, Faculty of Engi11t'eri11g, lJ niversity of K. Ruthven. Cambridge, 15.03.98 -- 29.03.98 Ghent, Sint-Pietersnieuwstraat 41, B-9000 Ghent., ( I\lalhematicalEducation) Bdgium. A. Adem, Madison, 09.04.98 - 15.08.98 (Algebraic Topology) .J.P. Greenlees, Sheffield, 14.04.98 - 04.05.98 ( Algebraic Topology) A. Viruel, Malaga, 14.04.98 - :H.07.98 (Algebraic CATALONIA Topology) W. Chacholski, Toront;o, 14.04.98 - 14.07.98 CENTER DE RECERCA MATEM (Algebra.ir Topology) ATICA J.A. Crespo, Barcelona, 14.04.98 17.07 .98 Li;,;t. of visitors from January till July 1998 (Algebraic Topology) J. Moller, Kobenhavn, 15.04.98 - 30.06.98 (Alge- E. Formanek, Pennsylvania, 01.01.98 - 31.01.98 braic Topology) ( Algdlra) D. Not.bohrn. Gottingen, 04.05.£18 - l(J.06.98 P. :Mattila, .Jyvasky!a, OLOU)S - :n.05.98 (Analysis) ( Algebraic Topology) A ..J. Bishop, Clayton, 04.0U.JS - OLOa.98 (Mathe .J. Berriek, Singapore, 07.05.98 ·- 03.07.98 (Algebraic matical Education) Topology) N. Balacheff. Grenoble. l LOU)8 - 01.02.98 D. Ravenel, Rochester, 10.05.H8 10.07.\)8 (!\iatlwrnat.icalEducation) (Algebraic Topology) N. Presnwg, Florida, 22.0U)8 - 07.02.98 (Mathe L. Schwartz, Paris, 10.05.98 Hl.06.98 (Algebrai{' matical Education) Topology) P. Nesher, .Jerusalem, 0 l.02.98 - l5.02.98 (Mathe F. Cohen. Rochester, 15.05.98 - 15.07.98 (Algebraic matical Education) Topology) V. Ka.novei, Bonn, 05.02.98 - 07.02.HS (Logic) Hi EURONEWS (�r;'.inada, 1:).Ctr).9K 1 f1.f)7 .0� ( (�oordinat«)ts: Prof _t\t:tn J. and Prof. �lirm ( ° Princeton, ! :d!5.H8 l :i.O(U)8 For furth1 r dd ai.\s. (·'·f!1ait:.. [email protected] or web W. Dwyer, Notn Dame. 26.0:).!)8 0:101.98 bHp://www .nrn.es (Algebraic 'Ihpology l "The 4!li Ban:eloua H. W. Henn, HeiddlH,rg. 27 iJ:'>Jl8 ;3()J)(U)8 ) Dat.es: [1, 6 and 7, 1998 s OU!1)98 · I3.07.H8 ( Plan:: ('entre de H.ecerca Bellal,errn 1 Scientilk and Organising Conunit1.1,, : ,Joan Bagaria II. Niiller, Cambridge, 01.0(U)8 :m OG.98 (Algebraic (Univt·rsit.al de Barcelona), Enrique Casanovas 'Iopology) (l_lniversitat. de Barcelona), Raimon Elgueta (Uni- versitat Poli!.iocnica de Catalunya), Friedrnau 0. Lillc, o:l.06.98 05 07.91j (Algebraic Topology) (Massachusetts Institute of Technology), Daniele Mu11dici (U11iversit.a di Milano), Bruno Poizat (Uni H Levi, Evanston, 04.06.98 2'.Ul1.fl8 (Algebraic versit6 Claude Bernard. Lyon I), Jordi Topology) Hebagliato ( U uiversitat de Barcelona). B. Oiiver, Paris, 28.0( U)8 20.07.!)8 ( Algebraic Invi1.ed prof,:,ssors: l\.Iatt.hias Baaz ('fodmische Topology) U niversitat \Vien), .Jose L. Balcazar ( V niversit.at. P.Kropholler, London, 01.07.98 :31.07.98 ( Algebra) Polit1"rnica de Catalunya), Andreas Baudisch (Hum boldt Uniwrsitiit, Berlin), Gregory Cherlin (Univer Activities organised by the ''C'.<·nt.re de Rccerca sity of Hut.gers), Viktor A. Gorbunov (lnst.itute of Matematica": l\fat.hematics, Novosibirsk), Alain Louveau (Univer· sitt; Pa1·is VI), Tomas R,:,cio (Universidad de San l) "Intensive winter term 011 mat.lwrnatical educa tander), A ntoni Torrt·ns (Universitat de Barcelona), tion (TIE Iv[ 98)' " Hugh Woodin (University of California at. Berkeley). Dates: .January 16 to March 30, 1!)98 For further details: e-mail: [email protected] or web Place: Centre de Recerca Maternatica, Bellaterra http://www.crm.es ( :oordinaton;: Prof. Alan .J. Bishop aud Prof. Nuria Gorgorio 4) "Topology Semester'' Invited professors: Guida d,• Abreu (Lutou DaU,s: April 14 to July 17, 1998 (i11iversity. UK), Nicolas Balachdf (Laborat.oire Leibniz IMAG, FR), Alan .J. Bishop (Monash Plac<': Cent.re de Reccrca Matematica, Bellaterra {iniversity, Ali), Brian Bolt (Fuiversity of Exel.er. Organis<'rs: Prof. .J. Aguadc, Prof C. Broto, l:f�). Ricardo Cant.oral (C>ntro de Invest,igacion y Prof. C. Casacubert.a ( lJniversitat Autonoma de de Estudios Avauzados del IPN, ME). Ken Clements Barcelona) (University of N oewcastle, AU), Tommy Dreyfus List of visitors: (( :enter for Technological Education, lL), Fred Goffree (Freudenthal Inst.itute, NL), Peter Hilton Alejandro Adem (University of.Wisconsin-Madison) (SUNY at Bingharnpt.on, USA), Pearla Neslwr (09.01,98 - 15.08.98) ( .vl inistry od Education and Culture, IL), Bernard .Jon Berrirk {National University of Singapore)(07.05.98 Parzysz (Universit<; de Metz, FR), .Jean Pedersen .. 0;1.07. 98) (Sant.a Clara University, USAJ Norma Presmeg ( Florida State Cniversity, USA), Kenneth Ruthven \Vojri,·ch ChadH)isky (The Fields Institute)( 14.04.98 (< :ambridge Ouiversity, UK). Ed Silver ( University - 14.07.1.18) of Pitt.sburg, USA). Frt�deric ('ohcn { l) nivcrsity of Ilochester)( l 5.0f1.98 - For furl hci· deiails: e-mail: crn,,(_1:crn1 or wd; 15.07 .98) linp://www.crrn.es Odavia11 Cornea ( Universit.e des Sciences et 'fodrnologics de LiHe)(O:Ul6.98 - Ofd)7.98) 2) ''\Vorkshop on current tre11ds iu research on Willian1 Dwyer (University of Notre Dame)(26.0!'U18 1nathcmar.ics 1,ducat ion·· - ();J.()7.D8) Dates: February 19, ::!O awl 21. 1998 ,John P. ( '. ( :reen lees { U oiversity of Sheffield)(14.04.!-)8 Place: (\;ntrc de I{eccrca Mat.emi1t.ira, Bdlatcrra .. 04.05.!i8) 17 f;Ull,ONEWS Han;.;-\'Vic·rner Henn ( ni;·erml,• l)at�::t.L ..l u.:ne 4 l (\ l 9fJ8 \Jnx·"·l'la.nl\. Jnstitut.f· in li{:inn.}{'27.0fi,98 Pb:tef. (::entrt, de Hecerc;i BeU:,ikrn, Prof. J. c 1 Prtrf. (� C\ts;�cubr::rta ( A.ut0JJ()rr�a dJ and \Vcsifidd A.I'\. Bousfiekl .t)f>.£1� F.H. Cohen ( Han Levi ( Nortinvt,s!.crn U {U 2�)J7 de Louvain), J P.Grernlee:" liayik-s Miller l .OG.!:18 · :HLOfi.98) ,I ..Lannes (Ecole Poly .frspn :r-.Ioller ( KobenIH.tVllS U rnversitet ){ 15 Jl4.H8 - kdrniquc, Paris), W. Lllck (Univ1:,rsidi.t .Munster), :l(U)6.98) R . .Mii gram ( Stanford Universi !y), G Misiin (ETH Ziiri1:h), D.Havenel (Universit.y of Rochester). DiNrich Notbohm (liniversitat Gottingen)(04.0:'i.98 - 10.06.98) For further details: e-1nail: [email protected] or web htt.p://www.rrrn.es Bob Oliver (Universitt• Paris Xlll)(28.06.98 - 20.07.98) Douglas Ravenel (University of Rochester)(10.05Jl8 - 10.07.\J8) Marta Santos (Universidad de Granada)(15.05.98 - CZECH REPUBLIC J::d)7.98) ,J1'.rome Scherer (Universite de Lausanne)(Ol.10.97 - SPRING SCHOOL ON :J0.09.98) FUNCTIONAL ANALYSIS Lionel Schwartz (Universit.e Paris XIII)( 10.05.98 - 10.06.98) First Announcement .Jdf Smith (Purdue University)(20.1 l.97 - 31.12.97) Antonio Viruel (Universidad dt• Malaga)(14.04.98 - 'What am I if I will not participate?' 31.07.98) Antoine de Saint-Exup'ery Stephen Wilson (The Johns Hopkins Univer sit.y )(Ol.06.98 - 15.07.98) Following a long-standing tradition, the Faculty of r For further details: e-ruail: crr!'Q>crm.es or web Mathematics and Physics of Charles University, is http://www.crm.es organising a Spring School on Functional Analysis. The School will be held at Paseky, in a chalet in the 5) ''Advanced Course on classifying spaces and Krkonose Mountains, from April 19 - 25, 1998. The rnhomology of groups'' progra.m1ne will consist of a series of lectures on Dates: May 27 till .June 2, 1998 Recent Trends in Banach Spaces Place: Centre de Recnca Matematirn, Bella.terra delivered by Speakers: William G. Dwyer { U niversit.y of Notre Darne, en Indianapolis). "'Finih' groups, homotopy .Jora1n Lindenstrauss rnlimit::;, and homology 18 EUHONEWS 'rhe {)i�fpnHt-' t)f this Arc(iil.\lfttHlat\i)1:, �"O!H�ist.::.: of P.)fJlTt•: for l'f..VO or v;h(,1 sl.iar1: B cxceUent fa.i..'iEtic:s ;.1.n:i cond�tun1�: !hid. f::w0 ,,port r01nnHtHitaJions aml s,11mn A hm, from students ;,nd leave Iii ,l jLllL Oil i\pn!, H)\tQ,. , ,U'f:r'rs are wiH arnvc in Prague on Aprii m. 'I h,· 1:ollfr:r<'nn· fr,,. tS (k,ilars. A 0 In nlli,' of iutf.'rest p!N1si, fill out th1. • cndrn,w,d lH.lWhl rak of rq.;istrntion fonn and rdurn it befnre lwfo1s• Jnuuary Hl9S. The rnmt fullfrr•'HCP fee iududei; all local cxpe1ises ( room A Hmd n1111mmccrncnt wit.h further detail,; will be a11d board) and transport.at.ion lwtween Prague and mailt>d i11 due tirrn.·. Due to the limited capacity Pa1wky. Ilie fr·1• is the same for a1.·c,,mp11uying of acromrnodation facilit.ies the organi,wrs may he {)l'l'SOJI&. fon·t'd io decline registration. We look forward to rneeting you in tlw Czech Th<' organisers may provide finaucial support to a Republi('. limited number of students. Applications must be sent before January 15, 1998. Jaroslav Luki•s, Jiri Kottas Payment of fees should be made in cash at the Mailing address: registration desk in Paseky, or it may be remitted Katedra nmtematicke analyzy by a bank transfer to Matematicko-fyzikalnifakulta UK Komercnibanka, Praha 1, Vaclavske nam. 42 account No. 38330-021/0100, v.s. 810 Sokolovska 8;{. 186 75 Praha 8 ( a ropy of the transfer should be presented at the Cze('h Republic r1·gistration desk at Pa.;;;eky). U ufortunatdy,cheques Phoue/Fax: 420 - 2 - 2:32 3390 rn1111ot be used and will not lw arn•pl.t' **************************************************** Preliminary registration form Spring School on Functional Analysis, Paseky 1998 �ame: Address: E-mail: Fax: Pho1w: I plan on attending the Spring Sfhool: Yes No 19 EURONEWS POLAND *********•••*****************• I,ONl)ON rvlAIHEf,,'!ATl(:AL SOCJET)" FIFTH CONFERBNGf: ON PROB� London \i\lJ V ONL ABILITY Td: Ol 71 ,t:i7 5:3'77; Fax: 0171 4:39 M,29 .E:..mail: hm;1i;ilms.oc.uk; VlVV\¥:http://wwwJms.ac.uk Czestochowa (Poraj) Poland, 18-22 May 1998 ****************************** Aim: the aim of thf' ('onforence is to report on and io discuss recent Location : Exeter is a city in South West England, about. 250 kilometres from London. UNITED KINGDOM Provisioual list of invited speakers : Among those HYPERBOLIC GEOMETRY who have already accepted invitations to speak are C. Huneke (Purdue), D. Katz (Kansas), D.Kirby First Announcement (Southampton), L. O'Carroll (Edinburgh), N.V. Trung (Hanoi), G.Valla (Genoa) and J.K. Verma A meeting of the London ?vlathematical Society will (Bombay). b<>held at the University of Southampton on Friday, 20 February and Saturday, 21 February 1998. The Seope of the conference : The conference, which is talks will be on Friday afternoon and Saturday open to all interested mathematicians, is expected morning. to co11ee11trat.e on recent and current research in aspects of commutative algebra related to the Speakers are: Werner Ballmann (University of work of David Rees, including reductions and Bonn), Yair Minsky(SUNY at Stony Brook), integral dosurt'A" of ideals, Rees rings and algebras, Caroline Series (University of \Varwick), Brian uniform Artin-Rees Theorems, mixed multiplicities Bowditch (University of Sout.harnpton), Alex and Hilbert functions. Participants from developed Lubotsky (Hebrew Vniversity), and Michael count.ries will be expected to pay a Registration Fee Kapovich (University of Utah). of $35. Details concerning overnight accommodation and the Friday night banquet will be made available in Financial support : The conference is supported fi nanciall:v by a grant from the London iv1athematical the se.con 20 EL'UONEl:VS fl('.adt1t.1r·.. ) ()b:,;,,,·r\,:-d1cn PJ::1:-1;,.,fe cin.;!d tt�.c· foilo·�vln�. io ,dd \ �.,f(ii.rt>·.lJ .. ut.. January Oi,, 199�. pr:tge ( ·,f a.b�t ra.�.-t in tt�xt or 20 ·- 24. lf)98 ;?H};,td_): :J8. 1998. ,1fG.rc,,w;vkh · ,\vrn:y Hill if .. vnu hk,· ;o e:,dubit .v(1ur soft,vettt:-: :1H1J 1-�rr�ducts. s ,'l\ii') Hill .Ru,:ld Lo:idcn SL!J. t'h 'tii)irt� ,,;{)!_; r i}i'.'f·,.i i)cf{>.l'f: Ff·brtia-v £8 � 1998. ill 1 1. i.gn• Local tC'(": Enwil: ddll .uk Clrn,rrnan: '.\·! 'ross ( (Gn··>i:v.·id11 F'il'si; Anuom1crnue11t and Call for Vice-Chairma.JL C - H Lui Donwin dn:rn1 1:s an artiH· and inkrtl.:sci Comrnilte<" 1\,fombt··rs: K Chen { Livnpool ), A Craig i'lcl!ary resr-anh area that lmi,; drawn I h.- ali.e11lion (Durlrntn), P Dn1f!hard (KZZ, Berlin, GermanyL of r<:'Stiardwrs ·working in differnit. ti1·lds. The effort. M C l•:wrdt. (Greenwich), I G Graham (Bath), during late seventies alld l:'ar!ier Pighi.ies wa.-; ron .J Pni,rnx (Dassault, St Clouds, Frano�). K A ce11tral('d in tlw substruct.uring alld block met hods Perideous (Greeuwich), .J E Roberts ([NRIA, for elliptic problems. Research work has now being Rocquencourt, France) ('Xt.cnded and applied in many branches of cotnput.a tioual mathemat.ics and scieuce and engineering. In Conferenn• Secretary: Mrs Francoise Barkshire part.icular, no11linear and multiphysics problems re (Greenwid1) latPd to industries and strategies suitable for paral h•l and distributed computing and high performance Student Participation: Limited funds will be computing are of interest to t.lte participants of this availabk for graduate students. Please contact the series of international conferences. organisers for details. This elcveuth meeting will take place in t.he United Students should mention their student status during Kingdom for the first t.ime. Its special focus will be submission of abstracts with the same deadline as on Nmuerical analysis, c01uputational issues, above. Full papers not less than 5 pages should be industrial applicatious and software develop submitted before May 20, 1998 in order to qualify ment for domain decomposition methods. for Graduate Paper Competition. High quality The couference will take the format of plenary talks, student. papers are being selected for Graduate miuisymposia, parallel sessions, s,•kct.NI graduate Paper Cmurwtit.ion hased on the submission of full papN pr<:'st•11t.ations and wndors 1'xhihit.io11. All as papers. Students will have their local expenses pects of OD-based nwtho 21 P.UOBLEM CO.RNEB. Pau.! \i\,;�rk•;rolkstr, l)..,fJ.U 26 .A Relic Old .A The Austrian N.lathmuaiical The Olyinpic Movement ha,, tlw 1not.to • High,•·r. to consider t.his umxirn in the light ofthe work of the large number ofm1tiomd mathenwt11.:,d h.f:__ ; is fai�te:r. our ancl structtH'<.1:sare AH this means that uv:re are SO�{.ttionB in which we find oi.,rsdves. But and The \,Vhat is about these veut.ures is thr· offer to nurture the best of 1.he y,,ung na(ionaI niat.hmnaJicians a.nd the Irrt;sr·natiomd Mai hei:natical c,w meet with the most gift,,d staff in mathematics around the This is invaluable for LhP individuals. Like the Olympic Games, being there and her own eountry is an honour in itself. lll rnosf; countries, major users of the available native rnathematical expertise fully appreciate the vital role tlrn.t mathernatics in both tbe development ofindigenous high technology industries and in other areas of professional life. In the future\ as our countries confront. increasingly competitive international markets, 1wople with high levels of inathe1natical abilities, and the problem-solving skills that mathematical learning engender;,, will !wcome an even great,,r natioual asset. It is, however, the case that mathematics does not. n'ceive anyt.hing like the degree of public and rnedia support which is given to sporting events. As the niuef,ies come to an end and we approach the year 2000, the need of rnany econmnies to be more competit.ive i11tema.tionally is growing rapidly. So does the requirement for today's youth to be skilled in mathematics, equipped to deveiop competence iu engineering, manufacturing, science, research and education - all key to successful national economic progress. If nations are going to play an active part in the world economy, they need t.o increase their intellect.ual capital. Mathematical ability is one key aspect of that knowledge base. Through mathematics Oiympiads, the finest mathematical minds are able to pit themselves against their peers around the world and i,o ext.endand refine their individual skills. The promotion of student skills in mathematics in Hungary The first impetus in nurturing problem-solving skills came from Hungary. In 1885, a group of Hungarian mathematicians and physicists started meeting together iu a restaurant near the University of Budapest for the purpose of discussing scientific problems au 22 PROBLEM CORNER aud, on that occasion, the Austrian authorities were officially invited to send a team to participate for the first. time. But the competent authorities exercised restraint and merely delegated an observer. Nonetheless, in order not to lose contact with the leading nations participating in the IMO, it wasdecided to commence special training courses for the mathematical Olympiad in as many schools as possible with the idea of picking the most capable students following a national contest to form a highly competitive team to participate in the IMO. Thus, the Austrian Mathematical Olympiad wasborn. Reaching out to Teachers Implementation of this project wasn't a particularly easy task, for there was hardly anyone who had experience to start it. The initiators decided on the following: the courses should be taught forthe most part. by mathematics school teachers, rat.her than university lecturers. Therefore it was necessary not only to find teachers able to attain the qualification required to coach preparatory courses, but also to arrange professional training schemes, where university mathematicians would tutor them in the art of problem solving at the appropriate level. The founders of the Austrian Mathematical Olympiad were faced at the same time with another dilemma: the lack of preliminary material available. Apart from questions posed at the IMOs prior to Moscow, only a book of problems edited in the then Soviet Union was then to hand. However, many highly qualified ma.t.hema.ticians stepped in an 23 PROBLEM CORNER jg prr:1p.:1ring ::-.tu,lPrth{ fnr tlre u::u.:c,t;iJ tnr1t�.:'.-:t \vfJhin his ·icl'H.:oL H>:Aa:rt , 21 Jiti:lLl:.!ernc.-\ t �{·::'.·I tf:a rh�:�;: ' b,,.:'•('d (� I a.t, ruunin,�; f-)1<":: HJPTt.1al t!.'(1-,n.1.ng ca.1np aJ1.d ti�e µrep;11 n'f,fif·,y c .r:u1:1p· fr)r th�:: )\ i2.Ntria.n. ·1 ��A() lnm• TiJ,o Hr�l four hr·lov1', th(JSt�u· front the 19fh5 1t.ic;1, -' ,·v•--nt;; the naJ,i.onaJ A. H;.:,q��::u; ford.t SL aud aisc, dernonst r�tt.e U1r: "J la:�t, twr, have lict-·1; bv n°adn·; Q 80 Hov; 1nany p.,,'( n ,.vith 1 ::C n �:;. 1996 ex:sr. that go}ve tJ�t: f n ·; f n 1 n 1 n ,. '" n r + ·:- -1 -; ! 7, l + 1 ·:- + i 1 i = ;;· 1. Js .1 1. 3 .-1i i. ''i':i. .; .� J 'i '; rn the not J:,) ( B,eginn,e,rs H<.H.Ul<..i) Q.81 Let a and b be non-negative reai numhers. Deterrniiw all set,;; of .solntionr; 'X2,, . i of the following systenu; of equat.ion (all i:, non-uegative int('g1,rs): Xl - UX:3 ::= b :i:2 - ax4 = b X94 - UX96 = b -ax1 + X95 = b -ax2 + X96 = b X1 + X2 + , , , + X96 = b (Regional Competition, Second Round) Q, 82 Let a, b, c, d, A and B be positive real numbers such that a2 + b2 = A2 and c + d = B hold. 2 2 Determine the greatest. and least possible values for the expression (a+ d) + (b - c) , (Final Round, First Day) Q, 83 How many joker numbers (i.e. six digit numbers composed of the digits Oto 9) exist, containing precisely four digits? (This question arose from the Austrian Lotto) (Final Round, Second Day) Q, 84 (Proposed by Dr Oddvar Iden, Department of Mathematics, University of Bergen) Given two intersecting circles and their centres, how can we construct the midpoint between the centres using only a ruler'? Q, 85 (Dr Z Reut, London) The Special Relativistic different.ial equations of motion of a particle, when presented in 3-dimensional vector form, are d) v2 )-1/2] ( [ mv ( 1-� dt =F, wherf' m and c are constants, and v and F are vector functions. Considering v as a vector function of time t, show that the differential equatio11s of motion can be represented in another :I-dimensionai form as foilows: 2 2 dv v 0_,, ' v 0.,, v(v F) 111- ( 1--) F- 1- ) dt = c2 ( c2. In this issue we will clear out the old questions from Newsletter No. 23. Dr J .N. Linington, VVinfrith Technology Centre, Dorchester, takes a st.art with problem 6:1, and he nearly enters a one-man show. However, questions 66, 69 and 72 remain unsolved. 24 PROBLEM CORNER 6}{ Sorneo.t1c b a;is, n.. bl -2 a-2 b-2<_ a <- b - c · Nmv it is not possible that ') �sa for otherwise (a : 2 ) c� 2 ) (5:� 2 ) > j which contradicts ( I). Therefore a _·) 1 ')')]/�< =:;,, a .• 7�; , (:::::9. 69) ::;;,- a:$ 9 (since a is an integer). O � S 2113 S Also a 2". S forotherwise if a S 4 then by (I), Z(a - 2) be = . (b -2 )(c - 2) S ( 6 - 2 )( c-2) a which is impossible. Thus we have proved that .5 ::; a s 9. If a=5 then by (I), (b- 12)(c- l2) = 120 = 2'.:L5. The 8 possible solutions are: (5, 1:3,1.32), (S, 14,72), (5, 15,52), (5, 16,42) , (5, 17,36), (5, 18, 32), (5, 20, 27), (5, 22, 24). If a=6 then by (I), (b- 8)(c- 8) = 48 = 24 .3. We get 5 blocks: (6,9,56), (6,10,:J2), (6,11,24), (6,12,20) and (6,14,16). 2 0 2 5 If a=7 then (I) becomes (b - � )(r - �) = ! = :; • This gives 4 blocks: (7, 7, 100), (7,8,:JO), (7, 9, 20) and (7, 10, 16). If a=8 then we have (b- 6)(c - 6) = 24 = 23 .:3. This gives 3 blocks: (8, 8, 18), (8,9 , 14) and (8, JO, 12). If a=9 similar working gives no further solutions. The tot.al number of different blocks is therefore 20. Also solved by Nico Lorentz, Howald, Luxembourg. Q. 65 Determine all integers x such that x2 + 19x + 97 is a square number. Solution (Nico Lorentz) Soit (x; n) E Z x Net soit n - x = k E Z. Alors 2 2 l 9 2 27 2 .c + 19x + 97 = n � (x+-) +-=(k-x)· . (1) 2 · 4 � (19 - 2k)(4.c + 19 + 2k} = -27 27 {::=} 4x = -1H - 2k + (2) -19 Corrnue k + n = n EN, on cltduit de (1) que k + J• > J' + .!}, soit.2 k-19 > 0. Ainsi, d'aprt\S (2) . .fa E Z 1.•xige 27 = 0 mod (2k Ill), soit 2k - 19 E {1;3;9;27}, ou encore k E {JO; 11: 14;23}. Dans ce cas x E {-3;-8;-1.l;-16}. Also solved by Dr .l. N. Lilliugt.on. 25 PUOBLEM CORNER 7(j SPH'Hli no fowrr than li(\lJ·Z<::rnnurnbr,r;, ar,· ·written on a biackhoanL ()n,:, may enist ,rny two rmrnlwr;, A c:\rnl B ,,1nd th,�H v;nh' the ·+ 1ta.ud B ·- th1· sr_·t c>f numbers on the blilddvs:mrd. :.dter anJ mimr>tr the ea.Hnot coincldr· wtth the· initiaJ s�:L Solution ( Di· J.N. Lilliugton) Let the numhers be Ao("'·'A), ·,:;.-; .lJ= ).Co( {'!. After OllE' • a."i-UBH': tl-v: number,; ,1r1·: Ai . Bi , c·, .. After ]I.' c,peralions the numbers are AN. BN, Ld S > J be tbr niinimum number1, such that all number,; coincide with the original set:. Then AN� A. l:Jr, =Band AN-1 + = il, fh:-.1 - == B 8ay Solving for il.v,... 1, BN-1 f1N-t =�(A - �) BN--1 = { ( B + 4) · Hence AN-z = �A, Ih,-i = fB. If N > 1 is even , then indud.ively, 4 N/Z (4)N/'2 Ao = Aand 8 B which contradicts (3). (5 ) 0 = 5 If N > 1 is odd, then 4 (N-l)/2 4 (N-1)/2 A1 ( ) A and B1 ( ) B implies = 5 = 5 B 4 (N-1)/2 ,,1 4 (N-1)/2 A+ - ( ) Aand B-- ::::: (-) B 4 2 = -5 2 5 ( ) But (4) has no non-trivial solutions in A and B. Hence forno N do the numbers coincide with the original set. Q. 71 An astronomer added all the distances between 50 stars that he observed with a telescope. The result was S. Suddenly a cloud obscured 25 of the stars. Prove that the sum of the distances between the 25 visible stars is less than f Solution (Niel!ii Bejlegaard, Stavauger, Norway) Let Abe the set of stars uncovered by cloud, and whose t.otal distance sum is SA . Similarly, for t.he set B of invisible stars, the sum is Sa. Beforethe cloud turns up, I group all interconnecting lines in three groups ...A, B, and all lines connecting points of A with those in B. I denote t.his set of segments C with sum Sc. If S denotes the sum of all possible distances then ckarly S =SA + Sa+ Sc. 25 We have ( = 300 dista11ces both in A and B, whereas there are 252 625 > 2 x 300 distances 2 ) = in set C. I can therefore choose points in A and B and apply the triangle inequality twice, in such a way t.hat each of the segments in set C used are counted only once, and some are left over. So we have 8.4 +SB< Sc. Now 1 5,,="A + :, ., B + "c ., < 2 s· c � ,',c·, > -,5., =>S' A+ D c B<-,,. lo 2 2 ThereforeS,4 < � and SB < if. (Editor's note: The solver asks: 'Why 50 stars?' Tlw argument dearly holds for 2n stars, since 2 (;) < r? (n 2: 2). Is it for pedagogical reasonsperhaps? Bejlegaardalso wonders whether the factor f is the 'best.' upper bound of this estimation. Indeed we cau replace the given bound by a better one. Let us denote the stars obscured hy t.he cloud by A1, A2 , ... , A2s and all the other stars by B , 8 , ... , 8 5. Now add all triangk inequalities of type IB,BI 5 jB;Akl IBAt 26 PROBLEM CORNER for I :s; j,i, k :s; JS.The left-hand side of the inequality is equal to 2ST, where T is the sum of the distances between visible stars. The right.-ha.nd side contains ea.eh distance IB,Akl exactly 24 times (as i =I= 1), and therefore is no greater than 24(5 -T). finally, we have 25T :s; 24(5-T) and thus T :s; *S < ts. with t.he bet.t.er bound *·) Also solved by Dr J .N. Lillingt.on. Q. 73 All possible sequences of seven digits are written down one afteranother, in a row, in any order at all, to form a 70,000,000-digit number. Prove that this number is divisible by 239. Solution (Dr J.N. Lilliugton) Let N be the number. Then 10 7 -1 N= L(a1+a210+ ... +a;l06)107" n=O where summation is over all possible sequences of digits O :s; a1, a 2, ••• , a, :s;9. Thus 10 7 -1 10 7 -1 6 6 7 N = L (a1 + a2l0 + ... + a1l0 ) + L (a.1+ a.210 + ... + a,10 )(10 - 1). n=O n.=O (5) (6) 7 Now 10 - 1 = 239 x 41841 = 239 x 9 x 4649 (7) 7 7n Therefore 239 divides 10 - 1 and also 10 - 1, n � 1, and is a divisor of (6). Also 10 7 -I 6 6 6 L (a1 + a2l0 + ... + ad0 ) = 10 (0 +I+ 2 + ... + 9)(1 + 10 + ...+ 10 ) n=O 6 = 10 x 45 x I, 111, 111 6 = 10 x 5 x 9 x 239 x 4649 (8) Therefore 239 also divides (5). (Editor"s note: 7 Lillingt.on indicates that (7) and (8) yield a much larger number, 10 - 1 to divide N. To cope wit.h this problem, we note that. the remainder of 10 7 modulo 239 is equal t.o 1, which can be easily verified by direct inspection. This shows that the given 70,000,000-digit number has the same remainder modulo 239 as I.he sum of all seven-digit numbers that. form it. + + 7 The latter sum is equal to 1 2 + ... 9, 999, 999 = ID' ( !0 - 1) /2 and thus is divisible by 239. 7 not As a matter of fact, the idea that 10 - l is a multiple of 239 does require a great feat of imagination. The problem asserts that divisibility of the given number by 239 does not depend on t.he order of t.he seven-digit numbers forming it, so the differencebetween any such 70,000,000-digit numbers must be a multiple of 239. Ta.king twonumbers only, we immediately conclude that 10; -1 must be a multiple of 239.) Another (incorrect) solution was sent in. That completes the Corner forthis issue. I need suitable exam materials, and I'm interested in programmes aimed at. a. much larger, and indeed increasing, group of ma.then1a.t.irsstudents. Furthermore, I am interested in t.he way you look for new I.a.lent. in schools and instil a love of 111athematics and problem-solving through the present.at.ion of interesting material and special tutoring. I would welcome your suggestions for the evolution of this feature in the Newsletter. Finally, you a.re invited to propose problems for which readers will send in solutions. Proposals should, whenever possible, be accompanied by a. solution, references, am! other insights which are likely Lo be of help for the editor. They can be anything from elementary to advanced, from easy to difficult. Original problems are particularly sought. So, please submit any interesting problems you come across, especially those from (problem) books and contests that. are not easily accessible. But other interesting problem, may also be acceptable provided they are not too well known and references are given as to their provenance. I hereby invite my readers to share t.hern with their colleagues and students. I welcome your input, and especially problem sets and solutions for use! 27 REVIEWS BRIEF REVIEWS Edited by Ivan Netuka and Vladimir Soucek. Books submitted for ,-eview should be sent to the following address: Ivan Netuka, MUUK, Sokolovska 83, 186 1!j Praha 8, Czech Republic. L.Schneps, P.Lochak (Eds.): Geometric Galois The notion of an operad was introduced in Actions 1: Around Grothendieck's Esquisse d'un the seventies as a tool for the study of Programme, LMS Lecture Note Series, vol.242, homotopy invariant structures on topologicalspaces. Cambridge University Press, Cambridge, 1997, 293 Independently, operads had existed under the name pp., GBP 24.95, ISBN 0-521-59642-4 (algebraic) PROP in universal algebra, where they Alexandre Grothendieck is one of the most modelled various kinds of categories determined influential mathematicians of the 20th century. His by given algebraic equations. At the beginning work on the foundations of algebraic geometry of this decade, an enormous revival of interest in operads was aroused by the discovery that has had a profound impact on almost all areas of pure mathematics. Since the early 1970s, some moduli spaces relevant for string field theory Grothendieck has been living and working in a have a natural operad structure underlying the largely self-imposed seclusion from the rest of the Segal's 'factorization axiom'. This, in turn, mathematical community. During the 1980's he stimulated an intensive research of applications had produced several mathematical manuscripts of of the operadic approach in more classical areas, monumental length. The main ideas of one of such as homological algebra, homotopy theory, them ("La Longue Marche travers la Theorie de theory of moduli spaces, etc. The volume of a proceedings contains 15 contributions which present Galois") were sketched in a famous not.e "Esquisse d'un Programme". In this note Grothendieck recent progress in the fieldsconcentrated around this sketched a rich arithmetical theory revolving around 'renaissance of operads.' The volume also contains arithmetical fundamental groups (=3D generalised two short overview papers, written by the founders Galois groups). He proposed two main lines of of the theory, J.P. May and J.D. Stasheff. We investigations: ( 1) Anabelian geometry: for a believe that the book will be useful to everybody interested in this exciting area of active research in suitable class of algebraic varieties (e.g. for all hyperbolic curves) their arithmetical fundamental which pure mathematics and mathematical physics groups contain all information about geometry; interact. (mm) (2) Teichmiiller tower: a highly nontrivial relation D.Cox, J.Little, D.O'Shea: Ideals, Varieties, and between the Galois group Gal(Q/Q) and geometry of Algorithms. An Introduction to Computational various moduli spaces of pointed curves. "Esquisse" Algebraic Geometry and Commutative Algebra. and an equally famous letter from G.Faltings Second Edition, Undergraduate Texts in Mathe to Grothendieck are for the first time published matics, Springer-Verlag, New York, 1997, xiii+536 in this volume (both in their original versions pp., 91 fig., DM 68.00, ISBN 0-387-94680-2 and in the English translation). The rest of Many problems of classical geometry lead to the the book consists of articles explaining various necessity of solving a system of non-linear algebraic aspects ofGrothendieck's anabelian programme and equations in several unknowns. The elimination its current status (the authors include F .Oort, procedures used to solve such problems lead usually L.Schneps, T.Oda, F.Pop, Y.lhara, J.-P.Serre, to many equations with a large number of unknowns, H.Nakamura, J.Wolfahrt, D.Harbater, B.Teissier). and this limited their use in the past. The The editors plan a companion volume containing recent development of computer algebra has led more specialized research articles. The two volumes to a removal of these limits in the size of the grew out. of the Luminy conference "Geometry equations considered and elimination algorithms aud Arithmetic of Moduli Spaces" ( August 1995) are now very fast. The book is an excellent and form a sequel to the book "The Grothendieck introduction to its subject matter. The theoretical Theory of Dessins d'Enfants", this series No.200. background to elimination theory is developed to (jnek) an extent. which is more than satisfactory for J.-L.Loday, J.D.Stasheff, A.A.Voronov (Eds.): practical use. Fundamental concepts of ideals, affine Operads: Proceedings of Renaissance Confer varieties and ordering are used to introduce the ences. Special Session and Inter.Conference Groebner basis as the basic tool for elimination. on Moduli Spaces, Operads and Representation The main theorems of ideal theory are explained, Theory, 1995, Contemporary Mathematics, vol.202, stated and proved. All algorithms are described American Mathematical Society, Providence, 1997, in great detail and demonstrated by practical ix+443 pp., GBP 60.00, ISBN 0-821-80513-4 examples. Each paragraph hasmany exercises which 28 RE'\TIEWS imn,·c,;1. It roniai11� wwfol infiYr.rn1.uion ahou! the A the kine111..a.tjr and t.he to ; IA f'()l.t(;li(B nt.td tc1. at.;. tc,,11at.it t.lit.�ort'n·,.. A not her i.llust.rat1• hnv: ! he nwthods of tht0 book Hmy BHi!t-in The book ,tJso coi;tai as n1ore advanu·,.:i whirl: contains a stwrt. description ,md "'dions on invariant of t.hc !!Re of built-in fundiorni. Although the At !lie end l he mo;,;l·· ;..Jat.!H'm,din,i Book is now w it.h Vi'rsion systems au· described The :J.0 oii CD 12MB on disk), it interested more convenient. to have the actual book to ,·omhine ! he f()l' use:. R.. t:C 29 llEVlEWS (��Gff\.''(• et<:' Rf:ftH to and H1.,lH i,ed Wur M trr:h.liti.f)llr:tf hut hf:11Jt1d tf.ir:,�e ria.rn(•s· l,hctc 1s l9i;.JL. 1M pp, GBP ;).Yi JSfp., �1 8 ! 1}·20,Jt:O-· 4 ,\ coikchon ,Jf fto:n, the fidd of d1ff,·1ential frorn various {1) Uworem on Hadon rnea::Hu·e,,;, R,1:· tlw c0Hecti1,11. The coi.mi,,er ,·ulm1m1ks iu dw (;,lfaud.. N course ddivcred ronstn.ic tion for Each HJ exen:iS•'.S. List of basir t.!H'oretic!H t:,ackgrnund 1s . contains Ji4 itenis. Substanl.ial Notiition and t,0xt. is no rneans a textbook that could be used a.-, Suh jeer, Indext'.S a.r<:: induded. Hecommettded for a sourr.e for a lecture. lvlost cmmter "'"'"n,r·,!r... graduate :,;tudents and researchers. are ;:om·erwcd with existenre (24), M.S.Agrrumvich, Y'u.V.Egorov, M.A.Shubin (Eds.) Md ( Partial Differential .Equations IX. Elliptic Bound H.Konig: Measure and Integration. An Ad ary Value Problems , Encyclopaedia of Mathemat- vanced Course in Basic Procedures and Appli ical Sciences, vol.79, Springer--Verlag, Berlin, 1997, cations. Springer-Verlag. Berlin, 1997, xxi+260 pp., 281 pp., DM 148.00, ISBN ::1-540-57044-G DM !J8.00. ISBN 3-540-61858-9 'J'his volmue of the Encyclopaedia consists of t.hree The book develops a new systernatic theory of the ext.(:nsive survey papers. In the firstpaper, ''Elliptic fundamf•nt.als in measure and integration theory. Bmmdary Problerns'' by M .S. Agranovich, the It is based on an recent approach started in the author introduces the concept of a geueral linear seventi,•s that was on the one hand motivated by d liptic operator of all arbitrary or 30 RE'VJE\VS n.. :..� ·f.1 il.M ,J,;; UO. lSBt', ;J.7(\,f.;1r,Oifi 8, LSBN \l-.filT9Z,O:i'.J.-S f'�_ti�dRJ11f·fi·t,,..:dfi cf ?·::1ea��Jtit(: __.. A 1•.uod thf i;,f inathrrwd,i,:s in t:h,P a.t!J,ntion nf .-'.'.'{·.sf�_:1rch \V\).rkes-s iin.d �.>i).t-�r1crt.1'l.::-:. :·i vvLi::lt tt:"ie EtJ{('.f n;JJn/. ·--,re.r e.is (-:X_f)Jd,,-�nt:{J. In t1:1ache::.�s in JY.1:athc'.J.�i:it.}.cal with ;he i,1.trodu,.:tion of R.Kaluz,1: d,,:,;cribes the contri!nnions Hl!J!3. x+l37 of fa.rnous 1m11hematician11 ,.o the, pp .• DM ISBN ;1 .. 7!}4. 1dat<·d Hu'l.ders of the book will. 1earn :t:5772 .:) not ih,, relation of to fl·:,-:, bcJok des('_t·�bf:s tfif? !ifr· f1ft.)!.lC: of,.t1c ri�ost famou,; madwnwxinaw, 01 thi.s fl'lli ury. WriU.en a ina.n 31 R.EVIEWS .J.M.S(dig: G 32 R.EVlEWS authc,r, M. L,:.,tirnirs, M. :3Hu.,ds for McJi.,;,,,u:· w St,;.1.1,.;t if,;, N·\�i,v \'ork., 1997. fidd L(rth,�iir-,v ;E thf1 e.;;1..n1t:· of tJv� cf C. ftroius !.S BN 1J.;�;1;.i-1 t�1�)· vv !.h) ()Ver Lc•t -.� r> a.nyc,:u· \,v,tb u si.a1v}1rd iflit�her:v:ii..tical 1\'l uft :1d1 ;1 tt-usi1-1n�:d d,,ais with medioifg rtiid c:1.n f.1e tiif·d as .:.1 1.J?xi.book. for rqlres<.'·ll1at.i(m of measurement;; of K..Doeh,: Bash: 1\.fodd Snidifs in anioug i,afr:,c of a,, distance'" in n. lovv- 1 ( SLt P11tdi(atioJ1s. dimem,imial span:. ·n,,, book ('(mta.im; :n GBP HUJ;,, lSBN l w hicli are into fi V<, Part I ;)ftl�·('inO,:tD-.X funda:m<"·nt:·il roun·pti, nf MOS. Par·! ! l pre:;entt1 :\1 D.S re�oit� mode-I niodeb awl 1m·H1od;; for MDS . ruld tiorut' t·'.xt1:-:ns101H� P;iri HI deal;; wnb pnrt iV i.;., devoted infinitary ! _ L.,,.,."' an· In J !Hid rnodds and sorne rnethods rc!al.ed t.o M DS. fn 2. WJJm•. fmHlanwntaJ notiow; of modd an availabk for w; modcL an· doing MDS arc iutroduc,· .J.R.Norris: Markov Chains, Cambridge Series (Here u = :JDu(x) is the density, a = .3Da,1 (x) in Statistical and Probabilistic Mathematics, Cam a diffusion matrix, b = 3Db,(x) a drift. vector, bridge l'niversity Press, Cambridge, lfJ97, xvi+2:l7 m = :Hhn( x) a sign indefinite weight.) The pp .. GBP 27.50, ISBN 0-521-48181-:l aut.hor's contribution coucerns a characterisation This is a textbook aimed at masters' level of t.ht> principal eigt>nvalue in the case when the students although the first half is also suitable for operator is noll self-adjoint and when t.he weight uud,-rgraduatcs. Bot.hdiscretc-t.inw aml cont.inuous function m (a "food" source in the ecological tim(' Markov chaiw, are treated. As tlwir state-space applirntious) is not. required to be of one sign. is at most count.able, the exposition can be done The research is based, among oth(ers, on the quit.1· rigorously, almost without measure-theoretical result.s of C. Cosner and S. Cantrell and P. Hess. prcreq11Jslt1es. A fow exceptions needed in t.he The book consists 5 chapters and an Appendix text. ( <'.g. monoto1w convergence theorem, Fuhini cont.aining prerequisite mathematical concepts. A theorem. the st.rougMarkov property) arf: rigorously compr<0heusive bibliography of 304 items is included disrnssf:d in an apr,wndix. The second half of t.lie which, together with the Literat1ut> Review, gives a boc)k is devot.ed to both tlicoretical and pradirnl good i11dication to the field. Wit.h its emphasis ou applicatious of 1'v1arkov chain,;: t.he former include applirntiow;. t.he book may he of interest not only disnet,• pot.Pntial theory or dedrirnl networks. t.iw t.o mal.hematirians but a!so t.o biologists, ecologists lat.tn rovcrr,. gen,,.t.ics, <'pidemics, qu(,\tt•s, r1�source aud <'ngincers. ( ()j) !ll,rnag,·iw.•ut. c,pl imal co11trol a!ld ]\Jarkov chain L.Fahrmeir. G,Tutz: Multivaria.t of CI,Lh ot·i�crYtibtr·· rkJndorn va,r,J..rihle abmn W '/('.Ct(:1 q· ;:,; pt\ :.:::.:: ,J \-Vhf'T('" 'i'l'lth up tbe tnd 't> a, 'lf:ttur ·Jf ur,Jo1(Jvvn patiHnf'ters, 'TlH� of 'Lt;i'. JJnh c,�n1.1.n·y. 1 ,,.rit.b the f('.Irtaind.er df··\:i)ted hnear rrtcH.ie2s l.t\1) h;·::vt· t1H:' fr>rrn fJ,i ;:� to 2(Ith ,vf)rk. i te:?JJ ir-, "i<:)lr<.r:vvft::ti. a sinooth i:cspunst' fonrtion. iHtrf:,ii'h1ct::.::� in the (\.:,at(:HL� .. hut thf: �uthort-:. A. \.VPU-ktH.r\VH model for a avoid a.ay r·valuasiion nr con1n1t\HtB f:·ver! f!W JW!(H !.H 'ii!:, with }:::,:ii :;., -rrV}H:'Ji the :";iOU!"\.(� �..,\.":> nc,t in ;{IJF�{ 1··r -=· JIJi.!:�:,} ::.: >llJ i.. exp\ z: ''fhe t.he c!a���f:iiraJ v,"cirks of Archirnr·des an!hurs introdui:e tb·,ir a Circk), Vii>l,e mn de Rebw, :\fot.htimat.ki" nu:dtivariaJt� .-::-:xtr--nsio.iJS ;:tn(l d<::scribe ntctbodf; for Newton \Of the \.fotliod of �uat.1 rnodels. SoHv� n101Jels a.re lOH, of 1nodt:ls for tint(� Sf•ri£'s a.nd Introduction to:'\ Li.�1ti.<�rna,nn df.r:d f,tat.e spafe ( Ubt'r die Zahl , to na.nw but a few, the reader mooei:.;, and s.u:·'liival rnodds. 'Ih,! book is ori'"nt.",d will find Hou;;,e No. :.:!!JH of lndian,,, mainly t.o data. Sornc State Legisiature to fix the value ir in to GLI\IJ are nut iududed in tlw !\iven\; simple proof that. rris irrational { 1'.)47), log-linear models for contingency t.ahles. (There collection of mathematical stories and icni.ecdotes arr special monogra.plis devoted to 1mch models.) about ir, Keith 's mnemonic for the first 402 decimal The met.hods t.reated arc illustrated on real data. places of r., etc. Related topics like articles on Technical details and proofs are deferred to an the transcendency of e, on the calculation of the aµpendix, or the reader is referred t.o the literature. Euler constant 1 or on the arithmetic-geometric The hook is suit.ed for applied statisticians and mean of Gauss are also included. The book is s1 udents of statistics. (ja) a very good tool to introduce seminar topics like J. W.P.Hirschfeld, S.S.Magliverns, M.J .de Resmini irrationality and transcendence, elliptic integrals (Eds.): Geometry, Combinatorial Designs and or just t.he history of r. - the authors provide Related Structures. Proceedings of the first readers with suggestions on where to start. As Pythagorean conference, London Mathematical works are reproduced, the book has an appealing Society Le<'ture Note Series, vol.245, Cambridge flavour of times gone by, even from the point of Univeniity Press, Cambridge, 1997, vii+258 pp., view of the graphics. An indispensable source for GBP 27.9.5, ISBN 0-521-,59538-X historians and scholars, and recommended for a The book contains 18 papers contributed by student's independent study of the development of participants of a conference held in Greece in June mathematics. (jv) 1996. About a half of the papers are more or less R.Isaac: The Pleasures of Probability, Under connected to finite projective spaces, including a graduate Texts in Mathematics. Readings in Math survey by P.J. Cameron that reviews results and ematics, Springer-Verlag, New York, 1995, xv+241 problems of projective geometry with respect to pp., 17 fig., DM 48.00, ISBN 0-387-94415-6 dassifica.tion of maxirnal subgroups of PGL(n, q). Although modern probability theory is a serious Ther(' is also an up-to-- ;34 R.El,JEl\lS i f fir':: ch,ihf:r1t !rhuJ l8 lh,r ,1itu: /hf' ;)tf;r.-'r ;_·h:id d:,t. fu t �tid o to t.Hldcr�L1urd the UJI rJ:,·· a1'11J,;)j' J;,ri t"f'S ht'� iy. fJ_�u::(i,ru�..i .:.A" teal v;trH�-bk:L�. ;: 1nh 11h' HS:,,{H!5pl: \ont, undt,r Vl.'iti�·h d1i6 ,'.�o!ut1�)n M.f:rc,idHi,: M.arkov Pn;,x•ss,B and Diffi:,r,md,d is cc,rH�ct h-:"tve b1::r·n dl�c.1}Shed Prohleuis. Ledin,'·,; in 'l'h1s jfa!i,iswatin-. ETH liirid,, ihr, book q-� l r):z pp , DM 1 JS Bf, :i 7(\ct.:J{;;fl'.?-9 iSBf\ .J .P.Kl<,)in, Jlsfoi\, sotTH.-' reo.. :,i- tr a.dYanci�r,; ia the H,·,dih. l hat aris• from t!i,· pp. :J{ uf d,ifr:r,·n1ir,i IS IJ\ '}- '.iK7 IJ.t�2!r-1'i cl Tvlark<.1v proccs:)cS1 l!1,· bC1nk dnot,..d lo sLal.istind SOJUP fitriJ.,; result:- ,.A wbL:h Mt' f("\'inv,0d for and Shrr vc dat.a atls�) r,cw Brownian i;;; kHC1\VH (() Of('Hf ulus] solutions lo 01dy in a n·rtaiJJ of tillif', Trnll('ali,m many prnhi<'ms of differetJt.ial equation;; uwaus that. only individuals wiic, have cxpcrienced lrnw natim1l aud usif11l sto,hastic representations) the event by a spcrific time ;ue included in tlw One can for exarnpie use the \Viener procf:ss sarnpk (right. truncation) or individuals who survive lo charnct-('rise the Dirichlct problems for which a sufficienttime are included (lefi truncation). After a solution exists, to ,onstruct it and to prove an introduction, the authors describe estimation uniqueness. The aut.hor tri;ats four complex topics of s1mu11ary survival statistics such as the survival in this book: the Dirichlet. problem with a small forn:Lion. cumulative hazard rate, and measures of parameter in higher derivatives; the averaging centrality. The next topic is hypothesis testi11g. One principle for processes and PDEs; homogenisation of the most. important parts of the book concerns in PDEs and stochasti, processes; wave-front n·gression analysis for Cf'11sored aud/or truncated propagation for semilinear equations and systems. data. l\foltivariate models for survival data are Thfc r<>ader is supposed to be actively familiar with discussed in the last part of the 111011ograph. The the theory of stochastic processes and to possess book is writ trn for i11vestigators who need to analyse a good background in PDEs. Tllf' author, as lifrtinw data. It can also h(' recom111ended as a a rule, does not. present detailed proofs that are textbook for students. The ma(,E·rial is presented elscwlwr(' available in the literature; the text will in an attractive and readable form. Mathematical serve, therefore, more as a reference and a guidt' theory is illustrated using real data, with many for specialist.s rat.her than as introductory lecture practical remarks and reconmwndations. The book C01Wif'. (.isle) is a pleasure to read. (ja) M.Simouuet: Measures and Probabilities, Uni Multigraph. A software package for multivari versit.ext, Springer-Verlag, New York, 199G, xiii+510 able calculus that fills the gap between graphic pp., DM 68.00, ISBN 0-387-94(544-6 calculators and high powered computer algebra This book presents a sophisticated treatment of systems.•. J.Wiley & Sous, Inc, New York, 19\JG, measure theory which should prove useful to both GBP 22.50, ISBN 0-471-10618-G practising mathematicians and advanced students in :\Iultigraph is a software package that is (kvoted to the fields of analysis and probability theory. The one part of calculus - multivariahle cakulus. It is reason is that. the text unifies in an elegant manner not a computer algebra system, and tlw prograrn t.he approach based on the notion of a measure is largely iut(clldt·d for a graphic representation of defined on a family of sPts wit.h that based on the funct.ious. It is possible to display ;JD-surface notion of Radon mea..<;ure understood as a liuear plots, rnutour plots and 2D-vedor fields. Users fuudio11al 011 the space of continuous functions nc,·d not d1oo&e ouly from paramet.erised predefined with <·ompart support. Bot.h integration theories, functions. they can also enter their ow11. The tlw fornwr of which is pPrlrnps better suited to proµ;rnrn also allows specification of tlw plot area. probability t.hPor,;\ a,re deduced a.s spf'cial case8 of Each i,ypc of graph offers several options an:ordi11g the intcgrat.ion with n:spect to a Daniell mea.,;;ure, to tltt·: requirements of t.he users. It is possible the coucc·pt of which is defined as a linear form on to seled, for instance, pa.ra.llel or perspedivi, a Ries,: subspace of the space of rnal-vaJued funt1om, projection, wire frame or· solid surface (surface plot), on a gi F'll set. (typically eit.her t.he space of simple number of contours or levd eurv,, outlines ( contour measurnhk functions on a ,H:miring or th,) space plui), The program lrns fort!wr rapa.bilit,ies: for of contiuuous functious with .:ompart support on a imd.anc1·, it is able to draw diredional derivat.in·'n locally cm11pact space). Tbe exposition leads quickly or comit v.1Jues of inkgrais. TI.is r-;oftwnre may he a and srnuolJdy to the important results of nwasuri� :�s Il.EVIEWS sud1 as extensmn dworrms for measures co1tre1·ned with products of ddh1ed on a Bookan sem1ring mea,<;ure;; both finik a.nd rmd proves tht•on•m,, fnr the Ld1es1lm: t!w exist.euct• ,:)f Markov chains associated with dio,,.,n by the authm transit.ioa kernels. The m.ain. convergence 1.lw hegiuning a fairly genel'al integration theory for rnndom variables are treated in Chapter IV. for Banach space-valued integrands and complex Thes,· 1.i'dllliques are employed to present aud to valu,·d rnea,,un·s. 'I'be book offem in Chap!.,ffr prow· the Kolmogorov law of nurnbers for Hl a nice introduction io probability that i.i. ::M .REVIEWS lwcanse each of them forms a coherent account of the problem of associating a simpler variational a subject of ind<2pendent mtercst (complex analy inequality to the original. For this they introduce sis. holomorphir functionals on Bauach spaces, Kat.o the concept. of homogenised inequality. The next t lwory, Flhptir partial differential equations in Lip problelll is to determine the relationships between ;;d,it.z domains, anJ, lastly. non-li1war partial dif respective topological degrees and how to calculate ff'reotial equal.ions). The thread !inkiug these dif the111. Another group of problems arises when ferent themes is the use of wavelets in Calder6n 's studying bifurcations from infinity. Chapters 3, 4 programme in operator theory. The books �-Vavelets deal wit.I: bifurcations in Hilbnt space. The abstract (Ill(/ Opt mlors and H'c11•elcts: ('a/dt't'11n-Zygmttnd and result.s ,Hf' appli<:'d t.o obstade problems for elliptic Muliilinear Opcmtor8 have been writt.t>n at a level ap operators and to unila.t.eral problems for plates and propriate for first-year post.graduat.Ps, and t.be au beams. In Chapter o, the bifurcations in Banach thors bave test.ed them in FranrP, and in the U.S.A, spaces an· studied. The results are applied to on various audiences of mat.liema.t.icians and engi inequalities containing the 1•-Lapla.cia.n. Chapters 5 nPers. Written by two of t.he leading experts in the and 7 cont.a.inthe theory of bifurcations frominfinity are-a, this book will be an <>ssenf.ial purchase for all and its applications. The book wi!I be of interest interested ill wavelets. ( knaj) to gra :H REVIEWS -----·------ teBd1>:>rs make lecture:,; xu1cmts,, Oxford L�:(,tme S1�ries in �'iathenialicB a.nd 111ore of eh(' trn,wrial is ,wce;;sible Hs Ch,rnndon at thf, the sd10ol levr·L !. 9ffi. xi+ 2::17 1>p., ISBN (t. J l/(>..!JOOW-7 P,Garrett: Bui.ldings and Classical Groups, This i& a revised version nf the hook Chapnu.tri & HalL L S.K.Stein: Strength in Numbers. Discovering holomorphic funct.ions, harmonic functions, various the Joy and Power of Mathematics in Everyday represent.at.ions of holomorphic functions, conformal Life. J .Wiley & Sons, Inc., New York. 1996. xiii+272 mappings. There is also a short chapter on Riemann pp., GBP 19.99, ISBN 0-471-15252-8 surfaces and a section on continuous fractions, the The book consists of three parts of which perhaps concept. not covered by most textbooks on complex the first is the most generally interesting. The functions. A nice feature of the book consists author touches on the problems of anticipation of the inclusion of topics of classical analysis, of numbers and mathematics by every citizen, no e.g. Bessel functions, Bernoulli numbers, special matter what their profession. The prejudice toward polynomials, double periodic functions, gamma numbers, the misuse of numbers in influencing function, zeta function ( accompanied by comments public opinion, what statistics can and what on prime number theorem), conformal mapping and t.hey cannot. tell, myt.hs about. mathematics and t.he Dirichlet. problem et.c. Numerous exercises, mat.hemat.icians, how pure mat.hernat.ics becomes historical notes, applications of the theory to applied and what. mat.hemat.ics is really applied problems of "hard analysis'', a detailed style of t.o at. present. in various occupat.ions in America, exposit.ion, a large amount of material is covered and how the reforms of mathematics education - this all makes the textbook attractive for both have contributed ( and contribute) t.othe significance students and teachers. (in) of mathematics education for the everyday life - A.Beauville: Complex Algebraic Surfaces. Sec all these topics are discussed in the first part. ond Edition, London Mathematical Society Stu In t.he second part, named "From High School dents Text.s, vol.34, Cambridge University Press, t.o Kindergarten" the author approaches several Cambridge, 1996, ix+132 pp., GBP 13.95, ISBN 0- problems from secondary-school mathematics in a 521-49510-5, ISBN 0-521-49842-2 spirit close to that of constructivism, whilst pointing The aim of the book is to present the Enriques to the weak points (or possible mishaps) of this classificat.ion of complex algebraic surfaces with approach, where this is necessary. The crucial proofs, but in a relatively elementary way. It is role in this and the last part (named "Closer and writ.ten as a textbook for students familiar with Closer") of the book is played by the concept of basic algebraic geometry and sheaf theory. The a geometric sequence, the sum of the first finite classification is very nicely explained. It begins with number of terms and t.he sum t.o infinity. The ruled and rational surfaces followedby surfaces with g<'ometric series is t.hen used t.o solve problems in small ho 39 UEVIE\:vs cc,11�1trurl1{)1tf·� !)��, ·::01,:p2ts;:;�t:i· a.nd nJ!f.·r, t-hc tht.' fir�t �YHJ.raL 'Wi��rh f,:)tH.iS i.h(: start ;)f th.f. rn.a,.in i; 1::�l�i�'.lt � ,·tt., .,. s bc·hii: d r,,r1,)Cf:!�;,� of .-�rlt·ct�i1u:. tf1e nit r··i.! t:(�a.rn ,Juicisaun:s.. 1tnd tf;e intrrni:ttii:::naJ The bcok r-onsi�ls of 1.cnli( led do not hut i,\VO n·!at.he:t:n.atjfs. VVha.t du v;hen: in fert· a.in a:retk1, \\'bich n.iost. cabf.'S u:ort io.fort;t,.tt�c�H on thr· !E l ..... 'I'· .1\. bCBOG! ' ' _ dif;cum,ed iu •:er M,il.lwrn;·,,rks t()c,1--k.·ff. fi<)Vf"fS i\,la,.;t�·r,:;lasscs an excdlew !'l'ad all f\'umber of age) int,·n�frd in matb,·ma.tics and r·ornmlae .r;\:enrnore �r)h"..tr tho:::h ') unintt:rt'.SLe:d iu nu·t.thf>iTH.ttif.s, Part l s(;,ndudf's with "Some books for yonr It �-�HJ1 aJsc, sr:rve as a ·very for ihof'..e bo,:,kslH0lf'', an t,Xti'nsive list of ex.ccllenl re,sourcn, mathelllal ics educators '-A'ho from da;;;sic sdwol textbooks of a for ,'ra to l.11(· iatest collt,d.ion,;of probler.rn,. Tlw author in muthcmat ics. (lboc) provides a brief comn1t,·nt. oii •each item listed. A.Piukm,, S.Zafrany: Fourier S,iries and Part H prei,ents t.lie problems from t.he first 32 Iutegral Trauc;fonw,,, Camhridg, t uiV('rsity Press, BMOs, hut in reverse order with the :J2nd first and Cambridge. l99'i. vii+l8!J pp., GBP l'.2.90, ISBN O t.hf' lstlast! This idiosynrrasycan be justifiedby the Ii:21-:'iffi71--4. ISBN 0-521--fi\J'.209-7 fact. that, as nwlltioned above, the latest papers are Th,• ain, of this book is to introduce the reader to the much more typical of a. mathematical competition ha.sic concepts in Fourier series, Fourier transforms, than the early ones, which were closer in spirit to Laplace transforrns aud their application;;. The standard school examination papers. material was prepared on the basis of a third Part III provides Hints and Outline Solutions for semester course forstudents at the Israel Institute of the papns back to 1975, the others being omitted, Technology, Haifa. This is a clearly written textbook again for t.he reasons indicated above. In each case, rnntaining the theory for piecewise continuous the outline solution consists of a number of steps. fu11ctions, solved examples, simple applications Some of the steps are in the nature of hints to nudge to ordinary and partial differential equations, the reader in the right direction. Others require the integral equations, signal processing and integration, reader to fill in blanks to obtain a detailed solution. togdher with exercises at the end of each section. The readt'r who uses Part III sensibly will end up A knowledge of calculus should be sufficient with a full solution for eac problem, obtained only background, as a cha.pt.Pr on imwr product spaces after some effort. Sometimes there is more than one and a short appendix on the residm' theorem and rnethod. In all cases, the reader will get a feel for Fuhini 's theorem are included. The book is a the problem and how it relates to other problems in good first introduction to Fourier series and integral the book (or elsewhere). transforms for students of enginening. (efa) For the last 10 - 15 years Tony Gardiner has been thf' dominant figureon the UK Olympiad scene. He A.Gardiner: The Mathematical Olympiad Hand has strong views, some of which appear at various book. Au Iutrodnction to Problem Solving. Ox stages in the book. In particular, able students " ford University Press, Oxford, HJ97, xii + 229 pp., require a diet which goes beyond mere textbook GBP 14.9::i, lSBN 0-19-850105-6 rxercises and examination questions". He expresses This int.roduction to problem solving is based on hop<' that the book will introduce such pupils to "a tl1t· first 32 British Mathematical Olympiads 1965 new world of challenging mathematical problems", Hl9(). The British Mat.h.-,matical Olympiad (BMO) as well as rnnvincing teachers that t.he problems are has changed it,1, format aand cha.meter over the not act uaJ!y as daunting as they might appear at Yf'ars. For example, the papers sd between l!J65 first sight. There is no doubt that the author's and 197'1 differ wnsidcrnh!y from thf' most recent hop,' will bP amply fulfilled. This book should be papers. Cnrrently I.he ffMO com;i:,;ts of two rounds. in i he library of every school, college and This book restrict.s attf'ntion t.o the probi1•ms from UlliVersity. ( arm) 40 CAMBRIDGE Finite Fields Representation Theory and Algebraic Second Edition Geometry Rudolf Lidl and Harald Niederreiter Edited by A. Martsinkovsky and G. Todorov The subject of this book is che theory of finice fields: a The variery of copies covered here reflects the breadth of branch of algebra char has come co rhe fore because of its Maurice Auslander's concribucion co marhemarics, which diverse applications in such areas as combinatorics, coding includes commutative algebra, homological algebra and rheory and rhe machemacical study of switching ciruirs. representation theory. £60.00 HB O 521 39231 4 769 pp. 1996 £20.95 PB O 521 57789 6 131 pp. 1997 Encycloped1a of Mathematics and its Appl1car,ons 20 London Mathematical Sooery Lecture Nore Series 238 Harmonic Maps, Loop Groups, and Algorithms for Modular Elliptic Curves Integrable Systems Second Edition J. E. Cremona Martin A. Guest This book presents a thorough treatment of many algorithms This book is an introduction co chis important area. Jc is concerning the arid,metic of elliptic curves. An cxcensive set accessible co universiry srudents, bur leads co copiesof current of cables is provided giving the results of the author's research in rhe theory of harmonic maps. le is the first book implementation of the algorithms. on chis subject at rhis level. £45.00 Full Canadian Binding £40 .00 HB O 521 58085 4 208 pp. 1997 0 521 59820 6 384 pp. 1997 £14.95 PB O 521 58932 0 London Mathematical Society Student Texts 38 Geometry, Combinatorial Designs and Related Structures Spectral Theory of the Riemann-Zeta Edited by J. W. P. Hirschfeld, S. 5. Magliveras Function and M. J. de Resmini Y. Motohashi This volume examines finice geometries and designs, a key Professor Mocohashi shows char rhe Riemann-Zeta function area in modern applicable mathematics. It includes scace-of is closely bound with aucomorphic forms and chat many the-arr surveys from leading international machemacicians in results from there can be woven with techniques and ideas cheir fields. from analytic number theory co yield new insights into, and £27.95 PB O 521 59538 X 266 pp. 1997 views of, the function itself. London Mathematical Society Lecture Nore Series 245 £29.95 HB 0 521 44520 5 237 pp. 1997 Cambridge Tracts in Mathematics 127 Principia Mathematica to *56 Alfred North Whitehead and Bertrand Russell Analytic Number Theory This abridged text of the great three-volume Principia Mathematica contains the material that is most relevant co an Edited by Y. Motohashi introductory study oflogic and the philosophy of mathematics. Contains up-co-dace contributions from leading international £32.50 PB O 521 62606 4 456 pp. 1997 figures in the field. Topics discussed include the theory of zeca Cambridge Mathematical Library functions, spectral theory of aucomorphic forms, and Diophantine approximations and equations. Representation Theory of Art in £27.95 PB O 521 62512 2 392 pp. 1997 Algebras London Mathematical Society Lecture Note Series 247 Maurice Auslander, ldun Reiten and Sverre 0. Smale Presentations of Groups This book is an introduction tO the contemporary Second Edition representation theory of Artin algebras, by three very D. L. Johnson distinguished practitioners in the field. Provides an introduction co combinarorial group theory. Any 'This book will be the major source for srudents srudying in this reader who has complered first courses in linear algebra, field, and a reference for the material it covers.' group theory and ring theory will find chis book accessible. Peter Webb, Bulletin of the London Mathematical Society £17.95 PB O 521 58542 2 228 pp. 1997 £22.95 PB O 521 59923 7 440 pp. 1997 London Mathematical Society Student Texts 15 Cambndge Studies ,n Advanced Mathematics 36 Cambridge books are available from good bookshops, alternatively phone UK+ 44 (0)1223 325588 to order direct using your credit card, or fax UK +44 (0)1223 325152. For further information, please email Giulia Williams on [email protected] or browse our Worldwide Web server http://www.cup.cam.ac.uk •CAMBRIDGE • UNIVERSITY PRESS I he· hli11burgh Building. ( .1111hridgc < II! !Ill ,------···--·-«-··---···-,-·------····------··-·------·-·------� methods based on the variational approaci, and the rheory of NEW IN 1998 topological degree of rnouotone cype nunlinear tn.appiugs. Journal Journal of Group Group 1'11�ocy OSU MATHEMATICAL RESEARCH INSTITUTE Theory PVBLICATIONS i/�� The Journal of Group Theory i, devorcd rn rhe pub!icarion of original 6 R.epresentation ��� research 3rtides in all aspects of group ,.__, fES�- __ theory. Articles conceming applica Theory of Finite «L ....� rions of group theory and articles from Gm ups ;;�Tu:: research areas which have a significant impact on group theory will also be fuile Groups Proceedings of a Special considered. Research Quarter at The Number 1 • Issue 1 • 1998 Ohio State University, JOHN G. "IHOMPSON, HELMUT V(JLKLEIN Spring 1995 Sympiectic groups as Galois groups AVINOAlvl MANN '!!� EDITOR: R. SOLOMON Enumeraring finite groups and rheir defining relarions MICHAEL VAUGH/IN-LEE 1997. 24 x 17 cm. XII, 151 pages. With 6 figures. Hardcover. On 7..el'manov's solution of the restricted Burnside problem DM 178,-/oS 1.299,-/sFr 158,-/approx. £ 62.00 JAMES HOW1E • ISBN 3-l l-015806-X Free subgroups in groups of small deficiency Contains articles by leading experts in the fieldof finite group Managing F,ditor representations. Both the general theory and the special theories J. S. Wilson, Birmingham related to the representations of the symmetric groups and the Editorial Board finitegroups of Lie type are covered. Laresr reports are given on A. J. Berrick• A. V. Borovik• M. Braue• K. A. Brown • important conjectures including the Lusztig conjecture, the F. Buekenhout• F. de Giovanni • R. Gobel• R. L. Griess, Jr. • Alperin-McKay-Dade conjectures and the k(G\/)problem. N. D. Gupta• T. 0. Hawkes• A. A. Ivanov• E. I. Khukhro• L. G. Kovac.s • V. D. Mazurov• F. Menegazzo• S. A. Morris• A. Yu. Olshanskii• C. W Parker• l. B. S. Passi• R. E. Phillips• DE GRUYTER PROCEEDINGS D. J. S. Robinson• R. Schmidt• Y. Segev• A. Shalev • W J. Shi• S. Sidki• D. M. Testerman• B. A. F. Wehrfrirz Geometry, Topology Subscription Information ISSN 1433-5883 and Physics 1998. Volume l (4 issues). 24 x 17 cm. Approx. 400 pages. Annual subscription rare Proceedings of the First OM 298,-/iiS 2.175,-/sFr 265,-/approx. £ 104.00 plus p & p. Brazil-USA Workshop held Single issue OM 84,-/oS 613,-/sFr 76,-/approx. £ 29.00 p & p. in Campinas, Brazil, June 30-July 7, 1996 DE CIWYTER SERIES IN NONLINEARANALYSIS EDITORS: AND APPLICATIONS 8. N. APANASOV 5. B. 8RADLOW 5 P. DRABEK • A. KUFNER W. A. RODRIGUES, JR. • K. K. UHLENBECK F. NICOLOSI 1997. 24 x 17 cm. XII, 348 pages. I-Iardcover. Quasilinear Elliptic DM 268,-/iiS 1.956,-/sfr 239,-/approx. £ 94.00 Equations with • ISBN 3-11-015594-X The work,hop attracted more than 100 participants from vari Degenerations and ous cenrers in Brazil, the US, Asia and Europe, ranging in expe Singularities rience from graduare students to leading experrs in their fields. Th� program covered topics in geometry, topologyand physics, 1997. 24 x 17 cm. XII, 2 l 9 pages. with special emphasis on harmonic maps, Kahler and contact With 3 figures. Hardcover. OM 198,-/ geometry, gauge theory, low dimensional t<>pology,and oS 1.445,-/sFr 176,-/ approx. £ 69.00 Seiberg-Witten theory. • ISBN 3-11-015490-0 S,1bjcct is the theory of nonlinear boundary value problems for elliptic operators with degeneration and s,ngularity.!t focuses on the existence and bifurcationof weak solutions in appropriate w,·ighred Sobokv spaces. The main tools are Functional analytic Prices are subject to change Mathematics with Birkhauser New and Recent Published------Titles ANALYSIS NUMBER THEORY PROBABILITY THEORY M. Kuga, formerly University ofTokyo, Japan M. Ram Murty, FRSC, Queen's University, A. Boyarsky/ P. Gora, Concordia University, Galois' Dream Kingston, Ontario, Canada/ V. Kumar Murty, Montreal, Quebec, Canada FRSC, University of Toronto, Ontario, Canada Laws of Chaos Group Theory and Differential Equations Non-vanishing of L-functions 1993. 160 pages. Hardcover. and Applications Invariant Measures and Dynamical 3rd printing 1997 Systems in One Dimension sFr. 58.- 1997. 208 pages. Hardcover ISBN 3-7643-3688-9 1997. 416 pages. Hardcover sFr. 68.- sFr. 108.- ISBN 3-7643-5801-7 ISBN 3-7643-4003-7 PM 157·Progress in Mathematics PA-Probability and Its Applications Albrecht Bottcher, TU Chemnitz, Germany/ Yuri I. Karlovich, Ukrainian Academy of Sciences, Odessa, Ukraine GEOMETRY Ch. M. Newman, Courant Institute of Mathematics, New York, USA St.I. Andersson, CECIL, Giiteborg, Sweden/ M.L. Lapidus, University of California, Topics in Disordered Systems Riverside, CA, USA (Eds) Progress in Inverse Spectral 1997.96 pages. Softcover sFr. 28. - Geometry ISBN 3-7643-5777-0 LM·Lectures in Mathematics PM 154·Progress in Mathematics 1997. 208 pages. Hardcover sFr.88.- ISBN 3-7643-5755-X TM·Trends in Mathematics HISTORY OF MATHEMATICS H. Triebel. Friedrich-Schiller-University, Jena, Germany ______J. Sakarovitch Fractals and Spectra OPERATOR THEORY Epures d'architecture related to Fourier analysis and a function spaces H.L. Gorbachuk / V.I. Gorbachuk, Ukrainian De la coupe des pierres la geometrie National Academy of Sciences,_�ev, Ukraine_ descriptive XVIe-XIXe siecles 1997.280 pages. Hardcover sFr. 128.- M.G. Krein's Lectures on 1996. Hardcover ISBN 3-7643-5776-2 sFr. 148. - MMA 91·Monographs in Mathematics Entire Operators ISBN 3-7643-5701-0 SN 21·Science Networks • Historical Studies 1997. 232 pages. Hardcover sFr.118.- NUMERICAL ANALYSIS ISBN 3-7643-5704-5 OT 9 ?·Operator Theory: Advances and Applications PARTIAL DIFFERENTIAL G. Niirnberger/ G. Walz, University of EQUATIONS Mannheim, Germany/ J.W. Schmidt, TU Dresden, Germany (Eds) ______ALGEBRA I. Kuzin / S. 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