The history and development of numerical analysis in Scotland: a personal perspective

Transcription

1 The history and development of numerical analysis in Scotland: a personal perspective Alistair Watson Mathematics Division University of Dundee The history and development of numerical analysis in Scotland:a personal perspective p. 1/33

2 Basic issues What is numerical analysis? How old is it? The history and development of numerical analysis in Scotland:a personal perspective p. 2/33

3 Basic issues What is numerical analysis? How old is it? Possible answers: Study of algorithms for the problems of continuous mathematics. The history and development of numerical analysis in Scotland:a personal perspective p. 2/33

4 Basic issues What is numerical analysis? How old is it? Possible answers: Study of algorithms for the problems of continuous mathematics. Goes back centuries. The history and development of numerical analysis in Scotland:a personal perspective p. 2/33

5 Modern numerical analysis. Association with calculating machines. The history and development of numerical analysis in Scotland:a personal perspective p. 3/33

6 Modern numerical analysis. Association with calculating machines. Usually with programmable computers. 1947: Paper by von Neumann and Goldstine. The history and development of numerical analysis in Scotland:a personal perspective p. 3/33

7 Modern numerical analysis. Association with calculating machines. Usually with programmable computers. 1947: Paper by von Neumann and Goldstine. 1947: Name. Formal use in Institute of NA at UCLA (J. H. Curtiss). The history and development of numerical analysis in Scotland:a personal perspective p. 3/33

8 Modern numerical analysis. Association with calculating machines. Usually with programmable computers. 1947: Paper by von Neumann and Goldstine. 1947: Name. Formal use in Institute of NA at UCLA (J. H. Curtiss). 1936: Papers by Comrie, Turing. The history and development of numerical analysis in Scotland:a personal perspective p. 3/33

9 Starting point: first treatment of what we now think of as numerical analysis, in conjunction with use of calculating machines. The history and development of numerical analysis in Scotland:a personal perspective p. 4/33

10 Starting point: first treatment of what we now think of as numerical analysis, in conjunction with use of calculating machines. 1913: Origin in Edinburgh, Scotland. The history and development of numerical analysis in Scotland:a personal perspective p. 4/33

11 Plan 1. Edinburgh: early years 2. Some personal stuff 3. Collaboration between Edinburgh and St Andrews 4. Dundee 5. Computing facilities in Dundee 6. Postscript The history and development of numerical analysis in Scotland:a personal perspective p. 5/33

12 1. Edinburgh: early years 1912: E T Whittaker ( ) arrives from Dublin. The history and development of numerical analysis in Scotland:a personal perspective p. 6/33

13 1. Edinburgh: early years 1912: E T Whittaker ( ) arrives from Dublin. 1913: Opens Mathematical Laboratory, where students trained to do machine calculations. Subjects taught include: interpolation, difference formulae, linear equations, numerical integration, least squares, numerical solution of DEs,... The history and development of numerical analysis in Scotland:a personal perspective p. 6/33

14 1. Edinburgh: early years 1912: E T Whittaker ( ) arrives from Dublin. 1913: Opens Mathematical Laboratory, where students trained to do machine calculations. Subjects taught include: interpolation, difference formulae, linear equations, numerical integration, least squares, numerical solution of DEs, : Book by David Gibb: A course in interpolation and numerical integration for the mathematical laboratory. Preliminary note on computation: The history and development of numerical analysis in Scotland:a personal perspective p. 6/33

15 1. Edinburgh: early years 1912: E T Whittaker ( ) arrives from Dublin. 1913: Opens Mathematical Laboratory, where students trained to do machine calculations. Subjects taught include: interpolation, difference formulae, linear equations, numerical integration, least squares, numerical solution of DEs, : Book by David Gibb: A course in interpolation and numerical integration for the mathematical laboratory. Preliminary note on computation: 1920: Honours course entitled Mathematical Laboratory. The history and development of numerical analysis in Scotland:a personal perspective p. 6/33

16 E T Whittaker in 1930 The history and development of numerical analysis in Scotland:a personal perspective p. 7/33

17 1924: Book by Whittaker and Robinson The Calculus of Observations; a Treatise on Numerical Mathematics. From Preface:.. present volume represents courses of lectures given during by Professor Whittaker to students in the Mathematical Laboratory... The history and development of numerical analysis in Scotland:a personal perspective p. 8/33

18 1924: Book by Whittaker and Robinson The Calculus of Observations; a Treatise on Numerical Mathematics. From Preface:.. present volume represents courses of lectures given during by Professor Whittaker to students in the Mathematical Laboratory : A C Aitken ( ) appointed to a Lectureship in Actuarial Mathematics. Applied matrix algebra to numerical analysis and statistics. Published on polynomial equations and eigenvalue problems,... The history and development of numerical analysis in Scotland:a personal perspective p. 8/33

19 1924: Book by Whittaker and Robinson The Calculus of Observations; a Treatise on Numerical Mathematics. From Preface:.. present volume represents courses of lectures given during by Professor Whittaker to students in the Mathematical Laboratory : A C Aitken ( ) appointed to a Lectureship in Actuarial Mathematics. Applied matrix algebra to numerical analysis and statistics. Published on polynomial equations and eigenvalue problems, : Book by Turnbull and Aitken: An introduction to the theory of canonical Matrices. Contains Householder matrices. The history and development of numerical analysis in Scotland:a personal perspective p. 8/33

20 A. C. Aitken The history and development of numerical analysis in Scotland:a personal perspective p. 9/33

21 1946: Aitken succeeds Whittaker to the Chair of Mathematics. The history and development of numerical analysis in Scotland:a personal perspective p. 10/33

22 1946: Aitken succeeds Whittaker to the Chair of Mathematics. 1946: Aitken teaches Mathematical Laboratory (up to 1961). The history and development of numerical analysis in Scotland:a personal perspective p. 10/33

23 1946: Aitken succeeds Whittaker to the Chair of Mathematics. 1946: Aitken teaches Mathematical Laboratory (up to 1961). Mathematics Department had lots of hand calculating machines. Aitken would pretend to use them. The history and development of numerical analysis in Scotland:a personal perspective p. 10/33

24 1946: Aitken succeeds Whittaker to the Chair of Mathematics. 1946: Aitken teaches Mathematical Laboratory (up to 1961). Mathematics Department had lots of hand calculating machines. Aitken would pretend to use them. 1961: Name Mathematical Laboratory changed to Numerical Analysis. The history and development of numerical analysis in Scotland:a personal perspective p. 10/33

25 Edinburgh Honours Exam 1960 The history and development of numerical analysis in Scotland:a personal perspective p. 11/33

26 Edinburgh Honours Exam 1961 The history and development of numerical analysis in Scotland:a personal perspective p. 12/33

27 1961: Edinburgh invited to apply for computer allocation in current funding round. Aitken decides no requirement. The history and development of numerical analysis in Scotland:a personal perspective p. 13/33

28 1961: Edinburgh invited to apply for computer allocation in current funding round. Aitken decides no requirement. 1963: Edinburgh University Computer Unit set up with Sidney Michaelson as Director. The history and development of numerical analysis in Scotland:a personal perspective p. 13/33

29 1961: Edinburgh invited to apply for computer allocation in current funding round. Aitken decides no requirement. 1963: Edinburgh University Computer Unit set up with Sidney Michaelson as Director. 1963: M R Osborne appointed Assistant Director (interests finite difference methods for ODEs and PDEs). The history and development of numerical analysis in Scotland:a personal perspective p. 13/33

30 1961: Edinburgh invited to apply for computer allocation in current funding round. Aitken decides no requirement. 1963: Edinburgh University Computer Unit set up with Sidney Michaelson as Director. 1963: M R Osborne appointed Assistant Director (interests finite difference methods for ODEs and PDEs). 1964: Donald Kershaw appointed (interests differential and integral equations). The history and development of numerical analysis in Scotland:a personal perspective p. 13/33

31 1961: Edinburgh invited to apply for computer allocation in current funding round. Aitken decides no requirement. 1963: Edinburgh University Computer Unit set up with Sidney Michaelson as Director. 1963: M R Osborne appointed Assistant Director (interests finite difference methods for ODEs and PDEs). 1964: Donald Kershaw appointed (interests differential and integral equations). 1964: Land-line link to Manchester Atlas established. 15 minutes per day. The history and development of numerical analysis in Scotland:a personal perspective p. 13/33

32 Manchester Atlas console The history and development of numerical analysis in Scotland:a personal perspective p. 14/33

33 M R Osborne (1977) The history and development of numerical analysis in Scotland:a personal perspective p. 15/33

34 2. Personal Stuff 1960: Entered University of Edinburgh to study Physics. Taught by Aitken from Determinants and Matrices. Some time set aside for tricks and demonstrations of his memory. The history and development of numerical analysis in Scotland:a personal perspective p. 16/33

35 2. Personal Stuff 1960: Entered University of Edinburgh to study Physics. Taught by Aitken from Determinants and Matrices. Some time set aside for tricks and demonstrations of his memory. 1962/63: Switched to Mathematics. Took Honours course in Numerical Analysis taught by James Fulton (took over from Aitken in 1961). The history and development of numerical analysis in Scotland:a personal perspective p. 16/33

36 2. Personal Stuff 1960: Entered University of Edinburgh to study Physics. Taught by Aitken from Determinants and Matrices. Some time set aside for tricks and demonstrations of his memory. 1962/63: Switched to Mathematics. Took Honours course in Numerical Analysis taught by James Fulton (took over from Aitken in 1961). 1963/64: Repeated NA course; lectures from Osborne on BVPs for ODEs. The history and development of numerical analysis in Scotland:a personal perspective p. 16/33

37 2. Personal Stuff 1960: Entered University of Edinburgh to study Physics. Taught by Aitken from Determinants and Matrices. Some time set aside for tricks and demonstrations of his memory. 1962/63: Switched to Mathematics. Took Honours course in Numerical Analysis taught by James Fulton (took over from Aitken in 1961). 1963/64: Repeated NA course; lectures from Osborne on BVPs for ODEs. Used books of tables (2 feet by 3 feet), hand operated calculating machines. The history and development of numerical analysis in Scotland:a personal perspective p. 16/33

38 Brunsviga (left) and Facit The history and development of numerical analysis in Scotland:a personal perspective p. 17/33

39 1964: Graduated. Joined Computer Unit as Demonstrator. Learned Atlas Autocode. Programs punched onto paper tape and sent by land line to Manchester Atlas. Started to work with Osborne on Chebyshev approximation problems: using linear programming. The history and development of numerical analysis in Scotland:a personal perspective p. 18/33

40 3. St Andrews and Edinburgh 1946: A R Mitchell joins staff at St Andrews, starts PhD with D E Rutherford. Rutherford worked in lattice theory; thesis on relaxation methods in compressible flow. Mitchell developed interest in NA, initially as means to tackle fluid dynamics problems. The history and development of numerical analysis in Scotland:a personal perspective p. 19/33

41 3. St Andrews and Edinburgh 1946: A R Mitchell joins staff at St Andrews, starts PhD with D E Rutherford. Rutherford worked in lattice theory; thesis on relaxation methods in compressible flow. Mitchell developed interest in NA, initially as means to tackle fluid dynamics problems. 1950: Awarded PhD; stays on staff at St Andrews. The history and development of numerical analysis in Scotland:a personal perspective p. 19/33

42 3. St Andrews and Edinburgh 1946: A R Mitchell joins staff at St Andrews, starts PhD with D E Rutherford. Rutherford worked in lattice theory; thesis on relaxation methods in compressible flow. Mitchell developed interest in NA, initially as means to tackle fluid dynamics problems. 1950: Awarded PhD; stays on staff at St Andrews. 1953/54: Teaches Honours course in numerical analysis The history and development of numerical analysis in Scotland:a personal perspective p. 19/33

43 1959: J D Lambert appointed to staff; becomes Mitchell s third PhD student. Worked on idea of Mitchell s to incorporate higher derivatives into ODE methods. The history and development of numerical analysis in Scotland:a personal perspective p. 20/33

44 1959: J D Lambert appointed to staff; becomes Mitchell s third PhD student. Worked on idea of Mitchell s to incorporate higher derivatives into ODE methods. 1965: St Andrews numerical analysis group expanded to about 7. (Fairweather, Keast, Gourlay, Morris, Shaw) The history and development of numerical analysis in Scotland:a personal perspective p. 20/33

45 1959: J D Lambert appointed to staff; becomes Mitchell s third PhD student. Worked on idea of Mitchell s to incorporate higher derivatives into ODE methods. 1965: St Andrews numerical analysis group expanded to about 7. (Fairweather, Keast, Gourlay, Morris, Shaw) Edinburgh and St Andrews main centres for numerical analysis in Scotland. Osborne and Mitchell keen for more interaction. Osborne suggested Conference, St Andrews was chosen. The history and development of numerical analysis in Scotland:a personal perspective p. 20/33

46 A R Mitchell and M R Osborne in Dundee in 1997 The history and development of numerical analysis in Scotland:a personal perspective p. 21/33

47 June 1965: Symposium on Solution of Differential Equations, St Andrews. Main speakers: Osborne, Mitchell, Kershaw, Lambert. 25 participants, 3 days. John Mason, Gary Tee, Ken Wright,.. attended. The history and development of numerical analysis in Scotland:a personal perspective p. 22/33

48 June 1965: Symposium on Solution of Differential Equations, St Andrews. Main speakers: Osborne, Mitchell, Kershaw, Lambert. 25 participants, 3 days. John Mason, Gary Tee, Ken Wright,.. attended. 1965: One day meeting on Chebyshev approximation in Edinburgh: speakers Curtis, Powell, Osborne, Watson. The history and development of numerical analysis in Scotland:a personal perspective p. 22/33

49 June 1965: Symposium on Solution of Differential Equations, St Andrews. Main speakers: Osborne, Mitchell, Kershaw, Lambert. 25 participants, 3 days. John Mason, Gary Tee, Ken Wright,.. attended. 1965: One day meeting on Chebyshev approximation in Edinburgh: speakers Curtis, Powell, Osborne, Watson. December 1965: Osborne moves to ANU. The history and development of numerical analysis in Scotland:a personal perspective p. 22/33

50 June 1965: Symposium on Solution of Differential Equations, St Andrews. Main speakers: Osborne, Mitchell, Kershaw, Lambert. 25 participants, 3 days. John Mason, Gary Tee, Ken Wright,.. attended. 1965: One day meeting on Chebyshev approximation in Edinburgh: speakers Curtis, Powell, Osborne, Watson. December 1965: Osborne moves to ANU. 1966: Lambert moves to Aberdeen, I move to ANU. The history and development of numerical analysis in Scotland:a personal perspective p. 22/33

51 June 1965: Symposium on Solution of Differential Equations, St Andrews. Main speakers: Osborne, Mitchell, Kershaw, Lambert. 25 participants, 3 days. John Mason, Gary Tee, Ken Wright,.. attended. 1965: One day meeting on Chebyshev approximation in Edinburgh: speakers Curtis, Powell, Osborne, Watson. December 1965: Osborne moves to ANU. 1966: Lambert moves to Aberdeen, I move to ANU. 1967: Mitchell organises second Conference on DEs in St Andrews. 85 participants. UK event. The history and development of numerical analysis in Scotland:a personal perspective p. 22/33

52 4. Dundee 1965: D S Jones appointed to Chair of Mathematics in Queen s College, Dundee. Starts up MSc in Numerical Analysis and Programming (taught mainly by R P Pearce). The history and development of numerical analysis in Scotland:a personal perspective p. 23/33

53 4. Dundee 1965: D S Jones appointed to Chair of Mathematics in Queen s College, Dundee. Starts up MSc in Numerical Analysis and Programming (taught mainly by R P Pearce). 1967: University of Dundee formed. Mitchell moved from St Andrews to Chair of Numerical Analysis. Joined by Lambert, Gourlay, Morris. The history and development of numerical analysis in Scotland:a personal perspective p. 23/33

54 4. Dundee 1965: D S Jones appointed to Chair of Mathematics in Queen s College, Dundee. Starts up MSc in Numerical Analysis and Programming (taught mainly by R P Pearce). 1967: University of Dundee formed. Mitchell moved from St Andrews to Chair of Numerical Analysis. Joined by Lambert, Gourlay, Morris. Research students recruited Wait finite element interest. Funding from MoD, NCR used to bring post docs. The history and development of numerical analysis in Scotland:a personal perspective p. 23/33

55 4. Dundee 1965: D S Jones appointed to Chair of Mathematics in Queen s College, Dundee. Starts up MSc in Numerical Analysis and Programming (taught mainly by R P Pearce). 1967: University of Dundee formed. Mitchell moved from St Andrews to Chair of Numerical Analysis. Joined by Lambert, Gourlay, Morris. Research students recruited Wait finite element interest. Funding from MoD, NCR used to bring post docs. Centre of gravity of numerical analysis in Scotland shifts to Dundee. The history and development of numerical analysis in Scotland:a personal perspective p. 23/33

56 1969: Conference on the numerical solution of DEs held in Dundee: 148 participants, 8 invited speakers all from overseas, 45 others from outside UK. Organized by Morris. I arrived in Dundee shortly after. The history and development of numerical analysis in Scotland:a personal perspective p. 24/33

57 1969: Conference on the numerical solution of DEs held in Dundee: 148 participants, 8 invited speakers all from overseas, 45 others from outside UK. Organized by Morris. I arrived in Dundee shortly after. 1970: D F Griffiths appointed. The history and development of numerical analysis in Scotland:a personal perspective p. 24/33

58 1969: Conference on the numerical solution of DEs held in Dundee: 148 participants, 8 invited speakers all from overseas, 45 others from outside UK. Organized by Morris. I arrived in Dundee shortly after. 1970: D F Griffiths appointed. 1970/71: UK SRC Funding for Dundee: to promote the theory of numerical methods and upgrade the study of NA in British Universities and colleges. The history and development of numerical analysis in Scotland:a personal perspective p. 24/33

59 1969: Conference on the numerical solution of DEs held in Dundee: 148 participants, 8 invited speakers all from overseas, 45 others from outside UK. Organized by Morris. I arrived in Dundee shortly after. 1970: D F Griffiths appointed. 1970/71: UK SRC Funding for Dundee: to promote the theory of numerical methods and upgrade the study of NA in British Universities and colleges. 5 Conferences, with 2 large ones in 1971: Conference on Applications of NA (170 participants); Numerical Methods for Nonlinear Optimization (200). 34 leading numerical analysts visited Dundee for periods up to a year. The history and development of numerical analysis in Scotland:a personal perspective p. 24/33

60 1973: Conference on Numerical Solution of DEs in July with 230 participants. I edited Proceedings (of invited talks) and recorded this as 5th in biennial series. The history and development of numerical analysis in Scotland:a personal perspective p. 25/33

61 1973: Conference on Numerical Solution of DEs in July with 230 participants. I edited Proceedings (of invited talks) and recorded this as 5th in biennial series. 1973: Roger Fletcher appointed from Harwell. The history and development of numerical analysis in Scotland:a personal perspective p. 25/33

62 1973: Conference on Numerical Solution of DEs in July with 230 participants. I edited Proceedings (of invited talks) and recorded this as 5th in biennial series. 1973: Roger Fletcher appointed from Harwell. 1975: Conference on Numerical Analysis (200 participants). Series survived departure of Morris for Waterloo. I took over organization. The history and development of numerical analysis in Scotland:a personal perspective p. 25/33

63 1973: Conference on Numerical Solution of DEs in July with 230 participants. I edited Proceedings (of invited talks) and recorded this as 5th in biennial series. 1973: Roger Fletcher appointed from Harwell. 1975: Conference on Numerical Analysis (200 participants). Series survived departure of Morris for Waterloo. I took over organization. Griffiths and I jointly organized meetings from The history and development of numerical analysis in Scotland:a personal perspective p. 25/33

64 5. Computer facilities in Dundee 1961: Stantec Zebra ( 13,000) Valve machine, i/o paper tape, 8K words, memory on magnetic drum ( 1990 programmable calculator but slower) The history and development of numerical analysis in Scotland:a personal perspective p. 26/33

65 5. Computer facilities in Dundee 1961: Stantec Zebra ( 13,000) Valve machine, i/o paper tape, 8K words, memory on magnetic drum ( 1990 programmable calculator but slower) 1965: Flowers Report (Computers for Research): Edinburgh proposed as Regional Centre, ICL machine for Dundee. The history and development of numerical analysis in Scotland:a personal perspective p. 26/33

66 5. Computer facilities in Dundee 1961: Stantec Zebra ( 13,000) Valve machine, i/o paper tape, 8K words, memory on magnetic drum ( 1990 programmable calculator but slower) 1965: Flowers Report (Computers for Research): Edinburgh proposed as Regional Centre, ICL machine for Dundee. 1967: Elliott K memory, magnetic tape, ALGOL, FORTRAN, punched cards. The history and development of numerical analysis in Scotland:a personal perspective p. 26/33

67 Punched card The history and development of numerical analysis in Scotland:a personal perspective p. 27/33

68 Card punch machine The history and development of numerical analysis in Scotland:a personal perspective p. 28/33

69 1971: Kent Operating System On-line remote programming in BASIC. Teletypes 110 baud (10 chars per second). The history and development of numerical analysis in Scotland:a personal perspective p. 29/33

70 1971: Kent Operating System On-line remote programming in BASIC. Teletypes 110 baud (10 chars per second). 1974: Dial-up modems at 2400 baud The history and development of numerical analysis in Scotland:a personal perspective p. 29/33

71 1971: Kent Operating System On-line remote programming in BASIC. Teletypes 110 baud (10 chars per second). 1974: Dial-up modems at 2400 baud 1977: DEC System 10 Campus wired for remote access. The history and development of numerical analysis in Scotland:a personal perspective p. 29/33

72 1971: Kent Operating System On-line remote programming in BASIC. Teletypes 110 baud (10 chars per second). 1974: Dial-up modems at 2400 baud 1977: DEC System 10 Campus wired for remote access. 1979: Microcomputers. Black and white VDUs (4800 baud). to limited range of contacts. The history and development of numerical analysis in Scotland:a personal perspective p. 29/33

73 1984: JANET (Joint Academic Network) Connected about 50 sites in UK. Terminal access for logging on to campus and national computers (file transfer, ). The history and development of numerical analysis in Scotland:a personal perspective p. 30/33

74 1984: JANET (Joint Academic Network) Connected about 50 sites in UK. Terminal access for logging on to campus and national computers (file transfer, ). 1985: Colour screens. The history and development of numerical analysis in Scotland:a personal perspective p. 30/33

75 1984: JANET (Joint Academic Network) Connected about 50 sites in UK. Terminal access for logging on to campus and national computers (file transfer, ). 1985: Colour screens. 1987: PRIME GB disk space. The history and development of numerical analysis in Scotland:a personal perspective p. 30/33

76 1987: Distributed systems replacing mainframes. Mathematics got SUN Workstations. SUN 3/160 file server, SUN 3s SUN 4s. through designated gateways. (US and UK used different address formats.) nroff, troff for wordprocessing LaTex. The history and development of numerical analysis in Scotland:a personal perspective p. 31/33

77 1987: Distributed systems replacing mainframes. Mathematics got SUN Workstations. SUN 3/160 file server, SUN 3s SUN 4s. through designated gateways. (US and UK used different address formats.) nroff, troff for wordprocessing LaTex. 1990: Kind of facilities we take for granted today. The history and development of numerical analysis in Scotland:a personal perspective p. 31/33

78 6. Postscript 1990s: Alterations in funding arrangements. Universities with large undergraduate numbers well placed for growth. The history and development of numerical analysis in Scotland:a personal perspective p. 32/33

79 6. Postscript 1990s: Alterations in funding arrangements. Universities with large undergraduate numbers well placed for growth. Strathclyde, Edinburgh, Heriot-Watt built up NA groups. The history and development of numerical analysis in Scotland:a personal perspective p. 32/33

80 6. Postscript 1990s: Alterations in funding arrangements. Universities with large undergraduate numbers well placed for growth. Strathclyde, Edinburgh, Heriot-Watt built up NA groups. 1992: Scottish Computational Mathematics Symposium annual series of one-day meetings alternating between Strathclyde and Heriot-Watt. The history and development of numerical analysis in Scotland:a personal perspective p. 32/33

81 6. Postscript 1990s: Alterations in funding arrangements. Universities with large undergraduate numbers well placed for growth. Strathclyde, Edinburgh, Heriot-Watt built up NA groups. 1992: Scottish Computational Mathematics Symposium annual series of one-day meetings alternating between Strathclyde and Heriot-Watt. 2007: Last Dundee biennial conference. The history and development of numerical analysis in Scotland:a personal perspective p. 32/33

82 6. Postscript 1990s: Alterations in funding arrangements. Universities with large undergraduate numbers well placed for growth. Strathclyde, Edinburgh, Heriot-Watt built up NA groups. 1992: Scottish Computational Mathematics Symposium annual series of one-day meetings alternating between Strathclyde and Heriot-Watt. 2007: Last Dundee biennial conference. Now more numerical analysts at Strathclyde than mathematicians (of all kinds) at Dundee. Shift in centre of gravity. The history and development of numerical analysis in Scotland:a personal perspective p. 32/33

83 THE END The history and development of numerical analysis in Scotland:a personal perspective p. 33/33