The history and development ofnumerical analysis in Scotland:
a personal perspectiveAlistair Watson
Mathematics Division
University of Dundee
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Basic issues
What is numerical analysis?
How old is it?
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Basic issues
What is numerical analysis?
How old is it?
Possible answers:
Study of algorithms for the problems of continuousmathematics.
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Basic issues
What is numerical analysis?
How old is it?
Possible answers:
Study of algorithms for the problems of continuousmathematics.
Goes back centuries.
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“Modern” numerical analysis.
Association with calculating machines.
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“Modern” numerical analysis.
Association with calculating machines.
Usually with programmable computers.1947: Paper by von Neumann and Goldstine.
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“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).
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“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.
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Starting point: first treatment of what we now think of asnumerical analysis, in conjunction with use ofcalculating machines.
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Starting point: first treatment of what we now think of asnumerical analysis, in conjunction with use ofcalculating machines.
1913: Origin in Edinburgh, Scotland.
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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
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1. Edinburgh: early years
1912: E T Whittaker (1873–1956) arrives from Dublin.
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1. Edinburgh: early years
1912: E T Whittaker (1873–1956) arrives from Dublin.
1913: Opens Mathematical Laboratory, where studentstrained to do machine calculations.Subjects taught include: interpolation, difference formulae,linear equations, numerical integration, least squares,numerical solution of DEs,...
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1. Edinburgh: early years
1912: E T Whittaker (1873–1956) arrives from Dublin.
1913: Opens Mathematical Laboratory, where studentstrained to do machine calculations.Subjects taught include: interpolation, difference formulae,linear equations, numerical integration, least squares,numerical solution of DEs,...
1915: Book by David Gibb: “A course in interpolation andnumerical integration for the mathematical laboratory”.Preliminary note on computation:
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1. Edinburgh: early years
1912: E T Whittaker (1873–1956) arrives from Dublin.
1913: Opens Mathematical Laboratory, where studentstrained to do machine calculations.Subjects taught include: interpolation, difference formulae,linear equations, numerical integration, least squares,numerical solution of DEs,...
1915: Book by David Gibb: “A course in interpolation andnumerical integration for the mathematical laboratory”.Preliminary note on computation:
� 1920: Honours course entitled Mathematical Laboratory.
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E T Whittaker in 1930
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1924: Book by Whittaker and Robinson “The Calculus ofObservations; a Treatise on Numerical Mathematics”.From Preface: “ .. present volume represents courses oflectures given during 1913 –1923 by Professor Whittaker tostudents in the Mathematical Laboratory..”.
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1924: Book by Whittaker and Robinson “The Calculus ofObservations; a Treatise on Numerical Mathematics”.From Preface: “ .. present volume represents courses oflectures given during 1913 –1923 by Professor Whittaker tostudents in the Mathematical Laboratory..”.
1925: A C Aitken (1895–1967) appointed to a Lectureshipin Actuarial Mathematics. Applied matrix algebra tonumerical analysis and statistics. Published on polynomialequations and eigenvalue problems,...
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1924: Book by Whittaker and Robinson “The Calculus ofObservations; a Treatise on Numerical Mathematics”.From Preface: “ .. present volume represents courses oflectures given during 1913 –1923 by Professor Whittaker tostudents in the Mathematical Laboratory..”.
1925: A C Aitken (1895–1967) appointed to a Lectureshipin Actuarial Mathematics. Applied matrix algebra tonumerical analysis and statistics. Published on polynomialequations and eigenvalue problems,...
1932: Book by Turnbull and Aitken: “An introduction to thetheory of canonical Matrices”. Contains Householdermatrices.
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A. C. Aitken
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1946: Aitken succeeds Whittaker to the Chair ofMathematics.
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1946: Aitken succeeds Whittaker to the Chair ofMathematics.
�
1946: Aitken teaches Mathematical Laboratory (up to1961).
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1946: Aitken succeeds Whittaker to the Chair ofMathematics.
�
1946: Aitken teaches Mathematical Laboratory (up to1961).
Mathematics Department had lots of hand calculatingmachines. Aitken would pretend to use them.
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1946: Aitken succeeds Whittaker to the Chair ofMathematics.
�
1946: Aitken teaches Mathematical Laboratory (up to1961).
Mathematics Department had lots of hand calculatingmachines. Aitken would pretend to use them.
1961: Name Mathematical Laboratory changed toNumerical Analysis.
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Edinburgh Honours Exam 1960
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Edinburgh Honours Exam 1961
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1961: Edinburgh invited to apply for computer allocation incurrent funding round. Aitken decides no requirement.
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1961: Edinburgh invited to apply for computer allocation incurrent funding round. Aitken decides no requirement.
1963: Edinburgh University Computer Unit set up withSidney Michaelson as Director.
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1961: Edinburgh invited to apply for computer allocation incurrent funding round. Aitken decides no requirement.
1963: Edinburgh University Computer Unit set up withSidney Michaelson as Director.
1963: M R Osborne appointed Assistant Director (interestsfinite difference methods for ODEs and PDEs).
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1961: Edinburgh invited to apply for computer allocation incurrent funding round. Aitken decides no requirement.
1963: Edinburgh University Computer Unit set up withSidney Michaelson as Director.
1963: M R Osborne appointed Assistant Director (interestsfinite difference methods for ODEs and PDEs).
1964: Donald Kershaw appointed (interests differential andintegral equations).
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1961: Edinburgh invited to apply for computer allocation incurrent funding round. Aitken decides no requirement.
1963: Edinburgh University Computer Unit set up withSidney Michaelson as Director.
1963: M R Osborne appointed Assistant Director (interestsfinite difference methods for ODEs and PDEs).
1964: Donald Kershaw appointed (interests differential andintegral equations).
1964: Land-line link to Manchester Atlas established. 15minutes per day.
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Manchester Atlas console
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M R Osborne (1977)
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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 hismemory.
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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 hismemory.
1962/63: Switched to Mathematics. Took Honours course inNumerical Analysis taught by James Fulton (took over fromAitken in 1961).
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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 hismemory.
1962/63: Switched to Mathematics. Took Honours course inNumerical Analysis taught by James Fulton (took over fromAitken in 1961).
1963/64: Repeated NA course; lectures from Osborne onBVPs for ODEs.
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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 hismemory.
1962/63: Switched to Mathematics. Took Honours course inNumerical Analysis taught by James Fulton (took over fromAitken in 1961).
1963/64: Repeated NA course; lectures from Osborne onBVPs for ODEs.
Used books of tables (2 feet by 3 feet), hand operatedcalculating machines.
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Brunsviga (left) and Facit
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1964: Graduated. Joined Computer Unit as Demonstrator.
Learned Atlas Autocode. Programs punched onto papertape and sent by land line to Manchester Atlas.
Started to work with Osborne on Chebyshev approximationproblems: using linear programming.
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3. St Andrews and Edinburgh
1946: A R Mitchell joins staff at St Andrews, starts PhD withD E Rutherford.
Rutherford worked in lattice theory; thesis on relaxationmethods in compressible flow.
Mitchell developed interest in NA, initially as means totackle fluid dynamics problems.
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3. St Andrews and Edinburgh
1946: A R Mitchell joins staff at St Andrews, starts PhD withD E Rutherford.
Rutherford worked in lattice theory; thesis on relaxationmethods in compressible flow.
Mitchell developed interest in NA, initially as means totackle fluid dynamics problems.
1950: Awarded PhD; stays on staff at St Andrews.
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3. St Andrews and Edinburgh
1946: A R Mitchell joins staff at St Andrews, starts PhD withD E Rutherford.
Rutherford worked in lattice theory; thesis on relaxationmethods in compressible flow.
Mitchell developed interest in NA, initially as means totackle fluid dynamics problems.
1950: Awarded PhD; stays on staff at St Andrews.
1953/54: Teaches Honours course in numerical analysis
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1959: J D Lambert appointed to staff; becomes Mitchell’sthird PhD student.
Worked on idea of Mitchell’s to incorporate higherderivatives into ODE methods.
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1959: J D Lambert appointed to staff; becomes Mitchell’sthird PhD student.
Worked on idea of Mitchell’s to incorporate higherderivatives into ODE methods.
1965: St Andrews numerical analysis group expanded toabout 7. (Fairweather, Keast, Gourlay, Morris, Shaw)
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1959: J D Lambert appointed to staff; becomes Mitchell’sthird PhD student.
Worked on idea of Mitchell’s to incorporate higherderivatives into ODE methods.
1965: St Andrews numerical analysis group expanded toabout 7. (Fairweather, Keast, Gourlay, Morris, Shaw)
Edinburgh and St Andrews main centres for numericalanalysis in Scotland. Osborne and Mitchell keen for moreinteraction.
Osborne suggested Conference, St Andrews was chosen.
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A R Mitchell and M R Osborne in Dundee in 1997
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June 1965: “Symposium on Solution of DifferentialEquations”, St Andrews.Main speakers: Osborne, Mitchell, Kershaw, Lambert.
� 25 participants, 3 days.John Mason, Gary Tee, Ken Wright,.. attended.
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June 1965: “Symposium on Solution of DifferentialEquations”, 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 inEdinburgh: speakers Curtis, Powell, Osborne, Watson.
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June 1965: “Symposium on Solution of DifferentialEquations”, 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 inEdinburgh: speakers Curtis, Powell, Osborne, Watson.
December 1965: Osborne moves to ANU.
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June 1965: “Symposium on Solution of DifferentialEquations”, 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 inEdinburgh: speakers Curtis, Powell, Osborne, Watson.
December 1965: Osborne moves to ANU.
1966: Lambert moves to Aberdeen, I move to ANU.
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June 1965: “Symposium on Solution of DifferentialEquations”, 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 inEdinburgh: 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 StAndrews. 85 participants. UK event.
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4. Dundee
1965: D S Jones appointed to Chair of Mathematics inQueen’s College, Dundee.Starts up MSc in Numerical Analysis and Programming(taught mainly by R P Pearce).
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4. Dundee
1965: D S Jones appointed to Chair of Mathematics inQueen’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 StAndrews to Chair of Numerical Analysis.Joined by Lambert, Gourlay, Morris.
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4. Dundee
1965: D S Jones appointed to Chair of Mathematics inQueen’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 StAndrews to Chair of Numerical Analysis.Joined by Lambert, Gourlay, Morris.
Research students recruited.1968 Wait � finite element interest.Funding from MoD, NCR used to bring post docs.
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4. Dundee
1965: D S Jones appointed to Chair of Mathematics inQueen’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 StAndrews to Chair of Numerical Analysis.Joined by Lambert, Gourlay, Morris.
Research students recruited.1968 Wait � finite element interest.Funding from MoD, NCR used to bring post docs.
Centre of gravity of numerical analysis in Scotland shifts toDundee.
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1969: “Conference on the numerical solution of DEs” heldin Dundee: 148 participants, 8 invited speakers all fromoverseas, 45 others from outside UK. Organized by Morris.I arrived in Dundee shortly after.
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1969: “Conference on the numerical solution of DEs” heldin Dundee: 148 participants, 8 invited speakers all fromoverseas, 45 others from outside UK. Organized by Morris.I arrived in Dundee shortly after.
1970: D F Griffiths appointed.
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1969: “Conference on the numerical solution of DEs” heldin Dundee: 148 participants, 8 invited speakers all fromoverseas, 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 thetheory of numerical methods and upgrade the study of NAin British Universities and colleges”.
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1969: “Conference on the numerical solution of DEs” heldin Dundee: 148 participants, 8 invited speakers all fromoverseas, 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 thetheory of numerical methods and upgrade the study of NAin British Universities and colleges”.
5 Conferences, with 2 large ones in 1971: “Conference onApplications of NA” (170 participants); “Numerical Methodsfor Nonlinear Optimization” (200). 34 leading numericalanalysts visited Dundee for periods up to a year.
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1973: “Conference on Numerical Solution of DEs” in Julywith 230 participants.I edited Proceedings (of invited talks) and recorded this as5th in biennial series.
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1973: “Conference on Numerical Solution of DEs” in Julywith 230 participants.I edited Proceedings (of invited talks) and recorded this as5th in biennial series.
1973: Roger Fletcher appointed from Harwell.
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1973: “Conference on Numerical Solution of DEs” in Julywith 230 participants.I edited Proceedings (of invited talks) and recorded this as5th in biennial series.
1973: Roger Fletcher appointed from Harwell.
1975: “Conference on Numerical Analysis” (200participants).Series survived departure of Morris for Waterloo. I tookover organization.
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1973: “Conference on Numerical Solution of DEs” in Julywith 230 participants.I edited Proceedings (of invited talks) and recorded this as5th in biennial series.
1973: Roger Fletcher appointed from Harwell.
1975: “Conference on Numerical Analysis” (200participants).Series survived departure of Morris for Waterloo. I tookover organization.
Griffiths and I jointly organized meetings from 1985.
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5. Computer facilities in Dundee
1961: Stantec Zebra (£13,000)
Valve machine, i/o paper tape, 8K words, memory onmagnetic drum( � 1990 programmable calculator but slower)
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5. Computer facilities in Dundee
1961: Stantec Zebra (£13,000)
Valve machine, i/o paper tape, 8K words, memory onmagnetic drum( � 1990 programmable calculator but slower)
1965: Flowers Report (Computers for Research):Edinburgh proposed as Regional Centre, ICL machine forDundee.
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5. Computer facilities in Dundee
1961: Stantec Zebra (£13,000)
Valve machine, i/o paper tape, 8K words, memory onmagnetic drum( � 1990 programmable calculator but slower)
1965: Flowers Report (Computers for Research):Edinburgh proposed as Regional Centre, ICL machine forDundee.
1967: Elliott 4130
32K memory, magnetic tape, ALGOL, FORTRAN, punchedcards.
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Punched card
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Card punch machine
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1971: Kent Operating SystemOn-line remote programming in BASIC.Teletypes – 110 baud (10 chars per second).
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1971: Kent Operating SystemOn-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
1971: Kent Operating SystemOn-line remote programming in BASIC.Teletypes – 110 baud (10 chars per second).
1974: Dial-up modems at 2400 baud
1977: DEC System 10Campus wired for remote access.
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1971: Kent Operating SystemOn-line remote programming in BASIC.Teletypes – 110 baud (10 chars per second).
1974: Dial-up modems at 2400 baud
1977: DEC System 10Campus wired for remote access.
1979: Microcomputers.Black and white VDUs (4800 baud).Email to limited range of contacts.
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1984: JANET (Joint Academic Network)Connected about 50 sites in UK.Terminal access for logging on to campus and nationalcomputers (file transfer, email).
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1984: JANET (Joint Academic Network)Connected about 50 sites in UK.Terminal access for logging on to campus and nationalcomputers (file transfer, email).
1985: Colour screens.
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1984: JANET (Joint Academic Network)Connected about 50 sites in UK.Terminal access for logging on to campus and nationalcomputers (file transfer, email).
1985: Colour screens.
1987: PRIME 6350
10 GB disk space.
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� 1987: Distributed systems replacing mainframes.Mathematics got SUN Workstations.SUN 3/160 file server, SUN 3s SUN 4s.
Email through designated gateways. (US and UK useddifferent address formats.)
nroff, troff for wordprocessing � LaTex .
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� 1987: Distributed systems replacing mainframes.Mathematics got SUN Workstations.SUN 3/160 file server, SUN 3s SUN 4s.
Email through designated gateways. (US and UK useddifferent address formats.)
nroff, troff for wordprocessing � LaTex .
� 1990: Kind of facilities we take for granted today.
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6. Postscript
1990s: Alterations in funding arrangements.Universities with large undergraduate numbers well placedfor growth.
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6. Postscript
1990s: Alterations in funding arrangements.Universities with large undergraduate numbers well placedfor growth.
Strathclyde, Edinburgh, Heriot-Watt built up NA groups.
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6. Postscript
1990s: Alterations in funding arrangements.Universities with large undergraduate numbers well placedfor growth.
Strathclyde, Edinburgh, Heriot-Watt built up NA groups.
�
1992: Scottish Computational Mathematics Symposium –annual series of one-day meetings alternating betweenStrathclyde and Heriot-Watt.
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6. Postscript
1990s: Alterations in funding arrangements.Universities with large undergraduate numbers well placedfor growth.
Strathclyde, Edinburgh, Heriot-Watt built up NA groups.
�
1992: Scottish Computational Mathematics Symposium –annual series of one-day meetings alternating betweenStrathclyde and Heriot-Watt.
2007: Last Dundee biennial conference.
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6. Postscript
1990s: Alterations in funding arrangements.Universities with large undergraduate numbers well placedfor growth.
Strathclyde, Edinburgh, Heriot-Watt built up NA groups.
�
1992: Scottish Computational Mathematics Symposium –annual series of one-day meetings alternating betweenStrathclyde and Heriot-Watt.
2007: Last Dundee biennial conference.
Now more numerical analysts at Strathclyde thanmathematicians (of all kinds) at Dundee.Shift in centre of gravity.
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THE END
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