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Arthur Sard

January 01, 1970

Arthur Sard (28 July 1909, New York City – 31 August 1980, Basel) was an American mathematician, famous for his work in differential topology and in spline interpolation. His fame stems primarily from Sard's theorem, which says that the set of critical values of a differential function which has sufficiently many derivatives has measure zero.[1]

Life and career edit

Arthur Sard was born and grew up in New York City and spent most of his adult life there. He attended the Friends Seminary, a private school in Manhattan, and went to college at Harvard University, where he received in 1931 his bachelor's degree, in 1932 his master's degree, and in 1936 his PhD under the direction of Marston Morse.[1] Sard's PhD thesis has the title The measure of the critical values of functions.[2] He was a member of the first faculty members at the then newly founded Queens College, where he worked from 1937 to 1970.[1]

During WWII Sard worked as a member, under the auspices of the Applied Mathematics Panel, of the Applied Mathematics Group of Columbia University (AMG-C), especially in support of fire control for machine guns mounted on bombers. Saunders Mac Lane wrote concerning Sard: “His judicious judgments kept AMG-C on a straight course, […]”.[3]

Sard retired as professor emeritus in 1970 at Queens College and then worked at La Jolla, where he spent five years as a research associate in the mathematics department of the University of California, San Diego. In 1975 he went to Binningen near Basel and taught at various European universities and research institutes. In 1978 he accepted an invitation from the Soviet Academy of Sciences to be a guest lecturer. In 1978 and 1979 he was a guest professor at the University of Siegen. Arthur Sard died on 31 August 1980 in Basel.[1]

From 1938 until his death Sard published almost forty research articles in refereed mathematical journals.[4] Also he wrote two monographs: in 1963 the book Linear Approximation and in 1971, in collaboration with Sol Weintraub, A Book of Splines.[4] According to the book review from the Deutsche Mathematiker-Vereinigung the content-rich („inhaltsreiche“) Linear Approximation is an important contribution to the theory of approximation of integrals, derivatives, function values, and sums („ein wesentlicher Beitrag zur Theorie der Approximation von Integralen, Ableitungen, Funktionswerten und Summen“).[5]

Works edit

Sard published thirty-eight research articles and the two following monographs:

  • Arthur Sard: Linear approximation. 2nd edn. American Mathematical Society, Providence, Rhode Island 1963, ISBN 0-8218-1509-1 (Mathematical Surveys and Monographs. Vol. 9).
  • Arthur Sard, Sol Weintraub: A Book of Splines. John Wiley & Sons Inc, New York 1971, ISBN 0-471-75415-3

Articles edit

  • Sard, Arthur (1942), "The measure of the critical values of differentiable maps", Bulletin of the American Mathematical Society, 48 (12): 883–890, doi:10.1090/S0002-9904-1942-07811-6, MR 0007523, Zbl 0063.06720
  • "The equivalence of n-measure and Lebesgue measure in En", Bull. Amer. Math. Soc., 49 (10): 758–759, 1943, doi:10.1090/s0002-9904-1943-08025-1, MR 0008837
  • "The remainder in approximations by moving averages", Bull. Amer. Math. Soc., 54 (8): 788–792, 1948, doi:10.1090/s0002-9904-1948-09081-4, MR 0028366
  • "Remainders as integrals of partial derivatives", Proc. Amer. Math. Soc., 3 (5): 732–741, 1952, doi:10.1090/s0002-9939-1952-0050645-6, MR 0050645
  • "Approximation and variance", Trans. Amer. Math. Soc., 73 (3): 428–446, 1952, doi:10.1090/s0002-9947-1952-0052688-x, MR 0052688
  • Sard, Arthur (1965), "Hausdorff Measure of Critical Images on Banach Manifolds", American Journal of Mathematics, 87 (1): 158–174, doi:10.2307/2373229, JSTOR 2373229, MR 0173748, Zbl 0137.42501 and also Sard, Arthur (1965), "Errata to Hausdorff measures of critical images on Banach manifolds", American Journal of Mathematics, 87 (3): 158–174, doi:10.2307/2373229, JSTOR 2373074, MR 0180649, Zbl 0137.42501
  • "Function spaces", Bull. Amer. Math. Soc., 71 (3, Part 1): 397–418, 1965, doi:10.1090/s0002-9904-1965-11282-4, MR 0185429
  • "A theory of cotypes", Bull. Amer. Math. Soc., 75 (5): 936–940, 1969, doi:10.1090/s0002-9904-1969-12302-5, MR 0245051

Sources edit

  • Franz-Jürgen Delvos, Walter Schempp: Arthur Sard – In Memoriam. In: Walter Schempp, Karl Zeller (eds.): Multivariate Approximation Theory II, Proceedings of the Conference held at the Mathematical Research Institute at Oberwolfach, Black Forest, February 8–12, 1982. Birkhäuser Verlag, Basel 1982, ISBN 3-7643-1373-0 (International Series of Numerical Mathematics. Vol. 61), pp. 23–24.

References edit

  1. ^ a b c d Delvos, Schempp (1982)
  2. ^ Notes. In: Bulletin of the American Mathematical Society. Vol. 43, No. 5, 1937, ISSN 1088-9485, (PDF)
  3. ^ Saunders Mac Lane: Requiem for the Skillful. In: Notices of the American Mathematical Society. Vol. 44, No. 2, 1997, ISSN 0002-9920, pp. 207–208 (PDF; 43 kB).
  4. ^ a b News and Notices. In: The American Mathematical Monthly, Vol. 88, No. 1, January 1981, Mathematical Association of America, ISSN 0002-9890, pp. 81–82 (online from JSTOR)
  5. ^ Manfred v. Golitschek, Paul Otto Runck: A. Sard, Linear Approximation. In: Jahresbericht der Deutschen Mathematiker-Vereinigung, Nr. 73, B. G. Teubner Verlag, Stuttgart 1971/72, ISSN 0012-0456, S. 31–33 (online from DigiZeitschriften in German)

External links edit

January 01, 1970
arthur, sard, july, 1909, york, city, august, 1980, basel, american, mathematician, famous, work, differential, topology, spline, interpolation, fame, stems, primarily, from, sard, theorem, which, says, that, critical, values, differential, function, which, su. Arthur Sard 28 July 1909 New York City 31 August 1980 Basel was an American mathematician famous for his work in differential topology and in spline interpolation His fame stems primarily from Sard s theorem which says that the set of critical values of a differential function which has sufficiently many derivatives has measure zero 1 Contents 1 Life and career 2 Works 2 1 Articles 3 Sources 4 References 5 External linksLife and career editArthur Sard was born and grew up in New York City and spent most of his adult life there He attended the Friends Seminary a private school in Manhattan and went to college at Harvard University where he received in 1931 his bachelor s degree in 1932 his master s degree and in 1936 his PhD under the direction of Marston Morse 1 Sard s PhD thesis has the title The measure of the critical values of functions 2 He was a member of the first faculty members at the then newly founded Queens College where he worked from 1937 to 1970 1 During WWII Sard worked as a member under the auspices of the Applied Mathematics Panel of the Applied Mathematics Group of Columbia University AMG C especially in support of fire control for machine guns mounted on bombers Saunders Mac Lane wrote concerning Sard His judicious judgments kept AMG C on a straight course 3 Sard retired as professor emeritus in 1970 at Queens College and then worked at La Jolla where he spent five years as a research associate in the mathematics department of the University of California San Diego In 1975 he went to Binningen near Basel and taught at various European universities and research institutes In 1978 he accepted an invitation from the Soviet Academy of Sciences to be a guest lecturer In 1978 and 1979 he was a guest professor at the University of Siegen Arthur Sard died on 31 August 1980 in Basel 1 From 1938 until his death Sard published almost forty research articles in refereed mathematical journals 4 Also he wrote two monographs in 1963 the book Linear Approximation and in 1971 in collaboration with Sol Weintraub A Book of Splines 4 According to the book review from the Deutsche Mathematiker Vereinigung the content rich inhaltsreiche Linear Approximation is an important contribution to the theory of approximation of integrals derivatives function values and sums ein wesentlicher Beitrag zur Theorie der Approximation von Integralen Ableitungen Funktionswerten und Summen 5 Works editSard published thirty eight research articles and the two following monographs Arthur Sard Linear approximation 2nd edn American Mathematical Society Providence Rhode Island 1963 ISBN 0 8218 1509 1 Mathematical Surveys and Monographs Vol 9 Arthur Sard Sol Weintraub A Book of Splines John Wiley amp Sons Inc New York 1971 ISBN 0 471 75415 3 Articles edit Sard Arthur 1942 The measure of the critical values of differentiable maps Bulletin of the American Mathematical Society 48 12 883 890 doi 10 1090 S0002 9904 1942 07811 6 MR 0007523 Zbl 0063 06720 The equivalence of n measure and Lebesgue measure in En Bull Amer Math Soc 49 10 758 759 1943 doi 10 1090 s0002 9904 1943 08025 1 MR 0008837 The remainder in approximations by moving averages Bull Amer Math Soc 54 8 788 792 1948 doi 10 1090 s0002 9904 1948 09081 4 MR 0028366 Remainders as integrals of partial derivatives Proc Amer Math Soc 3 5 732 741 1952 doi 10 1090 s0002 9939 1952 0050645 6 MR 0050645 Approximation and variance Trans Amer Math Soc 73 3 428 446 1952 doi 10 1090 s0002 9947 1952 0052688 x MR 0052688 Sard Arthur 1965 Hausdorff Measure of Critical Images on Banach Manifolds American Journal of Mathematics 87 1 158 174 doi 10 2307 2373229 JSTOR 2373229 MR 0173748 Zbl 0137 42501 and also Sard Arthur 1965 Errata to Hausdorff measures of critical images on Banach manifolds American Journal of Mathematics 87 3 158 174 doi 10 2307 2373229 JSTOR 2373074 MR 0180649 Zbl 0137 42501 Function spaces Bull Amer Math Soc 71 3 Part 1 397 418 1965 doi 10 1090 s0002 9904 1965 11282 4 MR 0185429 A theory of cotypes Bull Amer Math Soc 75 5 936 940 1969 doi 10 1090 s0002 9904 1969 12302 5 MR 0245051Sources editFranz Jurgen Delvos Walter Schempp Arthur Sard In Memoriam In Walter Schempp Karl Zeller eds Multivariate Approximation Theory II Proceedings of the Conference held at the Mathematical Research Institute at Oberwolfach Black Forest February 8 12 1982 Birkhauser Verlag Basel 1982 ISBN 3 7643 1373 0 International Series of Numerical Mathematics Vol 61 pp 23 24 References edit a b c d Delvos Schempp 1982 Notes In Bulletin of the American Mathematical Society Vol 43 No 5 1937 ISSN 1088 9485 PDF Saunders Mac Lane Requiem for the Skillful In Notices of the American Mathematical Society Vol 44 No 2 1997 ISSN 0002 9920 pp 207 208 PDF 43 kB a b News and Notices In The American Mathematical Monthly Vol 88 No 1 January 1981 Mathematical Association of America ISSN 0002 9890 pp 81 82 online from JSTOR Manfred v Golitschek Paul Otto Runck A Sard Linear Approximation In Jahresbericht der Deutschen Mathematiker Vereinigung Nr 73 B G Teubner Verlag Stuttgart 1971 72 ISSN 0012 0456 S 31 33 online from DigiZeitschriften in German External links editArthur Sard at the Mathematics Genealogy Project Retrieved from https en wikipedia org w index php title Arthur Sard amp oldid 1020360373, wikipedia, wiki, book, books, library,

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