Joseph Miller Thomas

Joseph Miller Thomas (16 January 1898 – 1979) was an American mathematician, known for the Thomas decomposition of algebraic and differential systems.[1]

Thomas received his Ph.D., supervised by Frederick Wahn Beal, from the University of Pennsylvania with thesis Congruences of Circles, Studied with reference to the Surface of Centers.[2] He was a mathematics professor at Duke University for many years. His graduate students include Mabel Griffin (later married to L. B. Reavis) and Ruth W. Stokes.[3] In 1935 he was one of the founders of the Duke Mathematical Journal. For the academic year 1936–1937 was a visiting scholar at the Institute for Advanced Study.[4]

Based upon earlier work by Charles Riquier and Maurice Janet, Thomas's research was important for the introduction of involutive bases.[5][6]

Selected publications

Articles
  • with Oswald Veblen: Veblen, O.; Thomas, J. M. (1925). "Projective Normal Coördinates for the Geometry of Paths". Proceedings of the National Academy of Sciences. 11 (4): 204–7. doi:10.1073/pnas.11.4.204. PMC 1085921. PMID 16576871.
  • Note on the projective geometry of paths. Proceedings of the National Academy of Sciences 11, no. 4 (1925): 207–209.
  • The number of even and odd absolute permutations of n letters. Bull. Amer. Math. Soc. 31 (1925) 303–304. MR1561049
  • Conformal correspondence of Riemann spaces. Proceedings of the National Academy of Sciences 11, no. 5 (1925): 257–259.
  • Conformal invariants. Proceedings of the National Academy of Sciences 12, no. 6 (1926): 389–393.
  • Asymmetric displacement of a vector. Trans. Amer. Math. Soc. 28 (1926) 658–670. MR1501370
  • with Oswald Veblen: Projective invariants of affine geometry of paths. Annals of Mathematics 27 (1926): 279–296. doi:10.2307/1967848
  • Riquier's existence theorems. Annals of Mathematics 30 (1928): 285–310. doi:10.2307/1968282
  • Matrices of integers ordering derivatives. Trans. Amer. Math. Soc. 33 (1931) 389–410. MR1501594
  • The condition for an orthonomic differential system. Trans. Amer. Math. Soc. 34 (1932) 332–338. MR1501640
  • Pfaffian systems of species one. Trans. Amer. Math. Soc. 35 (1933) 356–371. MR1501689
  • Riquier's existence theorems. Annals of Mathematics 35 (1934): 306–311. doi:10.2307/1968434 (addendum to 1928 publication in Annals of Mathematics)
  • An existence theorem for generalized pfaffian systems. Bull. Amer. Math. Soc. 40 (1934) 309–315. MR1562842
  • The condition for a pfaffian system in involution. Bull. Amer. Math. Soc. 40 (1934) 316–320. MR1562843
  • Sturm's theorem for multiple roots. National Mathematics Magazine 15, no. 8 (1941): 391–394. JSTOR 3028551
  • Equations equivalent to a linear differential equation. Proc. Amer. Math. Soc. 3 (1952) 899–903. MR0052001

Books
  • Differential systems. 1937.[7]
  • Theory of equations. McGraw-Hill. 1938; 211 pages
  • Elementary mathematics in artillery fire, by Joseph Miller Thomas with tables prepared by Vincent H. Haag. McGraw-Hill. 1942; 256 pages
  • Systems and roots. William Byrd Press. 1962; 123 pages
  • A primer on roots. William Byrd Press. 1974; 106 pages

References
  1. Thomas Decomposition of Algebraic and Differential Systems by Thomas Bächler, Vladimir Gerdt, Markus Lange-Hegermann, Daniel Robertz, 2010
  2. Joseph Miller Thomas at the Mathematics Genealogy Project
  3. Green, Judy; LaDuke, Jeanne (2009). Pioneering Women in American Mathematics: The Pre-1940 PhD's. American Mathematical Society. ISBN 9780821843765. (Griffin) Reavis and Stokes biographies on p.513-515 and p.580-582 of the Supplementary Material at AMS, respectively.
  4. Joseph Miller Thomas | Institute for Advanced Study
  5. Kondratieva, M. V. (1998). Differential and Difference Dimension Polynomials. Springer Science & Business Media. p. ix (preface). ISBN 978-0-7923-5484-0.
  6. Astrelin, A. V.; Golubitsky, O. D.; Pankratiev, E. V. (2000). "Involutive bases of ideals in the ring of polynomials". Programming and Computer Software. 26 (1): 31–35. doi:10.1007/bf02759177.
  7. Bochner, Salomon (1938). "Review: Differential systems by J. M. Thomas" (PDF). Bull. Amer. Math. Soc. 44 (5): 314–315. doi:10.1090/s0002-9904-1938-06724-9.
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