Joseph Miller Thomas Explained

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. 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.^[2] In 1935, he was one of the founders of the Duke Mathematical Journal. For the academic year 1936–1937, he was a visiting scholar at the Institute for Advanced Study.^[3]

Based upon earlier work by Charles Riquier and Maurice Janet, Thomas's research was important for the introduction of involutive bases.^{[4] [5]}

Selected publications

Articles

• with Oswald Veblen: Projective Normal Coördinates for the Geometry of Paths. Proceedings of the National Academy of Sciences. 16576871 . 11. 4. 1085921. 1925. 204–7. 10.1073/pnas.11.4.204. Veblen. O.. Thomas. J. M.. free.
• 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.
• 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.
• with Oswald Veblen: Projective invariants of affine geometry of paths. Annals of Mathematics 27 (1926): 279–296.
• Riquier's existence theorems. Annals of Mathematics 30 (1928): 285–310.
• Matrices of integers ordering derivatives. Trans. Amer. Math. Soc. 33 (1931) 389–410.
• The condition for an orthonomic differential system. Trans. Amer. Math. Soc. 34 (1932) 332–338.
• Pfaffian systems of species one. Trans. Amer. Math. Soc. 35 (1933) 356–371.
• Riquier's existence theorems. Annals of Mathematics 35 (1934): 306–311. (addendum to 1928 publication in Annals of Mathematics)
• An existence theorem for generalized pfaffian systems. Bull. Amer. Math. Soc. 40 (1934) 309–315.
• The condition for a pfaffian system in involution. Bull. Amer. Math. Soc. 40 (1934) 316–320.
• Sturm's theorem for multiple roots. National Mathematics Magazine 15, no. 8 (1941): 391–394.
• Equations equivalent to a linear differential equation. Proc. Amer. Math. Soc. 3 (1952) 899–903.

Books

• Book: Differential systems. 1937. ^[6]
• Book: Theory of equations. McGraw-Hill. 1938.

  211 pages

  . ^[7]
• Book: Elementary mathematics in artillery fire, by Joseph Miller Thomas with tables prepared by Vincent H. Haag. McGraw-Hill. 1942.

  256 pages

  .
• Book: Systems and roots. William Byrd Press. 1962.

  123 pages

  .
• Book: A primer on roots. William Byrd Press. 1974.

  106 pages

  .

Notes and References

1. https://arxiv.org/abs/1008.3767 Thomas Decomposition of Algebraic and Differential Systems by Thomas Bächler, Vladimir Gerdt, Markus Lange-Hegermann, Daniel Robertz, 2010
2. Book: Judy . Green . Judy Green (mathematician) . Jeanne . LaDuke . Jeanne LaDuke. Pioneering Women in American Mathematics: The Pre-1940 PhD's . 2009 . American Mathematical Society . Pioneering Women in American Mathematics . 9780821843765 . (Griffin) Reavis and Stokes biographies on p.513-515 and p.580-582 of the Supplementary Material at AMS, respectively.
3. https://www.ias.edu/scholars/joseph-miller-thomas Joseph Miller Thomas | Institute for Advanced Study
4. Book: Kondratieva, M. V.. Differential and Difference Dimension Polynomials. 1998. Springer Science & Business Media. 978-0-7923-5484-0. ix (preface).
5. 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. 10.1007/bf02759177. 29916317.
6. Bochner, Salomon. Salomon Bochner. Review: Differential systems by J. M. Thomas. Bull. Amer. Math. Soc.. 1938. 44. 5. 314–315. 10.1090/s0002-9904-1938-06724-9. free.
7. Review of Theory of equations by J. M. Thomas. The Mathematical Gazette. 23. 253. 117. February 1939.