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: "Projective Normal Coördinates for the Geometry of Paths". Proceedings of the National Academy of Sciences. 11: 204–7. 1925. 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. MR 1561049
• 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. MR 1501370
• 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. MR 1501594
• The condition for an orthonomic differential system. Trans. Amer. Math. Soc. 34 (1932) 332–338. MR 1501640
• Pfaffian systems of species one. Trans. Amer. Math. Soc. 35 (1933) 356–371. MR 1501689
• 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. MR 1562842
• The condition for a pfaffian system in involution. Bull. Amer. Math. Soc. 40 (1934) 316–320. MR 1562843
• 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. MR 0052001

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.
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.