Joseph Miller Thomas

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

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. 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.

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

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. Bibcode:1925PNAS...11..204V. 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.
Theory of equations. McGraw-Hill. 1938; 211 pages{{cite book}}: CS1 maint: postscript (link)
Elementary mathematics in artillery fire, by Joseph Miller Thomas with tables prepared by Vincent H. Haag. McGraw-Hill. 1942; 256 pages{{cite book}}: CS1 maint: postscript (link)
Systems and roots. William Byrd Press. 1962; 123 pages{{cite book}}: CS1 maint: postscript (link)
A primer on roots. William Byrd Press. 1974; 106 pages{{cite book}}: CS1 maint: postscript (link)

References

↑ Thomas Decomposition of Algebraic and Differential Systems by Thomas Bächler, Vladimir Gerdt, Markus Lange-Hegermann, Daniel Robertz, 2010
↑ Joseph Miller Thomas at the Mathematics Genealogy Project
↑ 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.
↑ Joseph Miller Thomas | Institute for Advanced Study
↑ Kondratieva, M. V. (1998). Differential and Difference Dimension Polynomials. Springer Science & Business Media. p. ix (preface). ISBN 978-0-7923-5484-0.
↑ 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. S2CID 29916317.
↑ 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.
↑ "Review of Theory of equations by J. M. Thomas". The Mathematical Gazette. 23 (253): 117. February 1939.

[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. S2CID 29916317.

[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.

[8] "Review of Theory of equations by J. M. Thomas". The Mathematical Gazette. 23 (253): 117. February 1939.

Authority control databases
International	ISNI VIAF GND FAST WorldCat
National	United States France BnF data Czech Republic Netherlands Israel
Academics	Mathematics Genealogy Project zbMATH MathSciNet
People	Trove
Other	IdRef Yale LUX