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Book Review

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Book Information:

Author: Andy R. Magid
Title: Lectures on differential Galois theory
Additional book information: University Lecture Series, vol. 7, Amer. Math. Soc., Providence, RI, 1994, xiii+105 pp., ISBN 0-8218-7004-1, $35.00

References [Enhancements On Off] (What's this?)

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  • 2. B. L. J. Braaksma and M. van der Put, Analytic and algebraic aspects of complex analytic differential equations, preprint, Groningen, 1994.
  • 3. F. Beukers, D. Brownawell, and G. Heckman, Siegel normality, Ann. of Math. 127 (1988), 279--308. MR 90e:11106
  • 4. L. Breen, Tannakian categories, Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 337--376. MR 95b:18009
  • 5. P. Deligne, Catégories tannakiennes, Prog. Math., vol. 87, Birkhäuser, Boston, MA, 1990, pp. 111--195. MR 92d:14002
  • 6. A. Fahim, Extensions galoisiennes d'algèbres différentielles, Publ. IRMA Lille, vol. 31, 1993, $n^\circ$ 10; C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), 1--4. MR 93b:12011
  • 7. E. Galois, Mémoire sur les conditions de résolubilité des équations par radicaux (R. Bourgne and J.-P. Azra, eds.), Gauthiers-Villars, 1962. [The quotation reads as follows: ``que toute fonction des racines, déterminable rationnellement, soit invariable par ces substitutions.'']
  • 8. I. Kaplansky, An introduction to differential algebra, Hermann, 1957. MR 20:177
  • 9. N. Katz, A conjecture in the arithmetic theory of differential equations, Bull. Soc. Math. France 110 (1982), 203--239.
  • 10. ------, Exponential sums and differential equations, Ann. of Math. Studies, vol. 124, Princeton Univ. Press, 1990. MR 93a:14009
  • 11. E. Kolchin, Existence theorems connected with the Picard-Vessiot theory of homogeneous LODE, Bull. Amer. Math. Soc. 54 (1948), 927--932. MR 10:349a
  • 12. ------, Differential algebra and algebraic groups, Academic Press, 1973. MR 58:27929
  • 13. J. Kovacic, On the inverse problem in the Galois theory of differential fields, Ann. of Math. 93 (1971), 269--284. MR 44:2732
  • 14. M. Kuga, Galois' dream: Group theory and differential equations, Birkhäuser, Boston, MA, 1993. MR 93k:34012
  • 15. C. Mitschi and M. Singer, Connected linear groups as differential Galois groups, to appear in J. Algebra.
  • 16. J.-P. Ramis, Phénomène de Stokes et filtration Gevrey sur le groupe de Picard-Vessiot, C.R. Acad. Sci. Paris Sér. I Math. 301 (1985), 165--167. MR 86k:12012
  • 17. J.-P. Serre, Gèbres, Enseign Math. 39 (1993), 33--85. MR 94h:16074
  • 18. M. Singer and F. Ulmer, Galois groups of second and third order linear differential equations, J. Symbolic Comput. 16 (1993), 1--36. MR 94i:34015

Review Information:

Reviewer: D. Bertrand
Affiliation: Institut de Mathématiques, Université de Paris VI
Journal: Bull. Amer. Math. Soc. 33 (1996), 289-294
Review copyright: © Copyright 1996 American Mathematical Society
American Mathematical Society