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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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George David Birkhoff and his mathematical work
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by Marston Morse PDF
Bull. Amer. Math. Soc. 52 (1946), 357-391
References
    1. George David Birkhoff, with H. S. Vandiver, On the integral divisors of $a^n b^n$, Ann. of Math. vol. 5 (1904) pp. 173-180.
  • George D. Birkhoff, On the asymptotic character of the solutions of certain linear differential equations containing a parameter, Trans. Amer. Math. Soc. 9 (1908), no. 2, 219–231. MR 1500810, DOI 10.1090/S0002-9947-1908-1500810-1
  • George D. Birkhoff, Boundary value and expansion problems of ordinary linear differential equations, Trans. Amer. Math. Soc. 9 (1908), no. 4, 373–395. MR 1500818, DOI 10.1090/S0002-9947-1908-1500818-6
  • George D. Birkhoff, Existence and oscillation theorem for a certain boundary value problem, Trans. Amer. Math. Soc. 10 (1909), no. 2, 259–270. MR 1500837, DOI 10.1090/S0002-9947-1909-1500837-0
  • George D. Birkhoff, On the solutions of ordinary linear homogeneous differential equations of the third order, Ann. of Math. (2) 12 (1911), no. 3, 103–127. MR 1503560, DOI 10.2307/2007241
  • 6. George David Birkhoff, with H. S. Vandiver, Note on the expansion problems of ordinary linear differential equations, Rend. Circ. Mat. Palermo vol. 36 (1913) pp. 115-126. 7. George David Birkhoff, with H. S. Vandiver, A theorem on series of orthogonal functions with an application to Sturm-Liouville series, Proc. Nat. Acad. Sci. U.S.A. vol. 3 (1917) pp. 656-659. 8. George David Birkhoff, with H. S. Vandiver, With R. E. Langer, The boundary problems and developments associated with a system of ordinary linear differential equations of first order, Proceedings of the American Academy of Arts and Sciences vol. 58 (1923) pp. 49-128.
  • G. D. Birkhoff and M. R. Hestenes, Natural isoperimetric conditions in the calculus of variations, Duke Math. J. 1 (1935), no. 2, 198–286. MR 1545876, DOI 10.1215/S0012-7094-35-00118-1
  • George D. Birkhoff, Singular points of ordinary linear differential equations, Trans. Amer. Math. Soc. 10 (1909), no. 4, 436–470. MR 1500848, DOI 10.1090/S0002-9947-1909-1500848-5
  • George D. Birkhoff, A simplified treatment of the regular singular point, Trans. Amer. Math. Soc. 11 (1910), no. 2, 199–202. MR 1500860, DOI 10.1090/S0002-9947-1910-1500860-4
  • 12. George David Birkhoff, with H. S. Vandiver, A theorem on matrices of analytic functions, Math. Ann. vol. 74 (1913) pp. 122-133. 13. George David Birkhoff, with H. S. Vandiver, The generalized Riemann problem for linear differential equations and the allied problems for linear difference and q-difference equations, Proceedings of the American Academy of Arts and Sciences vol. 49 (1913) pp. 521-568. 14. George David Birkhoff, with H. S. Vandiver, Infinite products of analytic matricest Trans. Amer. Math. Soc. vol. 17 (1916) pp. 386-404. 15. George David Birkhoff, with H. S. Vandiver, General theory of linear difference equations, Trans. Amer. Math. Soc. vol. 12(1911) pp. 243-284.
  • George D. Birkhoff, Formal theory of irregular linear difference equations, Acta Math. 54 (1930), no. 1, 205–246. MR 1555307, DOI 10.1007/BF02547522
  • George D. Birkhoff and W. J. Trjitzinsky, Analytic theory of singular difference equations, Acta Math. 60 (1933), no. 1, 1–89. MR 1555364, DOI 10.1007/BF02398269
  • 18. George David Birkhoff, with H. S. Vandiver, Quelques théorèmes sur le mouvement des systèmes dynamiques, Bull. Soc. Math. France vol. 40 (1912) pp. 305-323. 19. George David Birkhoff, with H. S. Vandiver, Proof of Poincaré’s geometric theorem, Trans. Amer. Math. Soc. vol. 14 (1913) pp. 14-22. 20. George David Birkhoff, with H. S. Vandiver, The restricted problem of three bodies, Rend. Circ. Mat. Palermo vol. 39 (1915) pp. 265-334. (Awarded the Quirini Stampalia Prize by the Royal Venice Institute of Science.)
  • George D. Birkhoff, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc. 18 (1917), no. 2, 199–300. MR 1501070, DOI 10.1090/S0002-9947-1917-1501070-3
  • 22. George David Birkhoff, with H. S. Vandiver, Recent advances in dynamics, Science vol. 51 (1920) pp. 51-55. 23. George David Birkhoff, with H. S. Vandiver, Surface transformations and their dynamical applications, Acta Math. vol. 43 (1920) pp. 1-119. 24. George David Birkhoff, with H. S. Vandiver, An extension of Poincaré’s last geometric theorem, Acta Math. vol. 47 (1925) pp. 297-311. 25. George David Birkhoff, with H. S. Vandiver, Stability and the equations of dynamics, Amer. J. Math. vol. 49 (1927) pp. 1-38. 26. George David Birkhoff, with H. S. Vandiver, Dynamical systems, Amer. Math. Soc. Colloquium Publications, vol. 9, New York, 1927. 27. George David Birkhoff, with P. A. Smith, Structure analysis of surface transformations, J. Math. Pures Appl. (9) vol. 7 (1928) pp. 345-379. 28. George David Birkhoff, with P. A. Smith, Une généralisation à n dimensions du dernier théorème de géométrie de Poincaré, C. R. Acad. Sci. Paris vol. 192 (1931) pp. 196-198.
  • George D. Birkhoff, Matter, electricity and gravitation in flat space-time, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 231–239. MR 8365, DOI 10.1073/pnas.29.8.231
  • George D. Birkhoff, Flat space-time and gravitation, Proc. Nat. Acad. Sci. U.S.A. 30 (1944), 324–334. MR 10795, DOI 10.1073/pnas.30.10.324
  • 31. George David Birkhoff, with D. C. Lewis, Jr., On the periodic motions near a given periodic motion of a dynamical system, Annali di Mat. Pura Appl. vol. 12 (1933) pp. 117-133.
  • George D. Birkhoff, Sur le problème restreint des trois corps (premier mémoire), Ann. Scuola Norm. Super. Pisa Cl. Sci. (2) 4 (1935), no. 3, 267–306 (French). MR 1556760
  • 33. George David Birkhoff, with D. C. Lewis, Jr., Nouvelles recherches sur les systèmes dynamiques, Mémoriae Pont. Acad. Sci. Novi Lyncaei vol. 1 (1935) pp. 85-216. (Crowned by the Pontifical Academy of Science.) 34. George David Birkhoff, with D. C. Lewis, Jr., Sur le problème restreint des trois corps (Second Mémoire), Annali della R. Scuola Normale Superiore Pisa (2) vol. 5 (1936) pp. 1-42.
  • George D. Birkhoff, Some unsolved problems of theoretical dynamics, Science 94 (1941), 598–600. MR 6260, DOI 10.1126/science.94.2452.598
  • 36. George David Birkhoff, with D. C. Lewis, Jr., Books on relativity, Bull. Amer. Math. Soc. vol. 28 (1922) pp. 215-221. 37. George David Birkhoff, with D. C. Lewis, Jr., The origin, nature and influence of relativity (Lowell Institute Lectures), New York, 1925. 38. George David Birkhoff, with D. C. Lewis, Jr., A theory of matter and electricity, Proc. Nat. Acad. Sci. U.S.A. vol. 13 (1927) pp.160-165. 39. George David Birkhoff, with D. C. Lewis, Jr., The hydrogen atom and the Balmer formula, Proc. Nat. Acad. Sci. U.S.A. vol. 13 (1927) pp. 165-169. 40. George David Birkhoff, with D. C. Lewis, Jr., A mathematical critique of some physical theories, Bull. Amer. Math. Soc. vol. 33 (1927) pp. 165-181. (Awarded the annual prize of the American Association for the Advancement of Science.) 41. George David Birkhoff, with D. C. Lewis, Jr., Some remarks concerning Schrödinger’s wave equation, Proc. Nat. Acad. Sci. U.S.A. vol. 19 (1933) pp. 339-344. 42. George David Birkhoff, with D. C. Lewis, Jr., Electricity as a fluid, Journal of the Franklin Institute vol. 226 (1938) pp. 315-325.
  • George D. Birkhoff, Matter, electricity and gravitation in flat space-time, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 231–239. MR 8365, DOI 10.1073/pnas.29.8.231
  • George D. Birkhoff, The mathematical nature of physical theories, Amer. Sci. 31 (1943), 281–310. MR 9000
  • 45. George David Birkhoff, with O. D. Kellogg, Invariant points in function space, Trans. Amer. Math. Soc. vol. 23 (1922) pp. 96-115.
  • George D. Birkhoff, A determinant formula for the number of ways of coloring a map, Ann. of Math. (2) 14 (1912/13), no. 1-4, 42–46. MR 1502436, DOI 10.2307/1967597
  • George D. Birkhoff, The Reducibility of Maps, Amer. J. Math. 35 (1913), no. 2, 115–128. MR 1506176, DOI 10.2307/2370276
  • 48. George David Birkhoff, with O. D. Kellogg, On the number of ways of coloring a map, Proc. Edinburgh Math. Soc. (2) vol. 2 (1930) pp. 83-91.
  • George D. Birkhoff, On the polynomial expressions for the number of ways of coloring a map, Ann. Scuola Norm. Super. Pisa Cl. Sci. (2) 3 (1934), no. 1, 85–103. MR 1556723
  • George David Birkhoff, General mean value and remainder theorems with applications to mechanical differentiation and quadrature, Trans. Amer. Math. Soc. 7 (1906), no. 1, 107–136. MR 1500736, DOI 10.1090/S0002-9947-1906-1500736-1
  • 51. George David Birkhoff, with O. D. Kellogg, Aesthetic measure, Cambridge, 1933.
  • George D. Birkhoff, A set of postulates for plane geometry, based on scale and protractor, Ann. of Math. (2) 33 (1932), no. 2, 329–345. MR 1503058, DOI 10.2307/1968336
  • 53. George David Birkhoff, with Ralph Beatley, Basic geometry, New York, 1940. 54. George David Birkhoff, with Ralph Beatley, Fifty years of American mathematics, Amer. Math. Soc. Semicentennial Publications, vol. 2, 1938, pp. 270-315.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 52 (1946), 357-391
  • DOI: https://doi.org/10.1090/S0002-9904-1946-08553-5
  • MathSciNet review: 0016341