21. BiosWorld What's New December 8, 2000. birkhoff, george David (18841944) (NEW); Bohr,Christian (1855-1911) (NEW); Bohr, Harald August (1887-1951) (NEW); http://scienceworld.wolfram.com/biography/whatsnew.html

22. Birkhoff, George David birkhoff, george David 18841944, American mathematician, b. Overisel,Mich.; father of Garrett birkhoff. birkhoff, george David. http://www.slider.com/enc/7000/Birkhoff_George_David.htm

ecomm pro - ecommerce solution Home Encyclopeadia B Bez - Bil ... Rope Ladders Trellian WebPage Slider Search: The Web Encyclopaedia Shopping Index Help Encyclopaedia Birkhoff, George David 1884-1944, American mathematician, b. Overisel, Mich.; father of Garrett Birkhoff. The son of a physician, he was educated at Harvard (B.A., 1905) and the Univ. of Chicago (Ph.D., 1907) After teaching shortly at Chicago and Princeton, he joined the faculty at Harvard (1912) where he taught until his death. Birkhoff, perhaps the first American mathematician of international repute, is known for his work on linear differential equations and difference equations. He was also deeply interested in and made contributions to the analysis of dynamical systems, celestial mechanics, the four-color map problem, and function spaces. In addition he wrote on the foundations of relativity and quantum mechanics and on art and music, e.g., Aesthetic Measure See his Collected Mathematical Papers (3 vol., 1950). Add URL Advertise Contact Us Rope Ladder

23. Bil - Bit Qarun Birkbeck, george Birkbeck, Morris Birkenhead Birkenhead, Frederick Edwin Smith,1st earl of birkhoff, Garrett birkhoff, george David birling Birmingham http://www.slider.com/enc/b_14.htm

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24. Birkhoff, George David birkhoff, george David (18841944). US mathematicians who made fundamentalcontributions to the study of dynamical systems such as the Solar System. http://www.cartage.org.lb/en/themes/Biographies/MainBiographies/B/Birkhoff/1.htm

Birkhoff, George David US mathematicians who made fundamental contributions to the study of dynamical systems such as the Solar System. He formulated the 'weak form' of the ergodic theorem. Birkhoff was born at Overisel, Michigan, and studied at the University of Chicago and at Harvard. From 1912 he taught at Harvard, and was made professor 1919. Birkhoff developed a system of differential equations which is still inspiring research. His work on difference equations was notable for the prominence he gave to the use of matrix algebra. With John Von Neumann , Birkhoff was chiefly responsible for establishing, in the 1930s, the modern science of ergodics. He arrived at the statement of his 'positive ergodic theorem', or what is known as the 'weak form' of ergodic theory, just before Von Neumann published his 'strong form' of it. Birkhoff also transformed the Maxwell-Boltzmann hypothesis of the kinetic theory of gases, which was undermined by the number of exceptions found to it, into a vigorous principle. Throughout his life Birkhoff argued that Einstein 's general relativity was an unhelpful theory.

25. Mathematicians Translate this page Thomas Beltrami, Eugenio Bernoulli, Daniel Bernoulli, Jakob Bernoulli, Johann Bessel,Friedrich Wilhelm Betti, Enrico, birkhoff, george David Black, Max Bode http://www.cartage.org.lb/en/themes/Biographies/Categories/Scientists/Mathematic

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26. Birkhoff, George David encyclopediaEncyclopedia birkhoff, george David. birkhoff, george David, 1884–1944,American mathematician, b. Overisel, Mich.; father of Garrett birkhoff. http://www.factmonster.com/ce6/people/A0807659.html

Encyclopedia Birkhoff, George David Birkhoff, George David, , American mathematician, b. Overisel, Mich.; father of Garrett Birkhoff. The son of a physician, he was educated at Harvard (B.A., 1905) and the Univ. of Chicago (Ph.D., 1907) After teaching shortly at Chicago and Princeton, he joined the faculty at Harvard (1912) where he taught until his death. Birkhoff, perhaps the first American mathematician of international repute, is known for his work on linear differential equations and difference equations. He was also deeply interested in and made contributions to the analysis of dynamical systems, celestial mechanics, the four-color map problem, and function spaces. In addition he wrote on the foundations of relativity and quantum mechanics and on art and music, e.g., Aesthetic Measure See his Collected Mathematical Papers (3 vol., 1950). Birkhoff, Garrett birling AD AD AD AD AD Print this page Cite this page Awards and Press Link to Fact Monster Add Fact Monster search ... Privacy

27. Scientists: Math Benedetti, Giovanni Battista; Bhaskara; birkhoff, Garrett; birkhoff,george David; Bolzano, Bernard; Boole, george; Bradwardine, Thomas; http://www.factmonster.com/spot/scibio5.html

Notable Scientists: Math Mathematicians and statisticians Jump to a category: Mathematicians Statisticians Mathematicians RELATED LINKS Numbers and Formulas Conversions and Equivalents Search for more scientists and other notable figures Abel, Niels Henrik Alembert, Jean le Rond d' Al-Khowarizmi Apollonius of Perga ... Zygmund, Antoni Statisticians Quetelet, Adolphe Petty, Sir William Achenwall, Gottfried Mayo-Smith, Richmond ... More Features ! AD AD AD AD AD Print this page Cite this page Awards and Press Link to Fact Monster Add Fact Monster search ... Privacy

28. Citations: Elimination By Nested Dissection - Birkhoff, George (ResearchIndex) Retrieving documents G. birkhoff and JA george. Elimination by nested dissection. G.birkhoff and JA george. Elimination by nested dissection. http://citeseer.nj.nec.com/context/457573/0

3 citations found. Retrieving documents... G. Birkhoff and J.A. George. Elimination by nested dissection . in Complexity of Sequential and Parallel Numerical Algorithms J.F. Traub, ed. Academic Press, New York, 1973. 15 Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: Space and Time Efficient Implementations of Parallel Nested .. - Deganit Armon Duke (1992) (Correct) No context found. G. Birkhoff and J.A. George. Elimination by nested dissection . in Complexity of Sequential and Parallel Numerical Algorithms J.F. Traub, ed. Academic Press, New York, 1973. 15 (Correct) No context found. G. Birkhoff and J. A. George, Elimination by nested dissection ., in Complexity of Sequential and Parallel Numerical Algorithms, J.F.Traub, ed. Academic Press, New York, (1973). Bibliography on the Solution of Sparse Linear Systems and Related .. - Arantes (1997) (Correct) No context found. Birkhoff, G. and George, A. Elimination by nested dissection . In Traub, J. F., editor, Complexity of Sequential and Parallel Numerical Algorithms. Academic Press, 1973. Online articles have much greater impact More about CiteSeer Add search form to your site Submit documents CiteSeer - citeseer.org

29. Space And Time Efficient Implementations Of Parallel Nested Dissection - Armon, A Separator Theorem for Planar Graphs (context) Lipton, Tarjan - 1979 2 Eliminationby nested dissection (context) - birkhoff, george - 1973 2 Applications http://citeseer.nj.nec.com/armon92space.html

Space and Time Efficient Implementations of Parallel Nested Dissection (1992) (Make Corrections) (3 citations) Deganit Armon Duke University John Reif Duke University ACM Symposium on Parallel Algorithms and Architectures Home/Search Context Related View or download: duke.edu/~reif/paper/deganit/pnd.ps Cached: PS.gz PS PDF DjVu ... Help From: duke.edu/~reif/vita/papers (more) Homepages: D.Armon J.Reif HPSearch (Update Links) Rate this article: (best) Comment on this article (Enter summary) Abstract: (Update) Context of citations to this paper: More n M(s(n) processors, Gazit and Miller [GM 90] gave bounds of parallel time O(log 2 n log log n) with n M(s(n) processors, Armon and Reif [ AR 92 ] decreased this parallel time to O(log 2 n) with n M(s(n) 1 ffl processors, for ffl 0; and Reif [R 94] gave bounds of parallel Cited by: More Fast And Efficient Parallel Solution Of Sparse Linear Systems - Victor Pan John (1993) (Correct) Space and Time Efficient Implementations of Parallel Nested .. - Deganit Armon Duke (1992) ... (Correct) Active bibliography (related documents): More All Bibliography on the Solution of Sparse Linear Systems and Related .. - Arantes (1997)

30. Encyclopædia Britannica birkhoff, george David Encyclopædia Britannica Article. To cite this page MLA style birkhoff, george David. 2003 Encyclopædia Britannica Premium Service. http://www.britannica.com/eb/article?eu=15573

31. Encyclopædia Britannica birkhoff, george David foremost American mathematician of the early 20th century,who formulated the ergodic theorem. More Articles. Video Media, http://www.britannica.com/search?query=george david cummins&seo

32. The George David Birkhoff Prize Ballroom. The george David birkhoff Prize. The george David birkhoffPrize, established in 1967, is awarded jointly by SIAM and AMS. http://www.siam.org/meetings/archives/an94/birkhoff.htm

Wednesday, July 27/3:30 PM/Grande Ballroom The George David Birkhoff Prize The George David Birkhoff Prize, established in 1967, is awarded jointly by SIAM and AMS. The prize is awarded for an outstanding contribution to applied mathematics in the highest and broadest sense. The recipients are Ivo Babuska, University of Maryland, College Park, and Srinivasa R. S. Varadhan, Courant Institute of Mathematical Sciences, New York University.

33. Birkhoff, George David birkhoff, george David. (b. March 21, 1884, Overisel, Mich., USd.Nov. 12, 1944, Cambridge, Mass.), foremost American mathematician http://www.phy.bg.ac.yu/web_projects/giants/birkhoff.html

Britannica CD Index Articles Dictionary Help Birkhoff, George David (b. March 21, 1884, Overisel, Mich., U.S.d. Nov. 12, 1944, Cambridge, Mass.), foremost American mathematician of the early 20th century, who formulated the ergodic theorem, which transformed the Maxwell-Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. Birkhoff taught at the University of Wisconsin, Madison (1907-09); Princeton University (1909-12); and Harvard University (1912-44). He was an extraordinarily stimulating lecturer and director of research. In the mid-20th century, many of the leading American mathematicians had either written their doctoral dissertations under his direction or had done postdoctoral research with him. He conducted research mainly in mathematical analysis and analysis applied to dynamics. His dissertation and much of his later work dealt with the solutions of ordinary differential equations and the associated expansions of arbitrary functions. Using matrix methods, he also contributed fundamentally to the theory of difference equations. His proof in 1913 of a geometric theorem of Henri topology (the study of surfaces and spaces) was a striking achievement. Birkhoff's formulation of the ergodic theorem (the so-called strong form), which was published shortly before the "weak" formulation of John von Neumann appeared, has important applications to modern analysis and is applicable in more cases than is the weak form. Birkhoff developed his own theory of gravitation after Albert Einstein had developed his, and he constructed a mathematical theory of aesthetics, which he applied to art, music, and poetry. All this internationally renowned creative work stimulated further scientific discoveries.

34. Harvard Libraries: George David Birkhoff Mathematical Library Home Help Search Site Map Harvard Home HOLLIS Catalog Other Catalogs EResourcesLibraries. george David birkhoff Mathematical Library. Library hours http://lib.harvard.edu/libraries/0108.html

George David Birkhoff Mathematical Library Library hours Alternate Names: Birkhoff Mathematics Library Mathematics Department Library Phone Numbers: Email Addresses: Address: Science Center 337, 1 Oxford Street, Cambridge, MA 02138 Access Information: Any member of Harvard University may use the library. Circulation Policy Holdings Description Services Resources for Persons with Disabilities ... Privacy Statement Last modified 28 Mar 2003

35. Harvard Libraries: George David Birkhoff Mathematical Library george David birkhoff Mathematical Library. Library hours Alternate Names birkhoffMathematics Library. Mathematics Department Library. Phone Numbers 4952147, http://lib.harvard.edu/libraries/0108FULL.html

George David Birkhoff Mathematical Library Library hours Alternate Names: Birkhoff Mathematics Library Mathematics Department Library Phone Numbers: Email Addresses: Address: Science Center 337, 1 Oxford Street, Cambridge, MA 02138 Access Information: Any member of Harvard University may use the library. Circulation Policy: The library is non-circulating Holdings Description: Summary description of collection: The library collects books and journals in pure mathematics. Size of collection: 12,000 monograph titles; 70 serial titles Expanded description of collection: The library collects books and journals in pure mathematics. Services: Internal ILL Policy: HARVARD: The library does not lend to other Harvard libraries. External ILL Policy: NON-HARVARD: The Library does not lend materials to non-Harvard libraries. ILL Borrowing Policy: BORROWING: The library does not borrow materials for patrons. Equipment and facilities available: Microfiche reader Photocopier Study rooms. Resources for Persons with Disabilities: The library is wheelchair accessible.

36. Aesthetic Measure (in MARION) Aesthetic measure. Title Aesthetic measure, by george D. birkhoff. Author birkhoff,george David. Published Cambridge, Mass., Harvard University Press, 1933. http://vax.vmi.edu/MARION/AAV-7909

Aesthetic measure Title: Aesthetic measure, by George D. Birkhoff. Author: Birkhoff, George David. Published: Cambridge, Mass., Harvard University Press, 1933. Subject: Aesthetics. Art. Proportion (Art) Music Philosophy and aesthetics. ... Poetry. Material: xii, [1] p., 2 ., 3-225, [1] p. illus. (incl. music) XXIII pl. (part col.) diagrs. 30 cm. System ID no: AAV-7909 Holdings: LOCATION: MAIN CALL NUMBER: HB201 .B5 c.1 Not Checked Out Back to Start

37. Records For Proportion (Art) (in MARION) Proportion (Art). Records 1 to 5 of 5. birkhoff, george David. Aesthetic measure,by george D. birkhoff. Cambridge, Mass., Harvard University Press, 1933. http://vax.vmi.edu/MARION/@PROPORTION ART/36fa20003000/0

Proportion (Art) Records 1 to 5 of 5 Birkhoff, George David. Aesthetic measure, by George D. Birkhoff. Cambridge, Mass., Harvard University Press, 1933. Holdings: LOCATION: MAIN CALL NUMBER: HB201 .B5 c.1 Not Checked Out Elam, Kimberly, 1951- Geometry of design : studies in proportion and composition / Kimberly Elam. New York : Princeton Architectural Press, c2001. LOCATION: MAIN CALL NUMBER: N7431.5 .E44 2001 c.1 Not Checked Out Gardner, Robert Waterman, 1866-1937. A primer of proportion in the arts of form and music [by] R. W. Gardner. New York, W. Helburn, inc., 1945. LOCATION: OVERSIZE CALL NUMBER: N76 .G3 c.1 Not Checked Out Richter, Irma A. (Irma Anne) Rhythmic form in art, an investigation of the principles of composition in the works of the great masters, by Irma A. Richter; with 72 illustrations. London, John Lane [1932] LOCATION: MAIN CALL NUMBER: N7430 .R5 c.1 Not Checked Out

38. BIRKHOFF, George Translate this page birkhoff, george Professor der Mathematik an der Universität Harvard. 597/13-1An HAUER, Joseph Matthias. birkhoff, george. HAUER, Joseph Matthias. MELODIE. http://ezines.onb.ac.at:8080/moravec/pub/schr/1120.htm

BIRKHOFF, George Professor der Mathematik an der Universität Harvard An HAUER, Joseph Matthias. L.a.s. 1f, 2pp. 9.6.1928, Szallo Suche nach einer mathematischen Erklärung für Melodie. Bitte um eine Terminvereinbarung. siehe auch Personen-, Orts- und Sachregister BIRKHOFF, George HAUER, Joseph Matthias MELODIE

39. BIRKHOFF, George Translate this page birkhoff, george 317 597/13_1. http://ezines.onb.ac.at:8080/moravec/pub/index/2211.htm

40. Basic Geometry Geometry Topology Mathematics George David Birkhoff Basic Geometry Geometry Topology Mathematics george David birkhoff. Subject GeometryTopology Mathematics Title Basic Geometry Author george David birkhoff. http://www.lyrics-shop.co.uk/George-David-Birkhoff-Basic-Geometry-0828401209.htm

Basic Geometry Geometry Topology Mathematics George David Birkhoff Subject: Geometry Topology Mathematics Title: Basic Geometry Author: George David Birkhoff Paul Hooper Introduction to Fi... Lucille N Breneman Once Upon a... Mary Lorenz Dietz Killing for ... Wilma James Gardening with Bib... ... Garber Klaus, Held Jutta Der...

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