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Topic: Joseph Liouville

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	Liouville biography
		In 1837 Liouville was appointed to lecture at the Collège de France as a substitute for Biot.
		Liouville investigated criteria for integrals of algebraic functions to be algebraic during the period 1832-33.
		Liouville was therefore a major influence in bringing Galois's work to general notice when he published this work in 1846 in his Journal.
	www-history.mcs.st-andrews.ac.uk /history/Biographies/Liouville.html (1842 words)

	Joseph Liouville - Wikipedia, the free encyclopedia
		Joseph Liouville (born March 24, 1809, died September 8, 1882) was a French mathematician.
		Liouville graduated from the École Polytechnique in 1827.
		Liouville was also involved in politics for some time, and he became member of the Constituting Assembly in 1848.
	en.wikipedia.org /wiki/Joseph_Liouville (303 words)

	Joseph Liouville: biography and encyclopedia article (Site not responding. Last check: 2007-10-15)
		Joseph Liouville (born March 24 1809, died September 8 1882) was a French (French: The Romance language spoken in France and in countries colonized by France) mathematician (mathematician: A person skilled in mathematics).
		Liouville graduated from the École Polytechnique (École Polytechnique: the école polytechnique (the "polytechnic school"), often nicknamed x, is the foremost...
		Liouville was also involved in politics for some time, and he became member of the Constituting Assembly (Constituting Assembly: the national assembly is the name of either a legislature, or the lower house of...
	www.absoluteastronomy.com /reference/joseph_liouville (494 words)

	Liouville number - Wikipedia, the free encyclopedia
		A Liouville number can then be approximated "quite closely" by a sequence of rational numbers.
		In 1844, Joseph Liouville showed that numbers with this property are not just irrational, but are always transcendental (see proof below).
		A Liouville number is irrational but does not have this property, so it can't be algebraic and must be transcendental.
	en.wikipedia.org /wiki/Liouville_number (743 words)

	Joseph Liouville Summary
		Although Joseph Liouville's primary contribution to mathematics was the first proof of the existence of transcendental numbers (real numbers that are not roots of polynomials with integer coefficients), he had a wide range of mathematical interests.
		Liouville was the son of a captain in Napoleon's army, causing him to live with his uncle until his father's return from the Napoleonic wars.
		In mathematical physics, Liouville made two fundamental contributions: the Sturm-Liouville theory which was joint work with Charles François Sturm is now a standard procedure to solve certain types of integral equations by developing into eigenfunctions, and the fact (also known as Liouville's theorem) that time evolution is measure preserving for a Hamiltonian system.
	www.bookrags.com /Joseph_Liouville (1875 words)

	Joseph Liouville
		Joseph Liouville went to the Collège St. Louis in Paris where he studied mathematics at the highest levels.
		In 1838, Liouville was appointed Professor of Analysis and Mechanics at the Ecole Polytechnique.
		Liouville investigated criteria for integrals of algebraic functions to be algebraic.
	www.stetson.edu /~efriedma/periodictable/html/Lu.html (742 words)

	Reference.com/Encyclopedia/Liouville's theorem (Hamiltonian)
		Liouville's theorem is also important in the study of symplectic topology, where it is formulated rather differently.
		The Liouville equation describes the time evolution of phase space distribution function (while density is the correct term from mathematics, physicists generally call it a distribution).
		The Liouville equation is integral to the proof of the fluctuation theorem from which the second law of thermodynamics can be derived.
	www.reference.com /browse/wiki/Liouville's_theorem_(Hamiltonian) (698 words)

	Liouville, Joseph (Site not responding. Last check: 2007-10-15)
		Liouville became professor at the École Polytechnique, Paris, in 1833.
		The Liouville theorem concerning the measure-preserving property of the Hamiltonian dynamics is basic to statistical mechanics and measure theory.
		In analysis Liouville was the first to deduce the theory of doubly periodic functions from general theorems (including his own) in the theory of analytic functions of a complex variable.
	www.phy.bg.ac.yu /web_projects/giants/liouville.html (309 words)

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