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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2000-2001 MATHEMATICS COLLOQUIUM SERIES 10/12/00 Colloquium DR. PAUL GAUTHIER DEPARTMENT OF MATHEMATICS UNIVERSITY OF MONTREAL Complex Extensions of the Weierstrass Approximation Theorem Abstract: The Weierstrass Theorem states that each continuous function on the unit interval (0,1) can be approximated by polynominals. By approximating on more general sets, one can construct interesting functions, including a "counterexample" to the best known theorem in complex analysis, Liouville's Theorem.