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Harmonic functions. The Riemann mapping theorem and conformal mappings. Other topics as time permits. Usually offered every year. Mr. Adler MATH 121a Topology I [sn] Fundamental group, covering spaces. Cell complexes, homology and cohomology theory, with applications. Usually offered every year. Mr. Levine MATH 121b Topology E [sn] Continuation of MATH 121a. Manifolds and orientation, cup and cap products, Poincare duality. Other topics as time permits. Usually offered every year. Mr. Schwarz M...ATH 150a Combinatorics I [sn] Emphasis on enumerative combinatorics. Generating functions and their applications to counting graphs, paths, permutations, and partitions. Bijective counting, combinatorial identities, Lagrange inversion and Mobius inversion. Usually offered every year. Mr. Gessel MATH 150b Combinatorics n [sn] Representations of finite groups, with emphasis on symmetric groups. Symmetric functions, Polya's theory of enumeration under group action, and combinatorial species. Usually offered in even years.
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