Cartan complex analysis 2 ndedition by bak newman

This preview shows page 94 - 98 out of 107 pages.

Cartan Complex Analysis, 2ndedition, by Bak-Newman Complex Analysis with Applications, by Silverman Topics List:1.Complex numbers, Riemann's sphere. Complex functions, elementary functions, Möbius transformations. 2.Holomorphic functions, Cauchy-Riemann equations. 3.Line integrals. Cauchy’s integration theorem and its consequences. 4.Harmonic functions. 5.Sequences and series of holomorphic functions. Power series, analytic functions. 6.Isolated singularities, meromorphic functions, the calculus of residues. 7.Conformal mappings, the Riemann mapping theorem. 8.Geometric principles. 9.Mittag-Leffler's and Weierstrass's expansions of meromorphic functions. 10.Analytic continuation, Riemann surfaces. 11.Applications to number theory, geometry, physics.
Page 1 2017-2018 Math 5529H Mathematics 5529H Honors Combinatorics Autumn (even numbered years) 5 credits Catalog Description: Techniques of combinatorial mathematics; connections with geometry, algebra, analysis, and probability. Prerequisite: C or better in 4182H, or in both 2182H and 3345; or credit for 264H, or for both 263H and 345; or permission of department. Text: Vary, for example: Discrete Mathematics, by Lovasz, Pelican & Vestergombi, published by Springer, ISBN: 9780387955858 Proofs from the Book, 4thedition, by Aigner, Ziegler & Hofmann, published by Springer, ISBN: 9783642008559 Combinatorics: Topics, Techniques, Algorithms, by P. Cameron, published by Cambridge University Press, ISBN: 9780521338936 Topics List: 1.Counting principles. 2.Generating functions. 3.Combinatorial probability. 4.Finite fields and applications. 5.Theory of partitions. 6.Famous graphs. 7.Ramsey theory. 8.Permutation groups.
Page 1 2017-2018 Math 5530H Mathematics 5530H Honors Probability Spring (odd numbered years) 5 credits Catalog Description: Theoretical treatment of probability, with applications within and outside mathematics. Prerequisite: C or better in 5529H, or permission of department. Purpose of Course: The acquaintance with rigorous probability theory, its history and its multiple connections, will better prepare honor students for graduate studies and will help them get involved in research at earlier stages of their careers. Text: Vary, for example: Heads and Tails. An Introduction to Limit Theorems in Probability, E. Lesigne, AMS, ISBN 0821837141 Elementary Probability Theory with Stochastic Processes, Kai Lai Chung Elementary Probability Theory, Kai Lai Chung and Farid AitSahlia,, 4th Edition, Springer, 2003 Topics List: 1.Historical origins of probability. 2.Diverse ways of sampling, allocation, models. 3.Random variables, expectation, moments. 4.Important distributions. 5.Limit theorems: law of large numbers, central limit theorem. 6.Random walks and Markov chains. 7.Statistical independence in analysis and number theory.
Page 1 2017-2018 Math 5540H Mathematics 5540H Honors Differential Geometry Spring (even numbered years) 5 credits Catalog Description: Geometry of curves and surfaces in 3-dimensional space, curvature, geodesics, Gauss-Bonnet Theorem, Riemannian metrics.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture