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m327pol7 - Math 327 Policy Statement Fall 2007 1 Instructor...

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Math 327 Policy Statement Fall, 2007 1. Instructor: B. Dodson, Room 207 XS, Phone x8-3745, Email bad0. 2. Text: Dummit-Foote, Abstract Algebra, 3rd. Edtn. Selected portions of Chapters 1-9 will be covered. There will be additional material handed out on “groups of medium order”, especially the 2-groups of order 512 and order 1024. We will also have additional material on the simple composition factors of the Jordan- Holder Theorem (section 3.4); including the orders and names of the finite simple groups, and the list of complex simple Lie algebras. For rings we will focus on rings of algebraic integers and polynomial rings, in- cluding the characterization of unique factorization domains. Special attention will be given to quadratic integers and cyclotomic integers, including the statement of Kronecker’s completeness theorem. Abstract group theory will feature examples, statements and proofs of Sylow theory. Attention will be given to p-groups and
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