Algebra Qualifying Exam Syllabus and Suggested References
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Algebra Oral Qualifying Exam Syllabus
algebra is the study of fundamental algebraic structures that occur throughout mathematics: groups, rings, modules, categories, and fields—as well as maps between them. A solid grasp of algebra can be useful to students of all mathematical stripes, and accordingly the suggested syllabus is a “strong core plus more” model: a student preparing for an oral qualifying exam in algebra should (1) fee...
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Exam Committee Exam Logistics Committee Chairperson: Date: Prof. Monica Vazirani Thursday September 3, 2015 Committee Members: Time: Prof. Dan Romik 11AM-2PM Assoc. Fu Liu Location: Prof. Greg Kuperberg MSB 3106 Prof. Francisco J. Samaniego 1 Proposed Research Talk 1.1 The Catalan numbers and q-analogues. A lattice path is a sequence of North N(0, 1) and East E(1, 0) steps in the first quadrant...
متن کاملQualifying Exam Syllabus
Basic constructions: The completeness and compactness theorems. The Löwenheim-Skolem theorem. Omitting types. Ultraproducts. Indiscernible sequences. Nice properties: Saturation, homogeneity, and the monster model. Elimination of imaginaries and Meq. Quantifier elimination. Model completeness. Countably categorical theories. Stable theories: Characterizations of a stable formula. Stable, supers...
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These notes are written as supplements to the textbook, “Numerical Linear Algebra” by Lloyd Trefethen and David Bau, for CAAM 454/554 students. Those who are preparing for the CAAM Ph.D Qualifying exam on Numerical Analysis should do the exercises provided in these notes. We will mostly follow the notation of the book. For instance, unless otherwise specified, the norm ‖ · ‖ refers to the Eucli...
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تاریخ انتشار 2012