prelims-syllabi.pdf - Preliminary Exam Syllabi Graduate...

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Preliminary Exam Syllabi Graduate Committee Department of Mathematics Wayne State University Winter 2012 These are 2-hour written examinations covering undergraduate-level material from a sophisticated point of view. Students are required to pass a preliminary exam in Algebra or Analysis, as well as one additional exam from the following four choices: Algebra; Analysis; Applied Mathematics; and Probability and Statistics. Students may choose to take exams in their first semester in the Ph.D. program, in which case they must satisfy the requirements by the end of their second semester; or they may choose to take exams in their second semester, in which case they must satisfy the requirements by the end of their third semester. Students must select exams at the beginning of each semester, to be taken later in that semester. Under special circumstances, the Graduate Committee may approve petitions on an individual basis for exceptions to these rules. Algebra Exam. Elementary group theory, ring theory, and field theory. Linear algebra including inner product spaces, diagonalization, and naive construction of canonical forms. The topics covered are similar to the topics covered in MAT 5420, 5430, and 6420. Typical References: Axler, Linear Algebra Done Right Beachy & Blair, Abstract Algebra Herstein, Abstract Algebra Hoffman & Kunze, Linear Algebra Analysis Exam.

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