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Information for Graduate Students

The Analysis Qualifying Exam

For the syllabus, you should consult the Department web site (which as syllabifor all the qualifying exams as well as information on the preliminary exams). This page is really for folks considering asking me to be on their qual committee. There is a "book" on me -- consult the other graduate students for details. In fact, Jody Trout and I decided to write our own set of practice questions. As a consequence, I expect anyone taking an exam from me to be familiar with those questions and their answers. Thus, I EXPECT YOU TO BE ABLE TO PROVIDE REHEARSED ANSWERS TO THOSE QUESTIONS -- especially those labeled "Basic". If it becomes apparent that you are not familiar with those questions, I reserve the right to stop the exam and ask you to come back after the required interval.

Note that our sample questions can be found via the same link as above: click here.

Of course, the exam may not, and probably will not, be taken completely from the sample questions, but you can expect me to ask a substantial subset of those questions.

Working in Operator ALgebras

Operator algebras is a deep and fascinating subject, but it requires a sophisticated understanding of functional analysis including, but not limited to, bounded linear operators on Hilbert space and their functional calculus. Math 103 and Math 113 are a good start, but you will also want to look at my lecture notes on the spectral theorem. In addition, I have written two books designed for graduate students embarking on the study of operator algebras (and especially for those planning to work with me). The first, written with Iain Raeburn, is entitled Morita Equivalence and Continuous-Trace C*-Algebras. The second is entitled Crossed Product C*-Algebras. Both have extensive appendices that should be useful.

As for choosing an advisor, or being chosen, that is a personal matter. But a successful partnership -- one that leads to a Ph.D. -- can be a lifetime affair. I certainly have depended on my advisor for advice, and not to mention countless letters of recommendation, throughout my career.

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Last modified on December 24, 2012