Recommended Exercises for UT's Analysis Preliminary Exam Jim Kelliher The only exercises I feel competent to recommend are those I have done myself, which means I have only a few sources of exercises. Two other obvious sources are Ahlfors and Palka, being on the syllabus, but I have worked only a few exercises from those books. Functions of One Complex Variable I, Second Edition by John B. Conway As a general rule Conway's exercises are easy for a graduate text, but many of his easiest exercises contain not-so-obvious facts that are useful for solving many other, harder problems. The exercises within a section tend to get progressively harder and to build on previous exercises, which is often not the case with Rudin. At least one of Conway's exercises appeared verbatim on a prelim, and some of them are similar to past prelim problems. List of Conway exercises Real and Complex Analysis, Third Edition by the master, Walter Rudin This is the most beautiful math textbook intended for the classroom ever written. (I ignore the sharp cries of disagreement.) Prelim problems are often taken directly from it, and many of its exercises are considerably harder than any prelim problem not appearing on the August 2001 prelim. Few people can safely ignore Rudin and hope to pass UT's analysis prelim. It is particularly important to work all or at least nearly all of the problems in the first three chapters and in chapter 10. This alone is a project for a normal summerwhich a prelim summer is notbut one cannot ignore chapters 6, 7, 8, and 12, so some compromise has to be made. I have taken | |
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