This document provides study guides for subjects in which written qualifying exams are given. Each guide lists topics that a student should know for the corresponding examination. An attempt has been made to put these topics in coherent order and to provide useful references. The study guides are not intended as syllabi for the corresponding graduate courses. For each of the subject areas, an introductory one-semester 8000-level course is designed to help prepare students for the qualifying exam. However, certain background material may be assumed in the 8000-level course, and the course might omit some of the topics in the study guide and include topics not appearing in the study guide. Thus it is the student's responsibility to prepare adequately for a written qualifying exam by mastering the topics on the study guide.

Written qualifying exams are offered in Algebra, Complex Analysis, Numerical Analysis, Real Analysis, Probability, and Topology. All Ph.D. candidates must pass the qualifying exams in both Complex Analysis and Real Analysis, and two other qualifying exams, including either Algebra or Topology. All of the exams are three hours in length. The written qualifying exams are offered every year in August before the start of fall semester classes, and in January before the start of spring semester classes. A link to the study guides is below and links to previous qualifying exams are on the right menu.

## Study Guides: