Prelim / Area Exam

The theory prelim is an oral exam, often followed by 1-3 written questions at the discretion of the committee.  Below we describe the goals, general format, and expectations of the exam.

Goals.  We hope you will take this opportunity to strengthen your preparation for your journey ahead, namely pursuing your own research and continuing to become part of a research community.  In particular, we invite you to choose topics and subtopics that will expand your knowledge and skills in directions you and your advisor feel are important for the work you want to do and the research community you want to be a part of.  That said, we also want our students to have broad knowledge within theoretical computer science, e.g. so they can converse with any CS theory researcher.  Hence we may not approve topics which are too narrow, especially within algorithms and complexity; see below.  We hope you will have fun with the exam, both in learning and preparing and in the exam itself, and remember, we are rooting for you!

Syllabus.  Roughly a semester before the exam, the student and committee will jointly agree on the exam syllabus, which consists of three topics.  Two of these topics should be algorithms and complexity, or could be broad subsets of these topics, such as approximation algorithms and parameterized complexity, respectively.  The third topic can be tailored to the student’s particular research area.  The topics are further specified by a list of subtopics; for the third topic, this list is often a collection of relevant research papers.  There are example syllabi from previous exams to help students calibrate.

Format.  The oral exam is 2 hours: 30 minutes for a short presentation from the student, followed by 90 minutes of questions from the committee.  The presentation should focus on one of the three topics, often the third topic, closest to the student’s research area.  Students should plan (and practice) for a 15-minute presentation, so that it stays within 30 minutes even with inevitable interruptions and clarification questions.  Following the presentation is an oral exam, where the faculty take turns asking questions on any of the subtopics on the syllabus.  The format is not meant to be adversarial, but rather to assess the students general knowledge of the topics; for example, the committee may give hints if a student gets stuck on an initial detail, so as to let the conversation continue.  Following the oral exam, if some gaps in knowledge surfaced in topics, or time ran out to adequately cover all topics, the committee may decide to assign 1-3 written questions to the student, with a deadline of roughly 1-3 days following the oral exam.  These questions will be relatively light, and often (though not always) open-book and open-internet.
Committee.  At least 2 members of the area exam committee should be from the core theory faculty.  The third may be any faculty member at CU with an appointment in the Graduate School that the advisor and student feel is appropriate.