Introductory Exam
The Introductory Exam is a written exam and tests (at no higher than the 400-level) for an understanding of the basic areas listed below, and for general proof-writing and integrative skills. This exam is designed to be taken and passed early in a student's graduate academic career.
The Introductory Exam will be offered just prior to each semester. It may be taken no more than four times (including a first try before the student's first semester). A student is required to pass the exam before beginning the fourth semester of study in order to continue in the Ph.D. program. In anticipation of the possibility of not passing the exam students are advised to plan for completion of the Master's degree during the student's second and final year in the department.
Scope
The Introductory Exam will consist of approximately 15 questions, with approximately 5 questions in each of the following four areas
- real analysis
- linear algebra
- probability
-
Syllabi for these topics are given on this page: link to syllabi
- At least 25% of the questions (and perhaps a significantly larger
percentage) will be proof-oriented and about 25% will be interdisciplinary
in nature. The intent is that each question be offered at a 400-level
(advanced undergraduate-level) of difficulty. The exam
may typically be constructed by taking problems directly (or with slight
modification) from relevant elementary textbooks. To the extent possible,
the questions will have unambiguous answers.
The faculty intend to design the exam so that a student can complete it in three to four hours, but students will be permitted to take longer (in fact, to the end of the business day) if desired. The exam is a closed-book exam.
Grading
Clear thinking and writing are important on the Introductory Exam, and the student’s grade will reflect this. Points per part should be clearly labeled on the exam. Exams will be graded as pass/fail, with 66 2/3% generally considered passing.
Administration
- The exam isl be offered twice per year near the beginning of each of the Fall and Spring semesters.
- The date and location of the exam will be announced at least one month prior to the exam.
- All students will take the exam at the same time.
- No prior sign-up for the exam will be required.
- The exam will be a closed-book exam.
- The exam will start at 8:30 AM on the day it is offered.
- The faculty will attempt to design the exam so as to require at most four hours by an average student.
- Students should plan on six hours (that is, five hours, with a recommended one hour rest for lunch).
- Students will be given until 5:00 PM to complete the exam.
- Students may leave the exam room only for short periods of time for valid reasons (such as use of the restroom).
- The department will supply lunch, drinks, and snacks.
Past introductory exams with solutions are available on the department web site.