The Catholic University of America

The Comprehensive Exam in Mathematics

OUTLINE

The Comprehensive Exam is taken in the fall semester of the student's senior year. It consists of two components: a sequence of three take-home exams and a written or oral in-class exam.

The take-home exams are scheduled in September and October; a student has 10 -12 days for solving problems of each of the exams.

The in-class exam, which can either be written or oral, takes place in the first half of November.

In order to pass the Comprehensive Exam, a student must pass both of its components. Any student who fails either component will be given a second chance to pass that component in the spring semester of the senior year. The Comprehensive Exam will be coordinated by the chair of the Comprehensive Exam/Contest Committee.

 

TAKE-HOME EXAMS

The sequence of three take-home exams reflects the material of the following courses: MATH 121 (Analytic Geometry and Calculus I), MATH 122 (Analytic Geometry and Calculus II), MATH 221 (Analytic Geometry and Calculus III), MATH 301 (Linear Algebra) and MATH 321 (Abstract Algebra I). Each of the three take-home exams is scored on scale of 0 - 10 points. The passing grade is 16 points or higher. To be considered for possible honors, the student must get at least 24 points.

It is understood that while some references are permitted, each student shall work INDIVIDUALLY. The problems are not to be discussed until they have been turned in.

Click HERE for sample problems for the take-home component of the comprehensive exam. 

 

IN-CLASS EXAM, WRITTEN OR ORAL

At the beginning of September the Department provides a list of specific questions that cover the material required for the in-class component of the Comprehensive Exam.  Click HERE for the list of specific questions that was provided in previous years.

By November 1, each student chooses either the written exam or the oral exam format for the second component of the Comprehensive Exam.

The procedure for the oral exam is as follows. A student receives two questions from the list he received in September and a problem from a course of the student's choice. The student will have one hour for preparing the answers. This is an OPEN BOOK EXAM and a student can use any literature in his (her) preparation. Then the student answers the questions and presents the solution of the problem at the blackboard. (The student can write his or her notes on the blackboard during the preparation.) The examiners will ask questions during the presentation; these questions will be related to the presentation, but there might be some additional questions on the topics outlined by the list of questions sent in September.

The students who take written exam will receive a test with eight problems: two problems in Calculus, two problems in Linear Algebra, two problems in Abstract Algebra, and two problems in the area (course) of the student's choice. The student must complete the exam within 3 hours. This is also an OPEN BOOK EXAM and a student can use any literature at the test.