Doctoral and Master's Comprehensive Exams⁷

 Purpose

The purpose of the comprehensive exams given by the Mathematics Department is to determine whether the student has mastered the concepts which the Department feels are minimal prerequisites for an advanced degree.

 When to Take the Exams

Students should take the Comprehensive Exams as soon as possible after they have completed the necessary course work, but not prior to completing this course work. Approval of a student's advisor is required prior to taking the exams. The timely completion of the Comprehensive Exams is one of the factors considered in the evaluation of a student's progress toward degree. Ph.D. and Ed.D. students should begin taking parts of the Comprehensive Exam the next examination period following completion of two of the core courses.  

 Schedule and Application Procedure

Exams are offered the week prior to the first week of classes for the fall semester and spring semester. Exact dates and times are announced at least one month before the exams are given.

Students wishing to take an exam should obtain an application form from the departmental secretary and return the completed form to the Graduate Committee.

A student who applies for an exam is expected to take it and will be considered to have failed the exam if it is not taken.

 Preparation and Administration

Exams cover several areas of mathematics. The exam for each area is prepared and graded, at the request of the Graduate Committee,  by a committee of members of the faculty. The exams are then administered by the Graduate Committee.

 The Grading Procedure

MASTER'S EXAMS 

Students are expected to exhibit competence in all of the areas in which they are tested. After a student has taken an exam, each part is graded ``Pass or ``Fail'' by the committee which prepared it. (Note: Advanced Calculus I & II make up a single part of the exam as do Modern Algebra I & II.) The Graduate Committee reviews the results of the Comprehensive Examinations and makes the final decision as to whether or not the student has passed each part of the exam. The Graduate Director informs the students by letter of the results of their exam. Exam results are not announced publicly. Upon request, the Graduate Director will discuss with the students their performance on the exams.

PH.D. AND ED.D. EXAMS  

Students are expected to exhibit competence in all of the areas covered on the exam. Students may take as many parts as they choose during each exam administration period. All parts must be passed within 25 months of the time that the first part is taken. After a student has taken one or more parts of the exam, each part taken is graded ``Pass'' or ``Fail'' by the committee which prepared it. The Graduate Committee then reviews the results and determines whether the student has passed the parts taken. A student will pass the exam if he has received ``Pass'' marks on all required parts of the exam. A student may attempt any one part of the exam at most three times. A student who fails any part three times or does not pass all of the required parts within the 25 month period has failed the exam.

It is the policy of the Graduate Committee to report exam scores as pass-fail only. The Graduate Committee will discuss exam performance in general terms with each student, if he/she wishes.

 Exam Formats

The Master's Exam is given in three sessions over two days with a rest day between the exam days. Each exam session is one or two hours depending on the exams. A typical format for these sessions is as follows:

Format for Pure Mathematics Option

1.

First Day - Morning Session: Advanced Calculus I and II (2 hours)

2.

Second Day - Morning Session: Modern Algebra (2 hours)

3.

Second Day - Afternoon Session: General Topology (1 hour)

Format for Applied Mathematics Option

1.

First Day - Morning Session: Advanced Calculus I and II (2 hours)

2.

First Day - Afternoon Session: Complex Variables (1 hour)

3.

Second Day - Morning Session: Advanced Linear Algebra (1 hour) and Numerical Analysis (1 hour)

The Ph.D. and Ed.D. exams are given in four sessions over two days with a rest day between the exam days. A typical format for these sessions is as follows:

Format for Ph.D. in Mathematics

1.

First Day - Morning Session: Real Analysis I and II (2 hours)

2.

First Day - Afternoon Session: Complex Analysis I and II (2 hours)

3.

Second Day - Morning Session: Algebra I and II (2 hours)

4.

Second Day - Afternoon Session: Geometric Topology and Algebraic Topology I (2 hours)

For the Specialization in Mathematics Education one of these may be replaced by the Statistics department exam over Stat 4113 and Stat 4223.

Format for the Ed.D. with Emphasis in Mathematics

1.

First Day - Morning Session: Real Analysis I and II (2 hours)

2.

First Day - Afternoon Session: Complex Analysis I and II (2 hours)

3.

Second Day - Morning Session: Algebra I and II (2 hours)

4.

Second Day - Afternoon Session: General Topology (1 hour) and the six credit-hour course sequence taken in Computer Science, Numerical Analysis, or Statistics (1 hour)

For the Ed.D. one of the exams in the first two sessions may be replaced by Advanced Calculus or the exam in the third session may by replaced by Modern Algebra but not both.

 Content of Exams

The syllabi for the exams can be found in this Graduate Program Handbook. Copies of the syllabi and old exams can also be obtained from the web pages.

The Comprehensive Exams are intended to cover the material outlined on the syllabi. This material is approximated by the corresponding courses but does not necessarily coincide with the course work.

 Failure and Re-examination

MASTER'S EXAMS

A student who fails a part of the Master's Comprehensive Exams must retake that part of the exam the next time it is offered. There is no limit to the number of times a student may take the Master's Comprehensive Exams. However, if a student fails any part of the exams twice, the Graduate Committee  will inform the Department Head that financial support  should be discontinued.

PH.D. AND ED.D. EXAMS

A student who fails one or more parts of an exam and has not failed any part three times may retake any part during any subsequent examination period within their 25 month ``window''. A student who fails any part three times or does not pass all of the required parts within the 25 month ``window'' has failed the exam. If a student fails the Comprehensive Exam, the student is suspended from the program and the Graduate Committee will inform the Department Head that financial support should be discontinued.

 Notebooks and Course Outlines

For the student's convenience, the exam syllabi and old exams are available on the graduate program web site.