University of Alaska Fairbanks
Department of Mathematics and Statistics

MS Mathematics Comprehensive Examination: Information

A written Comprehensive exam is required for all MS students.  The exam combines three subject exams; see the detailed rules below.

The same combined exam is the Qualifying exam for the PhD program for PhD students who do not already possess an MS degree in mathematics or applied mathematics.

Sample subject exams in PDF format:

Early each spring, the following form will be handed out to
 Each such student must complete this form and return it to the graduate coordinator or the Department Chair:


Comprehensive Exams for MS (and Qualifying Exams for PhD) students in Mathematics

These exams consist of three 1.5 hour written exams to be completed within one week. Dates and times will be determined in consultation with students, based on response to this form. MS students in mathematics are required to take these exams as comprehensive exams.  PhD students who hold a Master’s degree in Mathematics or in Applied Mathematics need not take these exams, but otherwise these are qualifying exams for  the PhD program in mathematics.

The subjects covered must include at least two of the four core courses (i.e. at least two of: Math 631 Algebra I, Math 641 Analysis I, Math 645 Complex Analysis, Math 651 Topology). The third subject may be chosen from some other 600-level lecture or independent-study course in mathematics. The choice of exam subjects requires the approval of the student’s committee. It is preferred that none of the exams cover courses in which the student is currently enrolled, but the committee has discretion on this. For each core subject, two faculty members will jointly prepare and grade each exam. For non-core subjects, the student’s committee must arrange the preparation and grading of the exam.

The exams will be at most as hard as the written final for the corresponding courses. Students will be given some choice of problems. Certain problems at a prerequisite level to the graduate course in question should be expected.

If the student does not pass two or three of the exams then he or she must wait at least one semester and then retake the entire comprehensive examination (i.e. three exams) again. If a student passes exactly two of the three parts, then the student has one try to retake the remaining part, preferably before the start of the following semester. If the student fails the remaining part then the entire examination must be retaken.

Only one retake of the entire examination is allowed.

These exams are qualifying exams for PhD candidates. These exams do not fulfill the comprehensive examination requirement for PhD students. A further comprehensive examination, possibly oral and possibly focussed in the area of the prospective dissertation, is expected.  It is the responsibility of the student’s committee.  


Student Name:______________________________________________  Date:_________________________
Semester of first enrollment in the MS/PhD Math program:________________
Do you plan to take the comprehensive exams in Spring/Summer 20XX?:   
      Yes  /  No
Signature of your Committee Chair (your advisor; signature required whether "yes" or "no" above):
_________________________________________________

If “Yes”  above, complete the following:
Core Subject 1:______________________   
Core Subject 2:______________________
Other Subject:_______________________       
        (Description of third exam if not core:____________________________________________________
 _____________________________________________________.)
 
Signatures of two faculty members who are willing to prepare and grade the third exam (if not core):
_______________________________________    
_______________________________________


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