Mathematics: Graduate Programs
The Graduate Programs offered by the Mathematics Department train students to be independent critical students and researchers with a broad and deep knowledge of modern mathematics. Our goals are to produce students with topquality scientific training, excellent teaching and communications skills, and broad professional development experiences.
Expected student learning outcomes for the PhD degree:
1. Demonstrate basic knowledge in a broad range of fundamental graduate level mathematics including real and complex analysis, abstract algebra, geometry and topology.
2. Demonstrate specialized knowledge at the forefront of a particular research area.
3. Effectively communicate mathematics through both written and oral communication.
4. Work and think independently to learn high level mathematics and create new mathematics through research.
Expected student learning outcomes for the MS degree:
1. A basic knowledge in one or more areas of fundamental graduate level mathematics including real and complex analysis, abstract algebra, geometry and topology.
2. More advanced knowledge in a particular subfield.
3. Communication skills, including verbal and written communication.
ASSESSMENT ACTIVITIES
PhD degree:
Graduate students are assessed at certain key points in their graduate program:
1. Qualifying Exams: Students take written qualifying exams during the first three years of the program until they complete the Qualifying Exams. These exams are in the fields of Algebra, Geometry/Topology, and Real Analysis. In addition, a masters thesis may be used as an exam. Each time a student takes an exam, they are evaluated as to whether they failed, passed, or high passed the exam. To complete Qualifying Exams, high passes in two exams and a pass in a third exam are required. These are used to assess Learning Outcome 1.
Under reporting, students are given a 2 for a high pass on an exam, a 1 for a pass on an exam, and a 0 for a fail. The average scores are reported, together with total number of students taking the exams (if a student takes an exam in summer and winter, they are counted twice) and the total number of exams taken. If students were to get two high passes and one pass in their only attempts, the average would be 1.67, so this is a goal. However, since students often take exams more than once, it is acceptable to have lower scores while still fulfilling this outcome.
Note also that we do not currently take into account the masters option for passing qualifying exams in this assessment. We plan to update this soon.
2. Comprehensive Exam: Students take their comprehensive exam by the middle of their fourth year in the program. Students are required to submit a written piece of the comprehensive exam and also expected to give a presentation and answer questions form a committee. The committee then evaluates the student’s progress according to the following rubric:
http://internal.math.arizona.edu/files/grad/forms/Comprehensive Exam Assessment Rubric.pdf
We are aiming for at least an average of 3.
3. Dissertation and Defense: The Ph.D. dissertation must be research of publishable quality. It is evaluated by an internal committee of experts in the field. The final oral examination is a presentation and defense of the student's dissertation. The committee then evaluates the student’s progress according to the following rubric:
http://internal.math.arizona.edu/files/grad/forms/Dissertation Assessment Rubric.pdf
We are aiming for an average of at least 3.
All of the above mechanisms are used to evaluate student progress and to make improvements to the graduate program. Data is collected on qualifying exam results, and evaluation rubrics from the Comprehensive Exam and the Dissertation Defense.
The assessments are summarized in the following table.
Assessment Activities 
Outcome 1: Basic knowledge 
Outcome 2: Specialized Knowledge 
Outcome 3: Communication skill 
Outcome 4: work and think independently 
Written qualifying exams/Masters thesis 
X 



Comprehensive Exam 

X 
X 

Written dissertation and dissertation defense 

X 
X 
X 
MS degree:
For the MS program, students are assessed in their courses through the traditional mechanisms such as problem sets and exams, and they also have the opportunity to write term papers. The MS thesis is evaluated by an internal committee. The student must also pass an oral defense of the thesis. Many of the activities are similar to the PhD requirements.
Here is a summary of the assessment activities:
Assessment Activities 
Outcome 1: Basic knowledge 
Outcome 2: Specialized Knowledge 
Outcome3: Communication skill 
Course work 
X 


Thesis and Thesis defense 

X 
X 
Here is a summary of the results for the PhD degree:
Assessment  Outcome 1: Basic Knowledge (out of 2)  Outcome 2: Specialized Knowledge (out of 4)  Outcome 3a: Verbal Communication (out of 4)  Outcome 3b: Written Communication (out of 4)  Outcome 4: Work and think independently (out of 4) 
Qualifying exam  1.21  
Comprehensive exam  3.13  3.29  3.25  
Dissertation defense  3.38  3.46  3.38  3.77 
These results are based on the following data:
Assessment  Number of students evaluated  Total number of evaluations  Dates 
Qualifying exam  25  47  8/1/20156/1/2017 
Comprehensive exam  6  24  12/1/20166/1/2017 
Dissertation defense  3  13  12/1/20166/1/2017 
Most results are acceptable. In trying to get a better outcome in qualifying exams, students have been advised to solidify background (either by recruiting students with more background or encouraging students arriving to take more remedial coursework). An updated description of the qualifying examinations will be posted to the website.
We also plan to update our Qualifying Exam assessment to take into account students who use a masters thesis for an exam.