Doctoral Program (PhD)

The main steps in obtaining a PhD in mathematics are: (A) Satisfactory completion of first year's coursework and evaluation exams; (B) Passing oral exam in intended area of research and advancing to candidacy; and, (C) Writing the dissertation and successfully defending it in a final oral exam. The aspects of each step are more fully discussed on this page.

The course schedule outlined below is for students in the PhD program who are supported by a teaching assistantship and tuition fellowship. It is 9-credits per semester. For students who do not have support an additional 3-credit course is require so as to be a full time student. 

Learning mathematics is a shared enterprise. Thus, all members of an entering doctoral class advance through the first year coursework as a cohort.

Fall semester:

1. Pure Track.
   1. MTH 534, Basic Measure Theory.
   2. MTH 519, Introduction to Abstract Algebra.
   3. MTH 527, Introduction to Topology I.
       
2.  Applied Track.
   1. MTH 539, Methods of Applied Mathematics.
      
   2. MTH 537, Introduction to Numerical Analysis I.
      
   3. One of:  MTH 534, Basic Measure Theory; or
      MTH 519, Introduction to Abstract Algebra; or
      MTH 527, Introduction to Topology I.
      

Spring semester offering:

1. Pure Track.
   1. MTH 625, Complex Variables.
   2. MTH 520, Advanced Linear Algebra.
   3. MTH 528, Introduction to Topology II.
       
2. Applied Track.
   1. MTH 540, Methods of Applied Mathematics II.
   2. MTH 538, Introduction to Numerical Analysis II.
   3. One of:  MTH 563 Topics in Applied Mathematics (Applied Complex Analysis), 
      MTH 625, Complex Variables,
      MTH 520, Advanced Linear Algebra, or
      MTH 528, Introduction to Topology II.

Evaluation Exams: Attached to each first year course is an evaluation exam. This exam will be given during the regularly scheduled final exam time. All first year evaluation exams are pass/fail.  To continue in the PhD program a student needs to achieve at least 4-out-of-6 exam passes. To continue in the MA program a student needs to achieve at least a 3-out-of-6 exam passes. To be in good standing in any graduate program a student needs a GPA of B or above.

Deficiency: Students whose performance at the end of their 1st year is judged to be significantly insufficient by the Graduate Director will be dismissed from the program before the beginning of their 2nd year. Students who are marginally below the mark (e.g., pass 2 out of 4 exams or better at PhD level) and/or are marginally below the required B-GPA level, so that they can still advance with their original cohort, have an opportunity to retake the relevant exams in the final exam week of the Fall and Spring semesters in their 2^nd year. If the student passes these “make ups’’ (i.e., pass 4-out-of-6 in total for PhD and 3-out-of-6 for MA), then the student will be allowed to advance through the program along with their original cohort. If not, then the student will be dismissed from the program.

After the first year's course work, the student will take more advanced courses at the 600 level and 700/800 level topics course. Students also typically arrange individual reading courses with professors and participate in area seminars.

There is a breadth requirement for students pursuing the Pure Track. They are required to take two out of three of the
following 600-level sequences: MTH 619-620 (algebra), MTH 627-628 (topology), and MTH 731-732 (analysis). Since the number of preparatory courses is more numerous for students pursuing the Applied Track (e.g., MTH 543-544 (fundamentals of applied math), MTH 645 (ODEs), MTH 649 (PDEs)), the breadth requirement will need to be individually tailored and will be administered by the Graduate Studies Director.

Entering their third year, students will be focusing on their preferred area of research and the faculty with whom they would like to work. Students will be required to form an oral examination committee of two or three faculty members chaired by a potential thesis advisor.

Students will work with their committee to prepare a syllabus outlining topics to be covered in the oral examination including a bibliography of books and/or articles. Typically the topics to be covered in the oral examination should be at the level of 600 to 800 level courses and include material that the student learned individually.

The syllabus must be approved by the Graduate Director’s office and the student’s committee members. Students should pass their oral examination prior to the end of the third year of the program.

The final departmental steps in attaining the degree is completion of a dissertation that must consist of original research of sufficient quality for publishing in a respectable mathematics journal. It is not unusual for the mathematics in a single dissertation to generate two or three published manuscripts.

Template forthcoming.