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PhD Degree

The following outline of requirements constitutes the basic structure of the PhD program but depending on the student's background, variations may be worked out with the Program Chair. Information about preparedness and prerequisites can be found on the Welcome page. Refer to the PhD Timeline below as your general guideline and refer to the Student Handbook for the complete description of requirements and policies. For more information, please use our UA Graduate College Request for Information form.

Overall Requirements for the PhD

Students must successfully complete the following requirements:

  1. Coursework and Dissertation Units
  2. PhD Qualification Process
  3. Oral Comprehensive Examination
  4. Research Proposal Writing requirement

Coursework Requirements

Students must complete 52 units of graduate-level coursework, exclusive of dissertation units, as approved by the Program. The coursework must include:

  • Core coursework: 
    • 18 units from MATH/APPL 581A–B, 584A–B, and 589A–B. See the Core Courses page for course details.
    • 4 units of MATH 586A–B
    • 3 units of MATH 599 Independent Study
  • 9 or more units of advanced 500-level Mathematics coursework
  • 9 or more units of coursework outside the Department of Mathematics
  • 9 or more units of elective coursework in Mathematics and/or interdisciplinary areas

If a student has completed coursework equivalent to one or more core courses, the Program may revise the core-course requirements. However, the 52-unit total requirement will not be reduced.

In accordance with Graduate College requirements:

  • At least 50% of graduate units must be in courses for which ABC grades are awarded.
  • Coursework must be at the 500 level or above, with the exception of up to 6 units of 400-level coursework outside the major area (for the Applied Mathematics Program, outside the Department of Mathematics), with prior Program approval.

Dissertation and Registration Requirements

Students must complete 18 dissertation units (APPL 920) for graduation. Students may register for additional dissertation units, but no more than 9 APPL 920 units may be taken in a single semester.

Students must register for a minimum of 6 units per semester until all coursework requirements are completed. After completing the coursework requirements, students must continue to register for 6 or more units per semester, unless other restrictions apply.

Students should register for APPL 900 (research units) and APPL 920 (dissertation units) in consultation with their advisor. The semester in which a student is preparing for the Comprehensive Examination may be an appropriate time to register for 900-level research units. APPL 920 should be taken after passing the Comprehensive Examination and when the student is ready to begin dissertation research. 

Foreign Language Requirement

There is no foreign language requirement for the PhD in Applied Mathematics.

PhD Recommended Timeline

Year 1

  • Complete Core Courses
  • Pass the Qualification Process at the PhD level
  • Identify Research Areas of Interest

Year 2

  • Begin research and identify possible research advisors
  • Complete 2 out-of-Math courses
  • Submit Masters Specialist Plan of Study and Masters Completion of Degree Requirements forms to receive MS Degree (if desired)

Year 3

  • Select an advisor
  • Complete Doctoral Plan of Study
  • Schedule and pass Oral Comprehensive Exam
  • Graduate College records Results of Oral Comprehensive Examination form
  • Begin doctoral research

Years 4 & 5

  • Identify employment opportunities (ongoing)
  • Complete doctoral research
  • Select committee members for Dissertation Defense Examination
  • Complete Committee Appointment Form (formerly known as Advancement to Candidacy) at least 6 months prior to Final Defense
  • Select outside dissertation reviewer
  • Complete Announcement of Dissertation Defense Examination Form
  • Submit Research Proposal Writing requirement
  • Pass Dissertation Defense Examination
  • Electronically submit final copy of dissertation to the Graduate College according to the specified deadline for the semester in which the final defense takes place.