Jun 17, 2024  
2024-2025 Graduate Catalog 
2024-2025 Graduate Catalog

Mathematics, Ph.D.

College of Arts and Sciences  
Department: Mathematics and Statistics 
  • Pure and Applied
  • Statistics


The Major provides the experience and knowledge to understand and appreciate prior accomplishments in the discipline and develops the skills necessary for a meaningful contribution to the intellectual advancement and applications of the discipline. It prepares its graduates to pursue long-term careers in their field by providing solid and cutting-edge knowledge. Graduates receive training that enables them to conduct independent research and write research papers publishable in peer-reviewed journals of their discipline, as well as a technical education enabling them to take on leading positions in a modern economy.

Major Research Areas
Algebra & Number Theory, Applied Statistics, Approximation Theory, Bio-Mathematics, Complex & Harmonic Analysis, Cyber-Security & Cryptography, Data Science, Differential Equations, Graph Theory & Combinatorics, Low-Dimensional Topology, Mathematics Education, Mathematical Physics, Operator Theory, Probability, Statistical Learning, Stochastic Processes & Modelling

Admission Information

Must meet University Admission and English Proficiency requirements as well as requirements for admission to the major, listed below.

  • A degree from an accredited institution relevant to the prospective concentration. Either
    • a Master’s degree or equivalent in mathematical sciences/statistics or a related area; or
    • a Bachelor’s degree or equivalent in mathematical sciences/statistics or related area with a strong record of undergraduate/graduate courses related to prospective concentration.
  • GRE - At least a 55th percentile Quantitative; Verbal and Analytical Writing scores are also considered.
  • At least a 3.50 GPA in graduate and/or upper undergraduate mathematics/statistics courses.
  • Three letters of recommendation (two of which should be from college level mathematics/statistics professors)
  • A completed departmental application form, including a statement of goals.
  • A completed departmental graduate teaching assistantship application form (if such a position is desired).

Applicants to the Ph.D. program may be offered admission to the M.A. program and move to the Ph.D. program after establishing a record of success in graduate courses. Graduate Teaching and Research Assistantships are available on a competitive basis. Contact the Department for recommended prerequisites for each concentration.

Curriculum Requirements

Total Minimum Hours:  72 hours post-baccalaureate, 42 hours post-masters

Students entering for the post-bachelor’s option must complete the requirements specified for the MA in Math at USF.

  • Core Requirements – 4 Credit Hours
  • Additional Required Courses - 6 Credit Hours
  • Concentration – 24 Credit Hours minimum
  • Dissertation – 10 Credit Hours minimum
  • Directed Research or Dissertation - 6 Credit Hours minimum
  • Additional hours taken in coursework, Directed Research or Dissertation, as needed, to meet minimum hours for the Major - 22 Credit Hours

Core Requirements (4 Credit Hours Minimum)

Additional Required Courses (6 Credit Hours)


Students must select from one of the concentrations below. Each concentration offers coherent pairs/triples of courses, to ensure a certain breadth and depth of disciplinary knowledge.

Pure and Applied Concentration (24 Credit Hours)

  • Required Concentration Courses:

  • Credit Hours: 3
  • Credit Hours: 3
  • Credit Hours: 3

    In addition to the required concentration courses, the student must complete at least two complete pairs of courses from the Fundamental Knowledge categories and two more groups from among the Fundamental Knowledge or Mathematical Depth categories with at least a 3.00 average in each pair or group. Substitutions may be allowed with prior approval of both the Concentration Director and Concentration Graduate Committee.

Fundamental Knowledge in Algebra, Analysis or Topology

Course Groups Representing Mathematics Depth

Applied Algebra and Number Theory

Applied Mathematics


Complex Analysis

Dynamical Systems

Functional Analysis

Graph Theory

Harmonic Analysis

Partial Differential Equations

Theory of Computing

Statistics Concentration (39 Credit Hours Minimum)

Fundamental Knowledge in Statistical Methods and Mathematical Statistics:

Group Courses Representing Statistical Depth:

Linear Models and Multivariate Analysis:

Industrial Statistics

Stochastic Processes and Time Series Analysis

Additional Hours Taken in Concentration or Electives (22 Credit Hours)

Students select additional graduate courses in the Concentration or electives, as needed, and in consultation with their advisor, to meet minmum hours for the Major.

Qualifying Examinations

The student is required to pass two Fundamental Qualifying Examinations at the Ph.D. level, which are based on their elective choices.  After passing two Fundamental Qualifying Examinations, the student will select a Dissertation Advisor, who will convene a Specialty Examination Committee to author a Specialty Examination.  Passing two Fundamental Qualifying Examinations and the Specialty Examination at the Ph.D. level is considered passing the Doctoral Qualifying Examination. 


Dissertation (10 Credit Hours Minimum)

Directed Research or Dissertation (6 Credit Hours Minimum)

  • Credit Hours: 2-19
  • Credit Hours: 1-19

    Students admitted to doctoral candidacy are required to take at least 10 hours in MAT 7980 Dissertation: Doctoral , and at least 6 combined hours of MAT 7980   and MAT 7912  .  For the Directed Research hours to be counted, it must be approved by the Major Advisor and the Program Director.  Students in the Doctoral Candidacy must enroll a minimum of 6 credits of dissertation hours accumulated during each previous 12-month period (previous 3 terms, e.g. Fall, Spring, Summer) until the degree is granted.


    The candidate will conduct original and significant research which is worthy of publication. The research will be described in the doctoral dissertation. Research towards the dissertation typically forms the major part of the work required for the Ph.D. in Mathematics. The Doctoral Dissertation Defense shall consist of an oral presentation of the research in the dissertation to the supervisory committee.


The student is responsible for familiarizing themselves with the additional program requirements and expectations listed in the program handbook, particularly those concerning timely progress.