May 28, 2023  
2020-2021 Graduate Catalog 
2020-2021 Graduate Catalog [ARCHIVED CATALOG]

Mathematics, Ph.D.

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Priority Program Admission Deadlines:

Pure and Applied

Contact Information

College: Arts and Sciences
Department: Mathematics and Statistics

Contact Information:

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:  90 hours post-baccalaureate, 60 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 – 9 Credit Hours
  • Concentration – 33 Credit Hours minimum
  • Electives – 2 Credit Hours minimum
  • Dissertation – 16 Credit Hours minimum

Core Requirements (9 Credit Hours Minimum)


Students must select from one of the concentrations below. Each concentration offers coherent pairs/triples of courses, referred to as sequences, to ensure a certain depth of disciplinary knowledge.   In addition to the primary concentration courses, the student must complete a total of four sequences: two Fundamental sequences for their concentration and a two more sequences from among the Fundamental and Elective Sequences for their concentration with at least a 3.00 average in each sequence.  Each course may count towards only one sequence.  Substitutions may be allowed with prior approval of both the Concentration Director and Concentration Graduate Committee. 

Pure and Applied Concentration (33 Credit Hours)

The student must complete at least one course from each of the following groups:

Group 1 – Algebra:

Group 2 – Complex Analysis:

Group 3 – Topology:

Fundamental Sequences

Students must complete two sequences.


Real Analysis:


Elective Sequences

Students must complete two sequences.

Applied Mathematics


Complex Analysis

Differential Geometry

Dynamical Systems

Functional Analysis

Harmonic Analysis

Partial Differential Equations

Theory of Computing

Statistics Concentration (48 Credit Hours)

Fundamental Sequences

Students must complete two sequences.

Statistical Methods:

Mathematical Statistics:

Elective Sequences

Students must complete two sequences.

Linear Models and Multivariate Analysis:


Stochastic Processes and Time Series Analysis:

Electives (2 Credit Hours Minimum)

All students select graduate course electives in consultation with their advisor.

Qualifying Examinations

An examination based on a Fundamental Sequence is called a Fundamental Qualifying Examination.  The student is required to pass two Fundamental Qualifying Examinations at the Ph.D. Level.  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 (16 Credit Hours Minimum)

  • Credit Hours: 2-19 (16 credit hours)

  • Students admitted to doctoral candidacy are required to take at least 16 hours in MAT 7980 Dissertation: Doctoral , with 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.

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