May 28, 2023

2020-2021 Graduate Catalog

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2020-2021 Graduate Catalog [ARCHIVED CATALOG]

Mathematics, Ph.D.

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Priority Program Admission Deadlines: http://www.grad.usf.edu/majors

Concentrations:

Pure and Applied
Statistics

Contact Information

College: Arts and Sciences
Department: Mathematics and Statistics

Contact Information: http://www.grad.usf.edu/majors

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 55^th 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)

MAA 5307 Real Analysis I Credit Hours: 3
MAS 5145 Advanced Linear Algebra Credit Hours: 3
MAE 5177 Teaching College Mathematics Credit Hours: 3

Concentrations

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:

MAS 5311 Algebra I Credit Hours: 3
MAS 6312 Algebra II Credit Hours: 3

Group 2 – Complex Analysis:

MAA 6406 Complex Analysis I Credit Hours: 3
MAA 6407 Complex Analysis II Credit Hours: 3

Group 3 – Topology:

MTG 5316 Topology I Credit Hours: 3
MTG 6317 Topology II Credit Hours: 3

Fundamental Sequences

Students must complete two sequences.

Algebra:

MAS 5311 Algebra I Credit Hours: 3
MAS 6312 Algebra II Credit Hours: 3

Real Analysis:

MAA 5306 Introduction to Real Analysis Credit Hours: 3
MAA 5307 Real Analysis I Credit Hours: 3 (taken as a core requirement)
MAA 6616 Real Analysis II Credit Hours: 3

Topology:

MTG 5316 Topology I Credit Hours: 3
MTG 6317 Topology II Credit Hours: 3

Elective Sequences

Students must complete two sequences.

Applied Mathematics

one of

MAP 5407 Methods of Applied Mathematics Credit Hours: 3
MAP 5345 Applied Partial Differential Equations Credit Hours: 3

one of

MAA 5405 Applied Complex Analysis Credit Hours: 3
MAT 5932 Selected Topics Credit Hours: 1-4 (Numerical Analysis)

Statistics Concentration (48 Credit Hours)

The student must complete the following courses:
STA 5446 Probability Theory I Credit Hours: 3
STA 6447 Probability Theory II Credit Hours: 3
STA 5526 Non-Parametric Statistics Credit Hours: 3
STA 6746 Multivariate Analysis Credit Hours: 3
STA 6876 Time Series Analysis Credit Hours: 3
HSC 6055 Survival Analysis Credit Hours: 3
Choose three of the following seven courses:
STA 6206 Stochastic Processes Credit Hours: 4
MAT 5932 Selected Topics Credit Hours: 1-4
Time Series Analysis II (3 Credit Hours)
Nonlinear Time Series Analysis (3 Credit Hours)
Multivariate Iterative Processes with Applications (3 Credit Hours)
Other Topics, with preapproval (3 Credit Hours)
MAT 6908 Independent Study Credit Hours: 1-19 (Preapproval required)
MAT 6932 Selected Topics Credit Hours: 1-4
Stochastic Dynamic Modeling (3 Credit Hours)

Fundamental Sequences

Students must complete two sequences.

Statistical Methods:

STA 5166 Statistical Methods I Credit Hours: 3
STA 6167 Statistical Methods II Credit Hours: 3
STA 6208 Linear Statistical Models Credit Hours: 3

Mathematical Statistics:

STA 5326 Mathematical Statistics I Credit Hours: 3
MAT 6932 Selected Topics Credit Hours: 1-4
Mathematical Statistics II (3 Credit Hours) (Proposed STA 6326)

Elective Sequences

Students must complete two sequences.

Linear Models and Multivariate Analysis:

STA 6208 Linear Statistical Models Credit Hours: 3
STA 6746 Multivariate Analysis Credit Hours: 3

Probability:

STA 5446 Probability Theory I Credit Hours: 3
STA 6447 Probability Theory II Credit Hours: 3

Stochastic Processes and Time Series Analysis:

STA 6876 Time Series Analysis Credit Hours: 3
STA 6206 Stochastic Processes Credit Hours: 4

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)

MAT 7980 Dissertation: Doctoral 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.

Handbook

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

Mathematics, Ph.D.

Contact Information

Admission Information

Curriculum Requirements

Core Requirements (9 Credit Hours Minimum)

Concentrations

Pure and Applied Concentration (33 Credit Hours)

Group 1 – Algebra:

Group 2 – Complex Analysis:

Group 3 – Topology:

Fundamental Sequences

Algebra:

Real Analysis:

Topology:

Elective Sequences

Applied Mathematics

one of

one of

one of

Combinatorics

Complex Analysis

Differential Geometry

Dynamical Systems

Functional Analysis

Harmonic Analysis

Nonlinear Analysis

Partial Differential Equations

Theory of Computing

Statistics Concentration (48 Credit Hours)

Fundamental Sequences

Statistical Methods:

Mathematical Statistics:

Elective Sequences

Linear Models and Multivariate Analysis:

Probability:

Stochastic Processes and Time Series Analysis:

Electives (2 Credit Hours Minimum)

Qualifying Examinations

Dissertation (16 Credit Hours Minimum)

Handbook