The Financial Mathematics track in the Mathematics PhD program is designed to prepare students for research and leadership positions in industry, government, non-governmental organizations, and academia requiring employment of financial mathematics.
The Mathematics PhD program consists of 75 credit hours of course work beyond the bachelor's degree. This includes a minimum of 45 hours of formal course work. Of the 45 hours, 33 hours are from required courses and 12 are from elective courses. In addition to formal coursework, 15 elective hours can come from independent study, directed research, and internship. Lastly, 15 credit hours of dissertation research (7980) are required.
Master en route is permitted and encouraged.
Total Credit Hours Required: 75 Credit Hours Minimum beyond the Bachelor's Degree
Track Prerequisites
Bachelor's degree in related field.
Students entering the graduate program with regular status are assumed to have a working knowledge of undergraduate calculus, differential equations, linear algebra (or matrix theory), boundary value problems, statistics, computer programming, and maturity in the language of advanced calculus (at the level of MAA 4226) and linear algebra (at the level of MAS3106).
Degree Requirements
Required Courses
33 Total Credits
- Complete all of the following
- All students are required to complete the following courses with grade of "B" or better.
- Complete the following:
- MAA5237 - Mathematical Analysis (3)
- MAS5145 - Advanced Linear Algebra and Matrix Theory (3)
- MAP5641 - Financial Mathematics I (3)
- MAP6642 - Financial Mathematics II (3)
- MAP5612 - Computational Methods for Financial Mathematics I (3)
- MAP6616 - Computational Methods for Financial Mathematics II (3)
- MAP6646 - Risk Management for Financial Mathematics (3)
- MAP5606 - Differential Equations for Financial Mathematics (3)
- MAP5931 - Proseminar for Financial Mathematics (1)
- MAP5933 - Seminar in Financial Mathematics (2)
- Complete at least 2 of the following:
- MAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3)
- MAP6197 - Mathematical Introduction to Deep Learning (3)
- MAP6207 - Optimization Theory (3)
- STA6857 - Applied Time Series Analysis (3)
- ECO6281 - Financial Economics I: Asset Prices, Risk, and Information (3)
- ECO6282 - Financial Economics II: Continuous-Time Models (3)
- Students may substitute some of the core courses with the approval of the graduate program director.
Elective Courses
27 Total Credits
- Earn at least 27 credits from the following types of courses: Elective courses require the approval of the adviser and the graduate program director. Except those listed as core courses, up to 9 credit hours of elective courses may be taken outside the department. At least one-half of the program courses must be taken at the 6000 level. At most 15 credit hours on independent study and directed research and internship can be used as Elective Courses. At least 12 hours of elective course work must be formal course work. Electives are chosen in consultation with the student's advisory committee and may be chosen from the suggested options: Discrete Mathematics, General Applied Mathematics, Mathematical Finance, Pure Mathematics, Data Science, and Mathematical Statistics. A list of elective course options can be obtained from the graduate program director. Courses that are taken outside the Mathematics department must be approved by the graduate program director. Internship is strongly encouraged to take, however it is not mandatory. The following courses (if not used as core courses) are encouraged to take as elective courses. • MAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3) • MAP 6197: Mathematical Introduction to Deep Learning (3) • MAP6207 - Optimization Theory (3) • STA6857 - Applied Time Series Analysis (3) • ECO6281 Financial Economics I—Asset Prices, Risk, and Information (3) • ECO6282 Financial Economics II—Continuous-Time Models (3) • MAA 6238: Measure and Probability I (3) • MAA 6245: Measure and Probability II (3) • MAP 6218: Stochastic Calculus (3) • MAP 6111: Mathematical Statistics (3) • MAP 6469: Bayesian Analysis and Approximation Theory (3) • MAA 7239: Asymptotic Methods in Mathematical Statistics (3) • MAD5205 - Graph Theory I (3) • MAD 6309: Graph Theory II (3) • MAA6306 - Real Analysis (3) • MAA6505 – Functional Analysis (3)
Dissertation
15 Total Credits
- Earn at least 15 credits from the following types of courses: MAP 7980 - Dissertation Research 15 Credit Hours (minimum) After passing the candidacy examination and meeting the other requirements that are required for admission to candidacy, the student can register for Doctoral Dissertation (MAP 7980). A minimum of 15 Doctoral Dissertation credit hours are required for the degree.
Examinations
0 Total Credits No Rules
Qualifying Examination
0 Total Credits
- The qualifying/comprehensive examination is based on the core course work. To continue in the PhD program, students must pass the examination at the PhD level. Two attempts are permitted. The examination will be administered twice a year: one in the Fall semester and the other in the Spring semester. To take the examination, students must have earned a "B" or better in each core course, must have a minimum grade point average of 3.0 (out of 4.0) in the program, or must obtain permission from the graduate program director. Students will normally take the examination after taking courses MAA 5237 and MAS 5145. Students are expected to have passed the examination by the end of the second year of study, unless a written request for a postponement has been approved by the Graduate Committee at least two months before the examination date. The student must pass the Qualifying Examination in at most two attempts. It is strongly recommended that the student select a dissertation adviser by the completion of 18 credit hours of course work, and it is strongly recommended that the student works with the dissertation adviser to form a dissertation committee within two semesters of passing the Qualifying Examination.
Candidacy Examination
0 Total Credits
- The Candidacy Examination consists of a written examination based on the materials from two selected two-semester sequence courses taken by the students. A committee formed or selected by the Graduate Committee or the graduate program director is responsible for preparing and grading the written examinations. Each sequence that is selected for the candidacy examination must be approved by the dissertation adviser, the dissertation committee, and the graduate program director. Students in the Financial Mathematics Track will ordinarily select one of the sequences for their candidacy examination to be MAP 5641/MAP6642 Financial Mathematics I and II, and MAP5612/MAP6616 Computational Methods for Financial Mathematics I and II. The student can apply for the candidacy exam waiver on one sequence and should discuss with the program director for the procedure and the requirement. The Candidacy Examination can be attempted after passing the qualifying examination. The Candidacy Examination must be completed within one and half years after passing the qualifying examination. A student must successfully pass the Candidacy Examination within at most two attempts.
Admission to Candidacy
0 Total Credits
- The following are required to be admitted to candidacy and enroll in dissertation hours: Completion of all course work, except for dissertation hours. Successful completion of the candidacy examination. The dissertation advisory committee is formed, consisting of approved graduate faculty and graduate faculty scholars. Submittal of an approved program of study.
Dissertation
0 Total Credits No Rules
Dissertation Proposal Examination
0 Total Credits
- After passing the candidacy examination, the student will prepare a dissertation proposal and orally present it to the dissertation advisory committee for approval. The proposal will include a description of the research performed to date and an agenda for the research planned to be completed for the dissertation. In addition to standards of correctness, indicating a suitable level of mastery of the material of the area of the dissertation, and suitability of the proposed dissertation topic, the presentation must meet current standards for professional presentations within the discipline of mathematics. For the successful completion of the Dissertation Proposal Examination, the presentation must be judged as passing the requirements for the examination by the majority of the dissertation committee. This exam must be passed within 18 months of passing the candidacy examination and not later than the end of the sixth year of graduate study. A candidate must pass this examination within at most two attempts.
Dissertation Defense
0 Total Credits
- Upon completion of a student's research, the student's committee schedules an oral defense of the dissertation. Most students complete the program within five years after obtaining their bachelor's degree. Students are expected to complete the dissertation in no more than seven years from the date of admission to the program.
Independent Learning
0 Total Credits
- The required 15 credit hours of dissertation will provide ample opportunities for students to gain the independent learning experience through studying published research papers and deriving, on their own, new and meaningful research results.
Grand Total Credits: 75
Application Requirements
Financial Information
Graduate students may receive financial assistance through fellowships, assistantships, tuition support, or loans. For more information, see the College of Graduate Studies Funding website, which describes the types of financial assistance available at UCF and provides general guidance in planning your graduate finances. The Financial Information section of the Graduate Catalog is another key resource.
Fellowship Information
Fellowships are awarded based on academic merit to highly qualified students. They are paid to students through the Office of Student Financial Assistance, based on instructions provided by the College of Graduate Studies. Fellowships are given to support a student's graduate study and do not have a work obligation. For more information, see UCF Graduate Fellowships, which includes descriptions of university fellowships and what you should do to be considered for a fellowship.
The department offers over 20 Graduate Teaching Assistantships every year on a competitive basis. A few Graduate Research Assistantships are also available for qualified students.
