Mathematics (PHD) - Financial Mathematics Track

Program Overview

The Financial Mathematics track within the Mathematics PhD program at the University of Central Florida prepares students for research and leadership roles in the financial industry, government, NGOs, and academia. The program requires 75 credit hours of coursework, including core courses in financial mathematics, elective courses, and a dissertation. Students must pass qualifying, candidacy, dissertation proposal, and dissertation defense examinations to complete the program.

Program Outline

Degree Overview:

The Financial Mathematics track within the Mathematics PhD program at the University of Central Florida (UCF) is designed to prepare students for research and leadership roles in various sectors. These sectors include:

• Industry: Positions requiring financial mathematics expertise.
• Government: Roles involving financial modeling and analysis.
• Non-governmental organizations (NGOs): Positions focused on financial management and impact assessment.
• Academia: Research and teaching positions in financial mathematics.
The program aims to equip students with the advanced knowledge and skills necessary to excel in these demanding fields.

Outline:

The Mathematics PhD program, including the Financial Mathematics track, requires a minimum of 75 credit hours of coursework beyond the bachelor's degree. This includes:

• Core Courses (36 credit hours):
• 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)
• MAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3)
• MAP6207 - Optimization Theory (3)
• STA6857 - Applied Time Series Analysis (3)
• MAP5931 - Proseminar for Financial Mathematics (1)
• MAP5933 - Seminar in Financial Mathematics (2)
• Elective Courses (24 credit hours):
• Students must earn at least 24 credits from a variety of elective courses, with approval from their advisor and the graduate program director.
• Up to 12 credit hours of electives can be taken outside the Mathematics department.
• At least half of the program courses must be at the 6000 level.
• At least 12 hours of elective coursework must be formal coursework, excluding independent study.
• Suggested elective options include: Discrete Mathematics, General Applied Mathematics, Mathematical Computer Tomography, Image Processing and Computer Graphics, Mathematical Finance, Mathematical Physics, Pure Mathematics, Data Science, and Mathematical Statistics.
• Dissertation (15 credit hours):
• MAP 7980 - Dissertation Research (15 credit hours minimum)
• Students must complete a dissertation after passing the candidacy examination and meeting other requirements for admission to candidacy.

Assessment:

The program includes several examinations to assess student progress and mastery of the material:

• Qualifying Examination:
• Based on core coursework.
• Students must pass the examination at the PhD level.
• Two attempts are permitted.
• Administered twice a year (Fall and Spring).
• Students must have a "B" or better in each core course and a minimum GPA of 3.0 in the program, or obtain permission from the graduate program director.
• Typically taken after the first year and expected to be passed by the end of the second year.
• Students must pass within two attempts.
• Candidacy Examination:
• Consists of a written examination based on two selected two-semester sequence courses.
• A committee prepares and grades the examinations.
• Students in the Financial Mathematics Track typically select MAP 5641/MAP6642 Financial Mathematics I and II, and MAP5612/MAP6616 Computational Methods for Financial Mathematics I and II.
• Can be attempted after passing the qualifying examination.
• Must be completed within three years of passing the qualifying examination.
• Students must pass within two attempts.
• Dissertation Proposal Examination:
• Students prepare a dissertation proposal and present it orally to their dissertation advisory committee for approval.
• The proposal includes a description of research performed and an agenda for future research.
• The presentation must meet professional standards within the discipline of mathematics.
• Must be passed within 18 months of passing the candidacy examination and no later than the end of the sixth year of graduate study.
• Students must pass within two attempts.
• Dissertation Defense:

Careers:

The Financial Mathematics track prepares students for a variety of career paths, including:

• Quantitative Analyst (Quant): Develops and applies mathematical models to financial markets.
• Financial Engineer: Designs and implements financial products and strategies.
• Risk Manager: Assesses and manages financial risks.
• Data Scientist: Analyzes large datasets to identify trends and insights in financial markets.
• Actuary: Evaluates and manages financial risks in insurance and other industries.
• Academic Researcher: Conducts research in financial mathematics and related fields.

Other:

• Track Prerequisites: A bachelor's degree in a related field is required.
• Working Knowledge: Students are expected to have a working knowledge of undergraduate calculus, differential equations, linear algebra, boundary value problems, statistics, computer programming, and advanced calculus.
• Independent Learning: The dissertation requirement provides opportunities for independent learning through research and analysis.
• Financial Assistance: Graduate students may receive financial assistance through fellowships, assistantships, tuition support, or loans.