The Master of Science in Mathematical Science provides a broad base in applied, financial and industrial mathematics.

Students in the program can specialize in one of many aspects of mathematics, including Approximation Theory, Applied and Computational Harmonic Analysis, Big Data and Mathematical Statistics, Combinatorics and Graph Theory, Commutative Algebra and Algebraic Geometry, Control and Optimization, Differential and Symplectic Geometry, Fluid and Plasma Dynamics, Functional Analysis, Inverse and Ill-posed Problems, Machine Learning, Mathematical Biology, Mathematical Finance, Nonlinear Waves and Nonlinear Dynamics, Numerical Analysis, Orthogonal Polynomials, Partial Differential Equations, Probability and Stochastic Analysis, and Tomography and Medical Imaging.

The Mathematical Science MS program requires 30 credit hours minimum beyond the bachelor's degree. There are two options for the master's degree: thesis and nonthesis.

**Total Credit Hours Required: 30 Credit Hours Minimum beyond the Bachelor's Degree**

## Program Prerequisites

A working knowledge of undergraduate calculus, differential equations, linear algebra (or matrix theory), and maturity in the language of advanced calculus (at the level of MAA 4226).

## Degree Requirements

### Required Courses

12 Total Credits

- Complete all of the following
- Complete at least 1 of the following:
- MAA5210 - Topics in Advanced Calculus (3)
- MAA5237 - Mathematical Analysis (3)

- Complete the following:
- MAP6385 - Applied Numerical Mathematics (3)
- MAS5145 - Advanced Linear Algebra and Matrix Theory (3)
- MAT5712 - Scientific Computing (3)

### Restricted Elective Sequences

6 Total Credits

- Complete 1 of the following
- After the completion of the core courses, the program requires all students to complete one of the following two-semester sequences. Sequences are pairs of related courses that give advanced knowledge in an area of mathematics. The following shows examples of acceptable sequences using current courses. Course sequences other than listed below must be approved by the graduate program director. We expect that other sequences will be developed as our program grows.
- Complete at least 2 of the following:
- MAA6238 - Measure and Probability I (3)
- MAA6245 - Measure and Probability II (3)
- MAP6218 - Stochastic Calculus (3)

- Complete at least 2 of the following:
- MAA6306 - Real Analysis (3)
- MAA6506 - Functional Analysis (3)
- MAA6508 - Hilbert Spaces with Applications (3)

- Complete the following:
- MAA6405 - Complex Variables (3)
- MAA6404 - Complex Analysis (3)

- Complete at least 2 of the following:
- MAP6111 - Mathematical Statistics (3)
- MAP6469 - Bayesian Analysis and Approximation Theory (3)
- MAA7239 - Asymptotic Methods in Mathematical Statistics (3)

- Complete at least 2 of the following:
- MAA6416 - Topology (3)
- MTG5256 - Differential Geometry (3)
- MTG6345 - Algebraic Topology (3)

- Complete the following:
- MAD5205 - Graph Theory I (3)
- MAD6309 - Graph Theory II (3)

- Complete at least 2 of the following:
- MAP5336 - Ordinary Differential Equations and Applications (3)
- MAP6356 - Partial Differential Equations (3)
- MAP7359 - Advanced Topics in Partial Differential Equations (3)

- Complete the following:
- MAP5641 - Financial Mathematics I (3)
- MAP6642 - Financial Mathematics II (3)

- Complete the following:
- MAP6197 - Mathematical Introduction to Deep Learning (3)
- MAP6195 - Mathematical Foundations for Massive Data Modeling and Analysis (3)

- Complete the following:
- MAP6207 - Optimization Theory (3)
- MAP6387 - Numerical Linear Algebra (3)

- Complete the following:
- MAP6416 - Applied and Computational Harmonic Analysis (3)
- MAP6445 - Approximation Techniques (3)

- Complete the following:
- MAS5311 - Algebra I (3)
- MAS6312 - Algebra II (3)

### Unrestricted Electives

6 Total Credits

- Earn at least 6 credits from the following types of courses: Students are encouraged to take more than one sequence of Restricted Electives. Unrestricted electives, other than Restricted Electives, should be chosen in consultation with the graduate program director or the student's thesis adviser and may be chosen from the suggested options: Approximation Theory, Applied and Computational Harmonic Analysis, Big Data and Mathematical Statistics, Combinatorics and Graph Theory, Commutative Algebra and Algebraic Geometry, Control and Optimization, Differential and Symplectic Geometry, Fluid and Plasma Dynamics, Functional Analysis, Inverse and Ill-posed Problems, Machine Learning, Mathematical Biology, Mathematical Finance, Nonlinear Waves and Nonlinear Dynamics, Numerical Analysis, Orthogonal Polynomials, Partial Differential Equations, Probability and Stochastic Analysis, and Tomography and Medical Imaging. A list of courses for these elective options can be obtained from the graduate program director. Courses taken outside the Department of Mathematics must be approved by the graduate program director. At most 6 credit hours earned from graduate courses outside the department can be used as Unrestricted Electives. At most 6 credit hours earned from Independent Study, Directed Research and Internship can be used as Unrestricted Electives.

### Thesis/Nonthesis Option

6 Total Credits

- Complete 1 of the following
Thesis Option- Earn at least 6 credits from the following types of courses: MAP 6971 - Thesis In this option, the MS degree requires a total of at least 30 credit hours comprised of at least 18 credit hours of course work and 6 credit hours of thesis. This includes the 12 credit hours of the core courses and 6 credit hours of a two-course sequence. No more than 6 credit hours of independent study or directed research or internship may be credited toward the degree. It is strongly recommended that the student select a thesis adviser and establish a program of study by the completion of the core courses. With the help of a thesis adviser, the student will form a thesis committee of three members, of which at least two must be from the Department of Mathematics. It is recommended that the thesis topic have potential for industrial applications. An oral defense of the thesis will be required.
Nonthesis Option- Earn at least 6 credits from the following types of courses: In this option, the MS degree requires a total of at least 30 credit hours comprised of at least 21 credit hours of course work. This includes the 12 credit hours of the core courses, 6 credit hours of a two-course sequence and at least one additional course offered by the program. No more than 9 credit hours of independent study or directed research or internship may be credited toward the degree. Compared with students taking the thesis option, students in the nonthesis option will take an additional 6 credit hours of course works or Independent Study or Directed Research. The electives should be chosen in consultation with the graduate program director. In addition, students the nonthesis option must pass qualifying examinations on Mathematical Analysis and on Advanced Linear Algebra and Matrix Theory both at the MS or PhD level. The qualifying examination is based on the core courses: MAA 5237 Mathematical Analysis and MAS 5145 Advanced Linear Algebra and Matrix Theory). The examination will be administered twice a year: one in the Fall semester and the other in the Spring semester. Two attempts at the examination are permitted.

### Independent Learning

0 Total Credits

- In the Mathematical Science MS program, the thesis option provides an independent learning experience through directed research, reading published research papers, and writing and defending the thesis. The nonthesis option requires students to take one of the two-semester sequences, where they apply mathematical principles to independent projects.

#### Grand Total Credits: **30**

## Application Requirements

## Application Deadlines

## 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.