Mathematical Science MS

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College : Sciences Degree :MS
Department : Mathematics Option : Thesis, Nonthesis
Program Websites : https://math.cos.ucf.edu/graduate/

PROGRAM DESCRIPTION

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

CURRICULUM

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

Thesis and nonthesis options are offered within the program. In both options, after completing the core courses, a student must establish an academic adviser for nonthesis MS option or a thesis adviser for thesis MS option. A program of study must be established by the end of the second semester and presented to the graduate program director for departmental approval. The program of study must include the completion of the core courses and one 2-semester sequence. At least one-half of the program courses in both options must be taken at the 6000 level.

Required Courses—15 Credit Hours

For thesis or nonthesis option, the master's program requires all students to complete the following five courses.

  • MAS 5145 Advanced Linear Algebra and Matrix Theory (3 credit hours)
  • MAA 5228 Analysis I (3 credit hours)
  • MAA 6229 Analysis II (3 credit hours)
  • MAT 5712 Scientific Computing (3 credit hours)
  • MAP 6385 Applied Numerical Mathematics (3 credit hours)

Elective Courses—9 Credit Hours

Restricted Electives—3–6 Credit Hours

After the completion of the core courses, the program requires all students to complete one of the following two-semester sequences. The following shows examples of acceptable sequences using current courses. We expect that other sequences will be developed as our program grows. Note that some sequences consist of a core course plus one elective, while others consist of two electives. Thus, the credit hours in this requirement are variable (3 to 6 credit hours).

  • MAP 6407 Integral Equations and Calculus of Variations (3 credit hours) / MAP 6408 Perturbations and Asymptotic Methods (3 credit hours)
  • MAA 6405 Complex Variables (3 credit hours) / MAA 6404 Complex Analysis (3 credit hours)
  • MAD 5205 Graph Theory I (3 credit hours) / MAD 6309 Graph Theory II (3 credit hours)
  • MAP 5336 Ordinary Differential Equations and Applications (3 credit hours) / MAP 6356 Partial Differential Equations (3 credit hours)
  • MAA 6238 Measure and Probability I (3 credit hours) / MAP 6111 Mathematical Statistics (3 credit hours) or MAA 6245 Measure and Probability II (3 credit hours)
  • MAA 6306 Real Analysis (3 credit hours) / MAA 6506 Functional Analysis (3 credit hours)

Unrestricted Electives—3-6 Credit Hours

Unrestricted 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, Mathematical Biology, Mathematical Finance, Nonlinear Waves and Nonlinear Dynamics, Numerical Analysis, Orthogonal Polynomials, Partial Differential Equations, Probability and Stochastic Analysis, Tomography and Medical Imaging, and Wave Propagation. A list of courses for these elective options can be obtained from the graduate program director. Approved graduate courses outside the department may also be used.

Thesis Option—6 Credit Hours

In this option, the MS degree requires a total of at least 30 credit hours comprised of at least 24 credit hours of course work and 6 credit hours of thesis. This includes the 15 credit hours of the core courses and 3-6 credit hours of a two-course sequence. No more than 6 credit hours of independent study or directed research 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.

  • MAP 6971 Thesis (6 credit hours)

Nonthesis Option—6 Credit Hours

Nonthesis students will take an additional 6 credit hours of electives. The electives should be chosen in consultation with the graduate program director or the student’s adviser.

Nonthesis students will receive independent learning experiences by taking one of the two-semester sequences, where they apply mathematical principles to independent projects. Other courses that also have substantial research projects include MAP 5117 Mathematical Modeling, MAT 5712 Scientific Computing and MAP 6111 Mathematical Statistics, MAP 6424 Transform Methods, MAP 6465 Wavelets and Their Applications, and may be taken as electives.

No more than 3 credit hours of independent study may be credited toward the degree. It is strongly recommended that the student select an academic adviser and establish a program of study by the completion of the core courses. In addition, the nonthesis student must pass a comprehensive written examination (by passing the qualifying/comprehensive examination at or above the MS level) based on the core courses. Two attempts at the examination are permitted. 

Independent Learning

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.

Application Requirements

For information on general UCF graduate admissions requirements that apply to all prospective students, please visit the Admissions section of the Graduate Catalog. Applicants must apply online. All requested materials must be submitted by the established deadline.

In addition to the general UCF graduate application requirements, applicants to this program must provide:

  • One official transcript (in a sealed envelope) from each college/university attended.
  • Official, competitive GRE score taken within the last five years.
  • 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).

Students who find they are not adequately prepared in one or more of the required mathematical subject areas can select appropriate courses from the undergraduate curriculum to make up such deficiencies. Such courses, unless specially approved, will not count toward the graduate degree. Applicants not qualified for regular status may be admitted initially to the university in a nondegree-seeking status. Transfer of credits from other programs will be considered on a course-by-course basis.

Meeting minimum UCF admission criteria does not guarantee program admission. Final admission is based on evaluation of the applicant's abilities, past performance, recommendations, match of this program and faculty expertise to the applicant's career/academic goals, and the applicant's potential for completing the degree.

Application Deadlines

All application materials must be submitted by the appropriate deadline listed below.

Mathematical Science MS *Fall Priority Fall Spring Summer
Domestic Applicants Jan 15Jul 15Dec 1Apr 15
International Applicants Jan 15Jan 15Jul 1Nov 1
International Transfer Applicants Jan 15Mar 1Sep 1Dec 15
*Applicants who plan to enroll full time in a degree program and who wish to be considered for university fellowships or assistantships should apply by the Fall Priority date.

FINANCIALS

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.

Fellowships

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. 


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