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## M.S. in Computational and Applied Mathematics

**Departmental Requirements for M.S. in Mathematics:****Computational and Applied Mathematics**

The Master of Science degree in computational and applied mathematics requires that the student demonstrate knowledge in certain core areas.

**Core course requirements:** All candidates for the M.S. degree in computational and applied mathematics must earn a grade of A or B in a prescribed 18 hours from the following list of core courses.

**1. Basic mathematics (3 hours)** One of Advanced Calculus I (MATH 5043) or Advanced Linear Algebra (MATH 5023)

**2. Numerical analysis (3 hours)** Numerical Analysis for Differential Equations (MATH 5543) or Numerical Analysis for Linear Algebra (MATH 5553)

**3. Applied analysis (12 hours)** Twelve hours from the following list: Intermediate Differential Equations (MATH 4233), Numerical Analysis (MATH 4513), Linear and Nonlinear Programming (MATH 4553), Fourier Analysis and Wavelets (MATH 5213), Partial Differential Equations (MATH 5233), Ordinary Differential Equations (MATH 5243), Advanced Ordinary Differential Equations (MATH 5253), Numerical Analysis for Differential Equations (MATH 5543), Numerical Analysis for Linear Algebra (MATH 5553), Finite Element Methods (MATH 5563), Case Studies in Applied Mathematics (MATH 5580), Methods in Applied Mathematics (MATH 5593)

**Industrial experience:** All students must either earn three hours credit under requirement 3 above for MATH 5580 or have industrial experience. The requirement of industrial experience is satisfied by a summer internship or full-time employment in a mathematical context for at least six months in either industry or business.

**Electives:** All candidates for the M.S. degree in computational and applied mathematics must choose six additional hours from the following list of elective courses:

Introduction to Partial Differential Equations (MATH 4263), Complex Variables (MATH 4283), Mathematical Interest Theory (MATH 4453), Combinatorial Mathematics (MATH 4663), Groups and Representations (MATH 4813), Advanced Linear Algebra (MATH 5023), Advanced Calculus I (MATH 5043), Advanced Calculus II (MATH 5053), Real Analysis I (MATH 5143), Real Analysis II (MATH 5153), Fourier Analysis and Wavelets (MATH 5213), Complex Analysis I (MATH 5283), Complex Analysis II (MATH 5293), General Topology (MATH 5303), Numerical Analysis for Differential Equations (MATH 5543), Numerical Analysis for Linear Algebra (MATH 5553).

**Alternative course selections:**

· A course chosen to satisfy a core requirement in one area cannot be used to satisfy a core requirement in another area. A course chosen to satisfy the elective requirement cannot be used to satisfy a core requirement and vice-versa.

· Courses taken as an undergraduate can be used to satisfy the above requirements, as long as they are consistent with the Graduate College requirements.

· Courses outside the Department of Mathematics must be approved by student's advisory committee. Computer science courses must be beyond programming courses. (The course Techniques of Computer Science for Science and Engineering, CS 4113, is considered a programming course.)

· Any of the 18 hours of core courses may be replaced by a higher level course for which it is a prerequisite. Any such change requires consent from the Graduate Committee.

· Substitutions for any of the six hours of electives requires consent from the Graduate Committee. In no case may more than nine hours outside the mathematical sciences (mathematics, statistics, or computer science) be counted toward the M.S. degree.

**Courses taken in graduate school:** The courses taken in graduate school must total 32 hours, which may include two hours for a Master's report. If a student elects to write a thesis, the minimum number of hours is reduced to 30. The courses taken on the M.S. degree program must include 21 hours of courses numbered 5000 or above. All the courses for the M.S. degree program must constitute a coherent whole and must be approved by the student's advisory committee.

Creative component, report, or thesis: Each student must complete a creative component, report, or thesis. Under any of these three options, a written document and a public presentation based on this individually directed project is required.

**Other requirements:** The university catalog contains detailed procedures applicable to all Master's degrees.