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**Master of Science Degree in Computational Applied Mathematics**

Mathematics is a universal language. Applied mathematics combines the beauty and function of mathematics to help us understand and improve the world around us. Since mathematics is universal, it can be applied anywhere. This is a particularly exciting aspect of applied mathematics. Applied mathematicians help to design satellites, explain how our mind works and improve MRI machines. Applied mathematics allows one to find patterns that are common to many disciplines with a unifying mathematical structure. A problem in neuroscience sometimes has the same mathematical structure as doing an internet search! Applied mathematics allows one to make that connection.

The Department of Mathematics at California State University, Fullerton offers a graduate program in computational applied mathematics leading to the Master of Science Degree. The program is intended for individuals who are seeking or who currently hold positions that involve mathematical or quantitative applications. It was developed in consultation with mathematicians and scientists in the local industrial community. The coursework emphasizes modern applied mathematics, modeling, and computation. Every class involves the use of modern interactive software for numerical computation and simulation modeling, including MATLAB, PYTHON, and R. Graduates have gone on into successful careers in industry and in teaching at the college level. Several have also obtained advanced degrees in Mathematics, Engineering, and Science.

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**PREREQUISITES**

Students seeking admission to the program must have the following:

- Bachelor's degree in mathematics or related area from an accredited college or university
- Four semesters of Calculus, a computer programming course or equivalent experience, and upper division courses in mathematical probability and advanced calculus/analysis
- Overall GPA of at least 2.5 and a GPA of 3.0 or higher in all upper division mathematics courses, or a combination of previous course work and work experience approved by the graduate committee of the Mathematics Department.

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**Application Procedure**

Students must submit the following:

- Official transcript sent to CSUF's Admissions and Records.
- Complete the online CSUF graduate application .
- Compete the supplemental application:
- (optional) Letters of recommendation.
- (optional) GRE Scores.
- International students should visit this International Admissions Office for additional information and requirements.

Applicants must upload the supplemental application (3) above in the "Program Materials" section of your online Cal State Apply application under “Other” in the Documents tab.

Application window for Fall:** December 1 to April 15.**

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Application window for Spring:
August 1 to December 1.
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Financial aid, including teaching/research assistantships and out-of-state tuition fee waiver, is available. Application due date is around the end of March. If you need more information, you may contact the Graduate Advisor Dr. Charles H. Lee at charleshlee@fullerton.edu or at (657) 278-2726. For administrative question please contact Renee Bennett at rbennett@fullerton.edu .

## TEACHING ASSOCIATE OPPORTUNITIES FOR QUALIFIED STUDENTS

We offer interested masters students, depending on availability, part-time instructor positions where they teach one or more of our elementary mathematics courses. Applications for the Teaching Associate (TA) position will be accepted during the spring and summer to teach the following fall semester. For our TA Job Description and application procedure please see the Math Departments TA Employment page . Application due date is around the end of June.

If you need more information, you may contact the Graduate Advisor Dr. Charles H. Lee at charleshlee@fullerton.edu or at (657) 278-2726. For administrative question please contact Renee Bennett at rbennett@fullerton.edu .

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**Courses**

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The program starts in the fall semester and can be completed in two academic years, including a summer in between. All required courses are offered sequentially during the evening with six units per semester.
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### Fall Semester (first year)

**Math 500A, Advanced Linear Algebra and Applications (3 units). **Prerequisites: linear algebra, advanced calculus and consent of instructor. Corequisite: MATH 500B. Topics and computational methods from linear algebra useful in graduate studies in computational applied mathematics. Finite and infinite dimensional vector spaces, linear transformations and matrices. Introduction to Hilbert spaces. Projection theorem and some of its applications.

**Math 500B, Applied Analysis (3 units). **Prerequisites: undergraduate calculus, linear algebra, advanced calculus and consent of instructor. Corequisite: MATH 500A. Topics from analysis useful in graduate studies in computational applied mathematics. Topics may include initial and boundary value problems, including series solutions, eigenvalues and eigenfunctions, Fourier analysis, generalized functions, an introduction to the calculus of variations, and transform methods.

### Spring Semester (first year)

**Math 501A, Foundations of Numerical Analysis (3 units). **Prerequisites: Computer programming and MATH 500A, MATH 500B. Numerical methods for linear and nonlinear systems of equations, eigenvalue problems. Interpolation and approximation, spline functions, numerical differentiation, integration and function evaluation. Error analysis, comparison, limitations of algorithms.

**Math 502A, Foundations of Probability and Statistics (3 units). **Prerequisites: MATH 335. Theory and applications of probability and statistical models including univariate and multivariate distributions; expectations and transformations of random variables.

### Summer Term (end of first year)

**Math 501B, Scientific Computing and Applications (3 units). **Prerequisites: Computer programming and MATH 501A. Numerical methods for initial and boundary-value problems for ordinary and partial differential equations. The finite element method. Error analysis, comparison, limitations of algorithms.

**Math 503A, Mathematical Modeling (3 units). **Prerequisites: MATH 500A, MATH 500B. Mathematical modeling concepts. Topics may include: dimensional analysis, scaling and sensitivity; system concepts, state space, observability, controllability and feedback; dynamical systems, models and stability analysis; optimization models.

### Fall Semester (second year)

**Math 502B, Computational Statistics and Data Analysis (3 units). **Prerequisites: MATH 335 and MATH 502A. Theory and applications of sampling theory, statistical estimation and hypothesis testing. Topics may include machine learning and data analysis techniques.

**Math 503B, Parameter Estimation and Inverse Problems (3 units). **Prerequisite: MATH 503A. Development and analysis of mathematical models, with the emphasis on estimating model parameters and solving inverse problems. Topics may include tomography, image processing, Tikhonov regularization, Monte Carlo methods.

### Spring Semester (second year)

**Math 597, Industrial Project in Computational Applied Mathematics (6 units). **Prerequisite: consent of instructor. May be repeated for credit. Students in the Computational Applied Mathematics Master’s Program earn a total of 6 units. Students work in teams on projects that are sponsored and funded by local industrial firms. Each team is supervised by a faculty member. The project is intended to provide a realistic industrial-like experience, complete with deadlines and a written final report, where students can put what they have learned to work, and where success is based on individual initiative, teamwork, and communication skills.

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**Faculty**

Derdei Bichara, Assistant Professor, *Mathematical Biology, Dynamical Systems, Control Theory*

Nicholas Brubaker, Assistant Professor, *Mathematical Modeling, Fluids, Electrostatics and Elasticity*

Laura Smith Chowdhury, Associate Professor,
*Mathematical Modeling, Complex Networks, Differential Equations*

Charles Hung Lee, Professor, *Computational Mathematics, Fluid Dynamics, Aerospace Engineering*

Kristin Kurianski, Assistant Professor, *Mathematical Modeling, Wave-Type Phenomena, Physical Systems*

Tyler McMillen, Professor, *Nonlinear Dynamics, Differential Equations, Neuroscience*

Stephanie Reed, Assistant Professor, *Mathematical Modeling, Stochastic Processes, Probability and Particle Systems*

Anael Verdugo, Associate Professor, *Nonlinear Dynamics, Differential Equations, Computational Biology*

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**Research and More**
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Faculty members in the modeling and computation track are actively involved in research areas which include aerospace engineering, social networks, cellular biology, epidemiology, and small-scale systems. They have obtained grants from the National Aerospace and Aeronautics and Space Administration (NASA) and from the National Science Foundation (NSF) to support their research.

Faculty members regularly work with students in their projects and have found funding for students from their research grants. Research is a wonderful way to use the ideas from courses in a “real world” situation. Faculty members work with students in research projects which often lead to publications and presentations by students at local and national meetings.

The industrial relevance of computational applied mathematics can be seen through the industrial projects in which faculty serve as consultants and the patents they obtain from their inventions.

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**CAREERS**

Graduates from the Master’s Program in Computational Applied Mathematics have a broad range of career options. Recent graduates work in industry as scientific programmers, go into doctorate programs in applied mathematics, statistics, or engineering, as well as become teachers in community colleges. The problem solving skills along with the mathematical and computing knowledge obtained through coursework are valued by employers and graduate schools.

Employers of applied mathematicians include aerospace companies (e.g., Boeing), biotech companies (e.g., Amgen), financial companies (e.g., PIMCO), internet companies (e.g., Google) and research laboratories (e.g., NASA). The beauty of applied mathematics is that it is both interesting and useful. Because of this, applied mathematicians are hired by a huge range of companies. More information about the types of jobs available to applied mathematicians can be found in the careers website of the Society for Industrial and Applied Mathematics (SIAM).