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**Applied Mathematics Concentration**

The Applied Mathematics Concentration is divided into two different tracks: (1) Classical Applied Track and (2) Modeling Track. Both of these combine a solid foundation in applied mathematics with different emphasis in rigor and critical thinking.

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**Classical Applied Track**

The Classical Applied Mathematics track combines a solid foundation in pure mathematics with upper division topics of vital importance for applications: differential equations, geometry, and analysis. As such, it provides training in rigor and critical thinking as found in pure mathematics, while focusing on theories and methods most commonly seen in applications. This traditional form of applied mathematics has evolved over centuries alongside its close cousin: physics. As such, it makes an excellent second major or minor for physics and engineering students. It predates - yet is enhanced by - the computer revolution, and it remains a key component to progress in both science and industry. The Classical Applied Mathematics track is also an attractive option for the student considering graduate school in pure or applied mathematics, particularly if combined with the Math or Research cognates.

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**Requirements**

The Applied Mathematics concentration, classical applied track, consists of five required courses providing background in pure mathematics, differential equations, and geometry:

Math 302 Modern Algebra (3 units)

Math 306 Vector and Tensor Analysis (3 units)

Math 310 Ordinary Differential Equations (3 units)

Math 406 Introduction to Partial Differential Equations (3 units)

Math 425 Differential Geometry (3 units)

Along with the five courses above, students choose two of the following analysis related courses:

Math 412 Complex Analysis (3 units)

Math 414 Topology (3 units)

Math 450 Advanced Calculus II (3 units)

Please see the prerequisite diagram of the classical applied track for the courses required in this concentration.

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**Careers**

A degree in mathematics trains a student to think quantitatively and critically. The development of these skills makes a math graduate rather broadly qualified for positions in industry, government, education, and business. As the Classical Applied Concentration combines pure mathematics and applied topics, graduates may find suitable careers with engineering and consulting firms, financial institutions, teaching institutions, and tech oriented companies in general. Due to the shared heritage with physics, employment opportunities may be found in the same sectors as for physics graduates. For a career in industry, additional experience in computer programming would be a significant advantage, while a teaching credential opens up the option of teaching at the high school level. Pursuing a graduate degree opens up higher-level opportunities, including teaching at the community college level (masters degree), joining the faculty of a four-year or research university (Ph.D.), or a more advanced position with a technical, financial or engineering oriented firm.

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**Faculty**

Alfonso F. Agnew, Professor of Mathematics, *Mathematical Physics, Quantum Field Theory and General Relativity Theory*

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**Research**

Research by faculty in the classical applied mathematics area centers around mathematical problems arising from theoretical physics. Projects involve mathematical problems in General Relativity Theory, Cosmology, and Quantum Theory, as well as issues at the interface of all three. Classical applied mathematics faculty members are also actively engaged in research with undergraduates. Undergraduate research is increasing in popularity and can provide a significant advantage when competing for jobs or graduate school admissions. There are many opportunities for students to get involved in research activities through faculty supervised independent study or a more in-depth faculty mentored research project.

Opportunities for undergraduates to participate in research projects in mathematics outside of the department include formal Research Experiences for Undergraduates programs, funded by the National Science Foundation. These competitive programs run for several weeks during the summer months at institutions around the nation.

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**Modeling Track **

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.

Students in the modeling and computation applied mathematics track take courses that will give them a broad and powerful set of tools to apply mathematics. Mathematics is used to model the world in a variety of ways which sometimes rely purely on theoretical analysis, other times through computer simulations and often through both. The courses in this concentration in differential equations, numerical methods, scientific computing, probability and modeling give students a solid foundation to model all these situations. Often an applied problem requires the combination of modeling the theoretical nature of the problem, the uncertainty in the measurements and using a computer program to arrive at a solution. The modeling and computation track trains students to do all of that.

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**Requirements**

In addition to the university and departmental requirements, the modeling and computation track is organized around five core courses:

Math 306 Vector and Tensor Analysis (3 units)

Math 310 Ordinary Differential Equations (3 units)

Math 335 Mathematical Probability (3 units)

Math 340 Numerical Analysis (3 units)

Math 370 Mathematical Model Building (3 units)

In addition to these core courses, students choose two advanced courses among three choices:

Math 406 Introduction to Partial Differential Equations (3 units)

Math 440 Advanced Numerical Analysis (3 units)

Math 470 Advanced Mathematical Model Building (3 units)

Please see the prerequisite diagram of the modeling applied track for the courses required in this concentration.

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**Careers**

Students in applied mathematics have a broad range of career options. Students can work in industry as scientific programmers, go to graduate school in applied mathematics, statistics, or engineering as well as go into a teaching credential program. Recent graduates have obtained jobs at local companies, gone to master’s and Ph.D. programs and obtained teaching credentials. 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 it 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) www.siam.org/careers/

A great way to prepare for an industrial career is to do an internship while being a student. Internships allow students to get paid while applying and learning mathematics. Applied mathematics students regularly obtain internships with local companies and sometimes these internships lead to job offers before they even graduate!

If your career goal is to teach at the university level, then a master’s degree (for a community college) or Ph.D. (for a university or four-year college) is needed. In these cases, it is useful to have some research experience. Students regularly do research during the academic year with faculty at CSUF and spend summers at national Research Experience for Undergraduates (REU) sites around the country.

An applied mathematics degree in the modeling and computation track will give you a broad background in mathematics that can be used in a huge range of scientific disciplines. The mathematical and computation tools in this degree are attractive to many types of employers.

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**Faculty**

Derdei Bichara, Assistant Professor, *Mathematical Biology, Dynamical Systems and 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*

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

Anael Verdugo, Assistant Professor, *Mathematical Biology, Nonlinear Dynamics, Bifurcation Theory*

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**Research, Consulting and Inventions**

Faculty members in the modeling and computation track are actively involved in research areas which include computational neuroscience, magnetic resonance imaging and satellite communications. They have obtained grants from the National Aerospace and Aeronautics and Space Administration (NASA) and from the National Institutes of Health (NIH) to support their research.

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

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