## Applied Mathematics and Scientific Computation

The Department of Mathematics at UAB is offering a new track in **Applied Mathematics and Scientific Computation** leading to the Bachelor of Science degree with a major in Mathematics.

A mathematical model is a rendering of some real-world system into the language of mathematics, usually taking the form of a single partial differential equation, or a system of such equations. The development of effective mathematical models is a fundamental need of our society, based as it is upon science and technology, and these models act as the indispensable link between us humans and the multitude of machines that we use to manage and investigate our world.

In weather prediction, data is gathered both globally and locally and used as input to a system of partial differential equations that now include not only effects related to the atmosphere, but also oceanic and even polar effects. This system of equations is large and complex, and good mathematics together with powerful supercomputer systems are needed for their solution. The end result is that today hurricanes and even tornadoes, while not exactly predicable, are much more predicable that in earlier times. The early warning systems generated by these models have saved many lives in recent years. There are many other examples of beneficial mathematical models. Many regions of the country depend crucially on groundwater, both for human and industrial/agricultural use. It is a renewable but fragile resource, and contamination and overuse is a constant problem. Once again, aquifers are modeled by a system of partial differential equations. The design of jumbo-sized jet aircraft, CAT-scan imaging in medicine, the effects of earth tremors on buildings in earthquake zones, and option pricing models in the stock market are some additional examples of mathematical models of value to society.

The new track is aimed at providing graduates with the mathematical and computational skills needed to develop and maintain mathematical models from the Sciences, Engineering, Medicine and the Biosciences, Business, and elsewhere.

The course sequence in this track in the Mathematics major include the following mathematics courses

- Calculus I-III (MA125-126-227),
- Introduction to Differential Equations (MA 252),
- Linear Algebra (MA 260 or MA 434),
- Scientific Programming (MA 360),
- Four electives chosen from Vector Analysis (MA 444), Partial Differential Equations (MA 455), Modeling with Partial Differential Equations: Finite Difference Methods (MA 465), Numerical Analysis (MA 468), Gas Dynamics (MA 467), Probability (MA 485), Statistics (MA 486) and the electives must include one of the following two-term sequences: MA 455-461, MA 455-467, MA 463-464, and MA 485-486.
- Two additional electives selected from Mathematical Modeling (MA 361), Geometry (MA 472), Mathematical Finance (MA 484), or any course numbered 420 or above.

A minimum grade of C is needed in each of the 12 mathematics courses counted toward the major. A minor in the sciences, engineering, or business is required. Also Track C (Computer Science-Technology Track) of the NSM school-wide requirements must be satisfied in addition to either Track A or B.

The upper level mathematics courses are also offered to graduate students.

Syllabi for the standard courses may be found from the University catalog. For convenience we list the course content for the courses in this track recently added to the department master course listing:

**MA 360/560. Scientific Programming**

This course is designed to provide the computational skills needed to attempt serious scientific computational tasks. Computers and floating point arithmetic; the GNU/Linux operating system and an introduction to the compiled programming languages FORTRAN (including FORTRAN 95) and C++ in the context of solving systems of linear equations and differential equations arising from practical situations; use of debuggers and other debugging techniques, and profiling; use of callable subroutine packages like LAPACK and differential equation routines; parallel programming a Beowulf system with MPI; introduction to Matlab. Co-requisite: Linear Algebra (MA 260 or MA 434). Prerequisite: MA 125 with grade of C or better. 3 hours.

**MA361. Introduction to Mathematical Modeling**

Mathematical modeling using computer software, including spreadsheets, systems dynamics software, and computer algebra systems; connections to calculus and systems of ordinary differential equations are emphasized. Students translate verbal descriptions into mathematical form using appropriate units and reasonable relationships, construct and interpret multiple representations of mathematical relationships, including tabular, graphical, and schematic, use quantitative evidence produced by models as a basis for reasoned argument to unambiguous conclusions, communicate the mathematical structure of models appropriately to an audience in written form, using proper grammar, usage, spelling, and mathematical modeling conventions of language. Prerequisite: MA 125 with grade of C or better. 3 hours.

**MA461/561. Modeling with Partial Differential Equations**

Practical examples of partial differential equations; derivation of partial differential equations from physical laws; introduction to MATLAB and its PDE Tool-box, and COMSOL using practical examples; an overview of finite difference and finite element solution methods; specialized modeling projects in topics such as groundwater modeling, scattering of waves, medical and industrial imaging, continuum mechanics and deformation of solids, Fluid mechanics including the class boat race, financial derivative modeling, and acoustic and electromagnetic wave applications. Written project reports required for all homework assignments. Prerequisites: MA 227 Min Grade: C