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Applied MathematicsApplied mathematics is the area of cross fertilization between mathematical theory and applications in the natural, economic, engineering, social, and psychological sciences. The Department offers a comprehensive program in Applied Mathematics. This document describes Masters program in Applied Mathematics (MA or MNS) Prerequisites There are no additional prerequisites. Course Work Master's students take courses in Real Analysis and Numerical Analysis (I or II) and additional courses from the following five areas with the condition that there are at least two areas selected and at least two courses are taken in each:
MA students may take up to six hours in an outside field related to Applied Mathematics, such as fluid mechanics, computer graphics or biomathematics. Examinations MA students who write a thesis and MNS students take one qualifying exam. MA students who do not write a thesis take one qualifying exam and a second exam which is another qualifying exam, a comprehensive exam, or a special Master's exam. Ph.D program in Differential Equations and Mathematical Biology Differential equations
central in mathematics, and one of their recent and most exciting
applications is in mathematical biology. ASU offers graduate
studies in ordinary, partial, and functional differential
equations and in related areas such as bifurcation, perturbation Prerequisites In addition to the general departmental prerequisites, proficiency in a computer language is required. Advanced Linear Algebra and a course in Complex Analysis are desirable. Course Work The Ph.D. student
takes 30 credit hours in the following six areas: intermediate
and advanced Real Analysis, Numerical Analysis, Ordinary Differential
Equations, Mathematical Biology, Partial Differential Equations,
Probability and Statistics. In addition, 30 credit hours are
taken in approved courses from the Department of Mathematics
and courses from outside the Department that are related to
mathematical modeling. The selection should ensure sufficient
breadth and coherence in the student's program of study. Students
who wish to place a greater emphasis on analysis would take
further courses in differential equations, perturbation theory,
dynamical systems, functional analysis, operator theory or
topology, or would take further Examinations Two qualifying examinations are taken out of the following four: Real Analysis, Numerical Analysis, Differential Equations, Mathematical Statistics. The written comprehensive examination covers two or three 500 level courses in Mathematical Biology (physiological modeling, models in population biology, biotechnology) and Differential Equations (ordinary differential Equations, partial differential equations, functional differential equations, dynamical systems, perturbation theory). Faculty For more information on specific aspects and content of this program, contact one of the Differential Equations and Mathematical Biology faculty: http://math.asu.edu/research/mathbio.html Ph.D program in Chaos and Nonlinear Dynamics In recent years research on nonlinear differential equations has become one of the most active areas in applied mathematics. Its most prominent feature has been the characterization of chaotic behavior of solutions of differential equations, i.e. unpredictable and very complicated behavior. Similar behavior occurs in almost all scientific and engineering models from astrophysics to population biology, fluid dynamics and laser physics which offers wide opportunities for interdisciplinary research. ASU offers graduate studies in nonlinear dynamical systems, chaos, fractals and in related areas of perturbation theory and ordinary, partial and functional differential equations. Applications in mathematical biology, flow instabilities, control theory and many others can be pursued. Prerequisites In addition to the general departmental prerequisites, proficiency in a computer language is required. Advanced Linear Algebra is desirable. Course Work Ph.D. students take 30 credit hours in Real Analysis, Numerical Analysis, Dynamical Systems, Chaos and Fractals, and Partial Differential Equations. For the remaining hours, students are particularly encouraged to choose additional courses in numerical analysis, partial differential equations and applied real analysis, and to take advantage of special courses offered by the Chaos and Nonlinear Dynamics group and the Mathematical Biology group. An interdisciplinary program of study containing courses in Control Theory, Computer Science, Mechanical or Electrical Engineering, Physics or Biology is desirable. Examinations Two qualifying exams are taken out of the following four:
Part of the Doctoral Dissertation research can be done at the Center for Nonlinear Studies, Los Alamos National Laboratory.. Faculty For more information on specific aspects and content of this program, contact one of the Chaos and Nonlinear Dynamics faculty: http://math.asu.edu/research/chaos.html Ph.D program in Control and Systems Theory Control and Systems Theory is a very active research area at the cross-roads of many disciplines of mathematics with engineering applications. On one side, both old and new, very deep results from a wide area of pure mathematics (e.g. functional analysis, differential and algebraic geometry, stochastics and probability, ordinary and partial differential equations) are utilized to solve engineering problems of practical importance. On the other hand, control theory has built a strong machinery of its own, contributing major results and methodologies to pure mathematics. Research by faculty at ASU is on the cutting edge in several areas in control and systems theory, including adaptive nonlinear and infinite dimensional control, (differential) geometry of highly nonlinear systems, stochastic partial differential equations, and applications to vision and pattern recognition. Prerequisites Besides the general departmental prerequisites, demonstrated strengths in several areas of mathematics (e.g. advanced undergraduate courses in linear algebra, algebra, analysis, differential equations, probability), and a familiarity with a modern programming language, such as MAPLE, are desirable. In view of the interdisciplinary nature of the program, alternative areas of individual strengths may be appropriate. Course Work Control and systems theory ties in with many disciplines of mathematics, and thus offers a variety of choices for building a strong knowledge base in pure mathematics which is necessary as a basis for research work in control. Typically a Ph.D. student takes 30 credit hours in
Differing programs of study may be developed with the student's supervisory committee. The remaining hours are usually devoted to building strengths in selected areas outside mathematics that use control. Courses may be taken in nearly all engineering disciplines, as well as in Physics, Chemistry, Biology, and Computer Science. Examinations Two qualifying examinations are taken from the Department's set of five. The comprehensive examination is designed by the student's supervisory committee and covers the areas of specialization. It is at a level that allows the student to demonstrate readiness to begin research work in control and systems. Faculty For more information on specific aspects and content of this program, contact one of the Control and Systems Theory faculty: |