Description

This exciting new graduate program is offered through the Nonlinear Dynamical Systems Group (NLDS). Dynamical Systems is an essential tool for the mathematical analysis of real life problems in fields that include: Physics, Engineering, Biology and Chemistry. This program provides the analytical and computational tools and skills required to formulate and tackle complex models of real life problems. This program is ideal in preparing students for recruitment in industry or government laboratories where a high level of mathematics and modeling is required.

An integral part of Dynamical Systems is the use of mathematical models and numerical techniques for which a strong knowledge of scientific computation is needed. Students in the Dynamical Systems program will acquire indispensable skills/tools in the use of computers for problem solving and hence increase their market value when seeking for a competitive employment opportunity.

Students enrolled in the program are mentored by faculty members actively engaged in research at the forefront of Dynamical Systems and Chaos, and its applications. Students in the program benefit from a dedicated Dynamical Systems state-of-the-art computer laboratory. Continuous interactions between the NLDS group and a large number of research groups/collaborators offers an ideal atmosphere for our graduate students to engage in scientific and industrial collaborations. For example the NLDS group has a strong link with the Space and Naval Warfare Systems Center (SPAWAR) in San Diego, including a couple of patents and student internships. The NLDS has also strong ties with the Physics and Computer Science departments at SDSU, as well as with the Naval Postgraduate School (NPS).

The NLDS group also offers a PhD program in Dynamical Systems and Applied Mathematics through the Computational Research Center (CSRC) at SDSU.

Nonlinear Dynamical Systems Group Faculty

Peter Blomgren – Numerical analysis, image processing, partial differential equations.
Ricardo Carretero – Applied mathematics, nonlinear lattices, nonlinear waves.
Joe Mahaffy – Mathematical biology, delay differential equations
Antonio Palacios – Applied mathematics, bifurcations, symmetries
Diana Verzi – Mathematical biology, Mathematical Physiology

Admission Requirements

To be admitted to the program, the student should have training equivalent to that required for an undergraduate degree in mathematics, applied mathematics, physics or electrical engineering. In addition, all students must satisfy the general requirements for admission to the university with classified graduate standing.

The Department maintains a web page with further information on admission and financial support.

Course Work

The following courses are required (3 units each):

MATH-531 Partial Differential Equations
MATH-537 Ordinary Differential Equations
MATH-538 Dynamical Systems & Chaos I
MATH-636 Mathematical Modeling
MATH-638 Dynamical Systems & Chaos II
MATH-799A Thesis or Project

Recommended electives (3 units each):
These M696 special topics courses are offered depending on demand and resources.

Nonlinear Waves
Pattern Formation
Applied Bifurcation of Dynamical Systems
Numerical Experiments and Methods in Dynamical Systems
Nonlinear Time Series
Fractal Geometry
Mathematical Biology / Neural Modeling

Other recommended electives (3 units each):
Other courses, even in other departments, may be approved by adviser.

MATH-541 Introduction to Numerical Analysis and Computing
MATH-542 Introduction to Numerical Solutions of Differential Equations
MATH-637 Theory of Ordinary Differential Equations
MATH-668 Applied Fourier Analysis
MATH-797 Research
CS-553 Neural Networks
PHYS-580 Computational Physics
PHYS-585 Computer Simulations in the Physical Sciences
PHYS-608 Classical Mechanics

Graduation Requirements

The graduate division requirements for a Master’s degree are that a student complete 30 units of course work at the 500, 600 or 700 level. As noted above under Course Work, this program has a number of required courses. In addition, a master’s thesis must be completed, which counts for 3 units of the 30.

The thesis is written under the direction of a faculty member who works closely with the student in both the research and the writing of the thesis. The student can choose any faculty member in the program to be the thesis adviser. The student and the adviser will determine the topic of the thesis, generally on a topic of interest to both. The average student takes 6 months or less to complete a thesis.

Advisors:
Ricardo Carretero, rcarretero@mail.sdsu.edu, GMCS 591
Antonio Palacios, apalacios@mail.sdsu.edu, GMCS 589