Program Overview

Introduction to the Graduate Degree in Applied + Computational Mathematics

The Computing & Mathematical Sciences department at Caltech offers an interdisciplinary program of graduate study in applied and computational mathematics, leading to the Ph.D. degree. This program is designed to provide students with a thorough training in fundamental computational and applied mathematics and to develop their research ability in a specific application field.

Program Description

The fields of application include a wide range of areas such as fluid mechanics, materials science, and mathematical biology, engineering applications, image processing, and mathematical finance. The training essential for future careers in applied mathematics in academia, national laboratories, or in industry is provided by completion of the requirements for a Ph.D. degree in applied and computational mathematics.

Research Areas and Interests

The research areas and interests of the applied and computational mathematics faculty cover a broad spectrum, including:

• Nonlinear dynamics
• Computational biology
• Numerical analysis and scientific computing
• Computational and theoretical fluid mechanics
• Theoretical materials science
• Multiscale computations and homogenization theory
• Computational methods for electromagnetics and acoustics
• Statistics
• Signal and image processing
• Probability theory and stochastic analysis
• Dynamical systems and geometric mechanics

Program Structure

Reflecting the interdisciplinary nature of the program, several different groups, in addition to the applied and computational mathematics faculty, contribute to the teaching and supervision of research. Students in applied and computational mathematics are expected to combine their basic mathematical studies with deep involvement in some field of application. Basic general courses are listed specifically under applied and computational mathematics, and these are to be supplemented, according to the student's interest, from the whole range of Institute courses in specific areas of physics, biology, engineering, etc.

Graduate Program Details and Requirements

Requirements for the Applied and Computational Mathematics graduate program are listed in the current Caltech Catalog. Further details and advice can be found in the document "Navigating the Ph.D. Options in CMS".

Graduate Options Administrator and Representative

• Graduate Options Administrator: Maria Lopez
• Graduate Option Representative: Thomas Hou, Applied and Computational Mathematics Option Representative

Conclusion

A regular colloquium provides the opportunity for visitors, faculty, and students to discuss current research. The program is designed to give students a thorough training in fundamental computational and applied mathematics and to develop their research ability in a specific application field, preparing them for future careers in applied mathematics in academia, national laboratories, or in industry.