Applied and Computational Mathematics

Source: https://catalog.caltech.edu/current/areas-of-study-and-research/applied-and-computational-mathematics/ Parent: https://catalog.caltech.edu/

An interdisciplinary program of study in applied and computational mathematics that leads to the Ph.D. degree is offered by the Computing & Mathematical Sciences department. In addition to various basic and advanced courses taught by the applied and computational mathematics faculty, broad selections are available in mathematics, physics, engineering, and other areas. Students are expected to become proficient in some special physical or nonmathematical field. A subject minor in applied computation is offered jointly with the computer science option.

In addition to the applied and computational mathematics faculty, professors from other disciplines such as mathematics, physics, engineering, and biology supervise research and offer courses of special interest. The applied and computational mathematics group has access to supercomputers and concurrent computers.

The present graduate program is one leading mainly to the Ph.D. degree. The curriculum consists of two types of courses: those that survey the methods used in applied and computational mathematics, and those that have a special applied and computational mathematics flavor and represent active research interests of the members of the faculty. Among the latter have been wave motion, perturbation theory, fluid mechanics, optimization, stochastic processes, wavelet analysis, signal processing, numerical analysis, computational electromagnetism, computational fluid dynamics, mathematics of data science, probability, random matrix theory, applied algebraic geometry and statistical inference, game and decision theoretic approaches to numerical approximation and learning, homogenization, multifidelity and multiscale analysis, and stochastic modeling, stochastic analysis, data assimilation, and inverse problems. Through study outside of applied and computational mathematics, each student is expected to become competent in some special physical or nonmathematical field. In this way, subjects for research appear naturally, and a broad educational program is provided.

The group primarily interested in applied and computational mathematics currently consists of approximately 25 students and eight professors. Also, each year many distinguished visitors come either to present lectures or remain in residence for large parts of the academic year.

Areas of Research

Research is particularly strong in theoretical and computational fluid mechanics, theoretical and computational materials science, computational electromagnetism, numerical analysis, ordinary and partial differential equations, multi-scale analysis, geometric integration, integral equations, linear and nonlinear wave propagation, water waves, bifurcation theory, perturbation and asymptotic methods, stability theory, variational methods, approximation theory, uncertainty quantification, randomized algorithms, continuous optimization, discrete optimization, statistical estimation, computational harmonic analysis, stochastic processes, signal and imaging processing, inverse problems, mathematical biology, large-scale scientific computing, mathematics of data science, and probability and random matrix theory, game and decision theoretic approaches to numerical approximation and learning, homogenization, multifidelity and multiscale analysis, and stochastic modeling and stochastic analysis, data assimilation, inverse problems, and related branches of analysis.

Published Date: March 21, 2025