MA 578 Principles of Mathematical Modeling
The course aims to introduce the students to the main principles of mathematical modeling: model construction, validation, and refinement. Models are largely divided into theory-driven and data-driven with the latter consisting of empirical and semi-empirical. They are constructed based on geometric, time-evolution, and physical considerations of the modeling phenomena: symmetry, continuous/discrete approximation, small increments approach, self-similarity and dimensional analyses, Markovian and heredity arguments, conservation laws, etc., and can further be classified into static/dynamic, deterministic/stochastic, etc. Models are analyzed by various computational methods including asymptotic, perturbation, blowup, averaging, and stochastic/statistical analyses. Thus, the course reviews and culminates several previous disciplines, gives an overview of various modeling techniques and enhances the earlier skills and knowledge of mathematical problem-solving. Models typically involve several parameters that can be identified by inverse approaches, which are an essential part of the course. To apply learned principles of mathematical modeling, the students will be offered a wide range of projects arising in science and industry.
Prerequisite
Undergraduate Students: MA 221 or equivalent.