Math 490 - Special Topics in Mathematics / Math 617 - Introduction to Industrial Mathematics

Class: MW 2:30PM - 3:45PM in Math & Psychology 412 (8/24-12/9/2026), Instructor: Bedrich Sousedik

Course description: The objective of this course is the survey of mathematical and statistical techniques traditionally important to quantitative modeling in industry and government. Topics might include, but are not restricted to, data acquisition and manipulation, discrete Fourier transform and image processing, linear programming, regression, random variables and distributions, Monte Carlo method, ordinary and partial differential equations, with applications of these concepts to industrial problems. The course is not designed to substitute for any course covering these topics in detail, but rather to link a survey of techniques to applications.

Prerequisite: Math 251, Math 225, Math 221, Stat 355 or consent of the instructor. Some programming experience is recommended.

8/24 Introduction. Industrial Mathematics through digital twins: What is a digital twin? See also National Academies report.

8/26 From simulation to a first epidemic model. See also Going viral and Going viral... again.

8/31 Model Simulation: the inner loop.

9/2 Overview of (Numerical) Linear Algebra.

9/7 Labor Day (no class).

9/9 Project launch: Epidemic digital-twin project.

9/14 Lecture 1: SEIR, calibration, and data assimilation.

9/16 Lecture 2: UQ, surrogates, and the five-node benchmark.

9/21 Lecture 3: Parameter identification.

9/23 Lecture 4: Data assimilation.

9/28 Lecture 5: Uncertainty propagation and surrogates.

9/30 Lecture 6: The project geography, the data, and the teams’ tasks.

10/5 Chapter 7A: Linear Systems, Stability, Controllability, and Observability.

10/7 Special event: Matt Robinson (Rampart Communications): Tactical Mathematics A Career, In Theory.

10/12 Fall Recess (no class).

10/14 Chapter 7B: Feedback, Observers, Optimal Control, and Identifiability.

10/19