MATH 87: Mathematical Modeling

Mathematical modeling provides a framework for understanding, analyzing, and solving practical problems arising in a variety of real-world contexts. In this course, we will study how mathematical models are formulated, analyzed, computed, and interpreted using tools from calculus, linear algebra, optimization, graph theory, probability, and differential equations. Topics will include optimization and linear programming, graph and network models, stochastic matrices and Markov chains, linear least squares and inverse problems, and discrete and continuous dynamical models. Computational experiments, primarily using MATLAB, will be used throughout the course to explore model behavior, test assumptions, and solve problems that may not be tractable analytically. The course will emphasize the connection between mathematical formulation, computational solution, and interpretation of results.