Modular Textbook in Mathematical Modeling

History of the book:

The SIAG-ED officers (Shelley B. Poole, Mario Bañuelos, Haley Yaple, and Emek Kose) began a large mathematical modeling book project in 2022, with the working title “Choose Your Own Adventure in Mathematical Modeling.” We are no longer the SIAG-ED officers, but we are publishing it with the SIAM editorial board, a not-for-profit publisher.

There is such diversity in the courses and content taught under the umbrella of mathematical modeling. Currently, faculty often assemble their own resources to meet the needs of their course. Our book is for instructors who may be required to teach the course for a first time or students seeking out a resource for the mathematical modeling topics they need: those who need the support of a textbook. 

While of course it’s impossible to meet the needs of every mathematical modeling course, we hope to get as close as possible. We want to make mathematical modeling more available and accessible to students and faculty through this project. We started with a title of “Choose Your Own Adventure in Mathematical Modeling,” but the “Choose Your Own Adventure” books have their brand trademarked, so we have chosen a more direct title “Build Your Course in Mathematical Modeling: A Modular Textbook in Mathematical Modeling.” It is named to describe its format: standalone chapters of mathematical modeling content. Our goal is to allow faculty to select the chapters for their course so that students can choose to purchase only the necessary sections, though the full book will also be available. 

The text is composed of chapters by 34 different authors around the world working in Mathematical Modeling fields. Most chapters stand alone with their own prerequisites; some only require an interest in the topic, while others may require knowledge of algebra, statistics, programming, calculus, and/or differential equations. The book is composed in two volumes due to the breadth of content, but individual chapters will also be available.

Here is an outline of what topics to expect: (More details will be provided as the book is finalized and published)

  1. Mathematical Modeling: the Core Intro
    1. Mathematical Modeling: process and experience
    2. Data-Driven Modeling
    3. Programming in Mathematical Modeling with MATLAB and Python
  2. Deterministic Modeling
    1. Difference Equations
    2. Differential Equations
    3. Systems of Differential Equations
    4. Dimensional Analysis
    5. Multiscale Modeling
    6. Regularizing Ill-Posed Inverse Problems
  3. Stochastic Modeling
    1. Probability Models and Monte Carlo Simulations
    2. Simulating Differential Equations Stochastically
    3. Uncertainty Quantification
  4. Computational and Data-Driven Modeling
    1. Numerical Modeling
    2. Parameter Estimation
    3. Machine Learning
  5. Agent-Based Modeling