Math 42: General Course Outline
Catalog Description
42. Introduction to DataDriven Mathematical Modeling: Life, The Universe, and Everything. (4). Lecture, three hours; discussion, one hour. Requisites: Math 31AB; 32AB; 33A; One of Statistics 1015, Statistics 20, and 21; PIC 10A. This course gives an introduction to datadriven mathematical modeling and to combining data analysis with mechanistic modeling of phenomena from various applications. Topics include model formulation, data visualization, nondimensionalization and orderofmagnitude physics, introduction to discrete and continuous dynamical systems, and introduction to discrete and continuous stochastic models. The class will include examples drawn from many fields and practice problems from the Mathematical Contest in Modeling. P/NP or Letter grading.
Course Information:
Students will learn the basic principles of mathematical modeling and data visualization. The focus will be on mechanistic models, but in a datadriven and problemdriven way. They will get handson practice with problems from the Mathematical Contest in Modeling, including an indepth exploration through a final project.
The grade will be determined based on homework, quizzes, a midterm, a final project (done in groups, with both written and oral components), and class participation.
Textbook
Required:
(MS) "A Course in Mathematical Modeling", by Douglas D. Mooney and Randall J. Swift
(Tufte) "The Visual Display of Quantitative Information" (2nd edition), by Edward R. Tufte
Important Supplementary Booklets:
(BFG) "Math Modeling & Getting Started", by K. M. Bliss, K. R. Fowler, and B. J. Galluzzo (a free booklet from the Society for Industrial and Applied Mathematics)
(BGKL) "Math Modeling: Computing & Communicating", by K. M. Bliss, B. J. Galluzzo, K. R. Kavanagh, & R. Levy (a free booklet from the Society for Industrial and Applied Mathematics)
Supplementary material through past Mathematical Contest in Modeling questions and handouts on specific topics.
Schedule of Lectures
Lecture  Section  Topics 

Week 1 
MS 0, BFG p.144 
Introduction and Basic Principles of Modeling 
Week 2 
Tufte 13, BGKL 3 
Visualization of Data 
Week 3 
MS 1 
Discrete Dynamical Systems 
Week 4 
MS 2 
Discrete Stochastic Models 
Week 5 
MS 3, BFG: Appendix B 
Stages, States, and Classes 
Week 6 
MS 5 
Continuous Dynamical Systems 
Week 7 
BGKL 45, Handouts 
Continuous Dynamical Systems (continued) and Related Topics 
Week 8 
MS 6 
Continuous Stochastic Models 
Week 9 
Mathematical Contest in Modeling (MCM): Practice 

Week 10 
Mathematical Contest in Modeling: Student Discussions and Projects 