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Math 42: General Course Outline

Catalog Description

42. Introduction to Data-Driven Mathematical Modeling: Life, The Universe, and Everything. (4). Lecture, three hours; discussion, one hour. Requisites: Math 31AB; 32AB; 33A; One of Statistics 10-15, Statistics 20, and 21; PIC 10A. This course gives an introduction to data-driven mathematical modeling and to combining data analysis with mechanistic modeling of phenomena from various applications. Topics include model formulation, data visualization, nondimensionalization and order-of-magnitude 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 data-driven and problem-driven way. They will get hands-on practice with problems from the Mathematical Contest in Modeling, including an in-depth 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.1-44

Introduction and Basic Principles of Modeling

Week 2

Tufte 1-3, 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 4-5, Handouts

Continuous Dynamical Systems (continued) and Related Topics

Week 8

MS 6

Continuous Stochastic Models

Week 9

Mathematical Contest in Modeling (MCM): Practice
Reading from past questions and solutions from mathematical modeling contests, available at https://www.comap.com/undergraduate/contests/mcm/

Week 10

Mathematical Contest in Modeling: Student Discussions and Projects