Many phenomena arising in engineering, life sciences, and other disciplines of science are usually formulated by mathematical models, for instance, algebraic equations, ordinary differential equations (ODEs), or partial differential equations (PDEs). The focus of this course will be on seeking the connections between mathematics and physical systems, studying and applying various modeling techniques to creating mathematical description of these systems, and using this analysis to make predictions about the system’s behavior. More generally, this course provides an introduction to mathematical modeling and applied mathematics.

This course is designed for senior undergraduate/graduate students majoring in mathematics as well as mathematically inclined senior undergraduate/graduate students. Generally, the objectives of this course will be able to 

• convert information of a physical phenomena into a mathematical framework;
• learn how to synthesize techniques from various areas of mathematics to develop mathematical models;
• learn how to assemble basic assumptions to formulate their own solutions to problems and test the validity of their results based on the science of the problem;
• interpret results of modeling (what do all those numbers and variables and equations and diagrams and graphs and charts actually mean);
• communicate the entire process (abstraction, hypothesis, analysis, conclusion) to your intended audience (which may know less, the same amount of, or more mathematics than you do);
• introduce students to critical thinking within the context of mathematics and science.