Mathematical Modeling

Mathematics is more than just numbers and symbols on a page. Applications of mathematics are indispensable in the modern world. Math can be used to determine whether a meteor will impact Earth, predict the spread of an infectious disease, or analyze a remarkably close presidential election. In this course, students create and evaluate mathematical models to represent and solve problems across a broad range of disciplines, including political science, economics, biology, and physics.

Students begin with a review of some of the core mathematical tools in modeling, such as linear functions, lines of best fit, and exponential and logarithmic functions. Using these tools, students examine models such as those used in population growth and decay, voting systems, or the motion of a spring. Students also learn how to use Euler and Hamilton circuits to find the optimal solutions in a variety of real-world situations, such as determining the most efficient way to schedule airline travel. A introduction to probability and statistics lead into a study of using deterministic versus stochastic models to predict the spread of an epidemic and explore classic mathematical problems such as the traveling salesman problem, birthday paradox, and light switching problem.  Students are introduced to logic proofs by induction and contradiction.  Students leave this course familiar with all steps of the modeling process, from defining the problem and making assumptions, to assessing the model for strengths and weaknesses.