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.

So small yet so powerful … We cannot see it, but it can change our everyday life! “Nano” indicates something small, something minute, about a billion times less than a meter. In these dimensions materials can go ‘crazy’ and display unique, unprecedented properties. How does the size of a material affect its properties? How do some plants manage to repel water and clean themselves? How can I make my clothes stain resistant? How does the gecko lizard walk on the ceiling? How can a robot climb onto a glass window? How do all this relate to bio-mimicry and everyday life?

Nanotechnology is linked to many disciplines, such as physics, biology, chemistry and mathematics, to produce useful applications with innovative properties. Through a series of approaches, including problem-solving, designing and conducting experiments, games, studying natural and artificial nanomaterials, searching for information, modeling, and group activities, students are introduced to the exciting world of science and technology at a nanoscale!