Most high school courses focus on two-dimensional geometry, leaving students unable to answer questions about the three-dimensional world around them. Fortunately, it’s relatively easy to generalize geometry and algebra to higher dimensions using vectors!
In this course, students will explore the geometry and algebra of vectors in both two and three dimensions. Students will learn to find the equations of curves, planes, and their possible intersections, and to parameterize them in useful ways. Students will soon be able to answer interesting questions, like “What is the bond angle in a tetrahedral molecule?” and “How much leather does it take to make a soccer ball?”
Students familiar with calculus can also explore more advanced topics, such as derivatives and applications of vector valued functions, directional derivatives of scalar functions, multiple integrals, path and surface integrals, gradient vectors, divergence, curl and Green’s theorem, and Gauss’s law. Knowledge of calculus is not required for this course, although we recommend students have at least two years of high school-level math.