Most high school courses focus on two-dimensional geometry, leaving students mystified by 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 are the bond angles in a molecule?” and “How much leather does it take to make a soccer ball?”
Building upon vectors, interested students can explore relevant and related applications of matrix algebra. With these tools and insights, students can make conclusions and interpret possibilities of 3D space in practical and concise ways.
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 completed coursework in Algebra 2 Trigonometry or Precalculus.