Precalculus

Modern mathematical concepts are like swords that have been honed by thousands of brilliant minds over many hundreds of years. To continue the analogy, many students are shown how to use safety scissors and then either walk away uninterested or terrified of working with something that might actually be sharp. The power and beauty of the sword is lost. To combat this (pun intended), this course will go to the forge and start working with metal directly.

In more concrete terms (now he’s doing construction analogies??), we will be doing algebra, geometry, trigonometry, and even some calculus. We will not be applying theorems and formulas handed down from above. Instead we will make our own conjectures, prove theorems, and use these core concepts to study new types of mathematical objects like fractals, matrices, and dynamical systems. We are also not restricted to the traditional pen and paper used for mathematical reasoning (or even our TI-89s and phone calculators). We will program with Python and use it as a tool for computational thinking.

If successful, this course will prepare you for calculus, not in the sense that you will have the right set of tools for the challenge (although that is important of course), but that you will be ready to perceive the subject as a profound manifestation of human reason rather than a requirement for graduation.