Precalculus

Welcome to Students

What does this math course have to offer?
Precalculus builds on your algebra foundation to explore further implications of the function concept, starting with graph transformations of the functions we already know. We draw on geometry knowledge to develop the circular functions, which enjoy a beautiful connection to the exponential function by way of the complex numbers and infinite series. Armed with these tools, we then consider polar coordinates, vector-valued functions (AKA parametric equations), and the algebra of vectors in Cartesian coordinates.
What are some skills that I can take from this class?
  1. Strengthened algebraic manipulation emerges as you work through proofs of identities and simplification of transcendental expressions. This fluency will remove for you one of the major obstacles to success in calculus.
  2. Deepened mathematical appreciation follows from revisiting the same result in different settings, e.g. proving the addition formulas for sine and cosine by using a coordinate transformation, or by multiplying two exponential functions of imaginary arguments and interpreting the result in both polar and rectangular coordinates.
  3. Expanded mathematical vocabulary will allow you to talk about periodic phenomena with circular functions and to model Euclidean geometry problems with vectors.
What do I need to succeed in this class?
Just as you would for any class you take in college, be sure to read the assigned text before each lecture. Make sure you read actively, with pen or pencil in hand and a dedicated math notebook ready for jotting down the key ideas. Adopt a skeptical attitude toward the expositions provided, coming up with questions that force the words on the page to reveal meanings and connections buried under the surface. Play with math as if you were a toddler trying a new toy, looking for all the ways it can be broken or repurposed. After you think you understand a new concept from all possible angles, attempt to solve the end-of-section exercises without referring to the example problems in the text.

Further Thoughts on My Precalculus Teaching Philosophy