As the saying goes, there are many mansions in the house of mathematics. Pre-Calculus introduces students to the breadth and variety of mathematical thought. The year is organized as a series of short courses on number theory, data analysis, cryptography, analytic trigonometry, game theory, linear algebra, and graph theory. One aim of the course is to show students that there is something to love in mathematics for everyone. Throughout the course, we focus on functions as a tool to think about mathematical objects, and examine the different styles of argument and proof present in the different branches of mathematics. We read original sources, including some Euclid, Euler, and Diophantus. We also read modern mathematical writing, including texts by Conway, Rivest, Shamir, and Adleman, Calkin, and Wilf.
The course offers students many opportunities to construct mathematical arguments of their own. Our school gives outside the box awards to students who develop ideas new to the teachers, and this course generates most of the math awards because students have many opportunities to construct creative answers to beautiful questions. The course culminates in a thesis of sorts where students choose a hard problem from one of the areas they’ve studied and spend several weeks tackling it as best as they can. They then present the results to their classmates!