Course Description:

A negative times a negative is positive. a^2 + b^2 = c^2. The quadratic formula. If the sum of digits in a number is a multiple of three then that number is divisible by 3. Throughout their mathematical education, students learn many formulas, rules, theorems, and techniques that they apply to solve problems. However, few courses devote time to demonstrating how and why these rules work. College level math courses begin to emphasize understanding the “why” and require students to prove the validity of rules– a task for which students often find themselves unprepared.

This course will expose students to proof techniques and more abstract mathematical thinking by examining major results from their coursework and proving their validity. It is geared towards students who are considering pursuing mathematics as a major in college. Students who have completed precalculus or higher will get the most out of the course, but it will be tailored to the level of any student.