A robust bridge between high school and higher level mathematics, this text presents some of the most fundamental and beautiful ideas in pure mathematics. It covers not only standard material but also many interesting topics not usually encountered at this level, such as solving cubic equations, studying the five Platonic solids, coding secret information, and comparing the sizes of two infinite sets. This third edition contains three new chapters that provide an introduction to mathematical analysis. It also includes solutions to all of the odd-numbered exercises. A solutions manual is available upon qualifying course adoption.