An exploration of ten intriguing areas of mathematics, from prime numbers and graph theory to fractals and knots This engaging book invites readers to dive into ten intriguing topics often left out of the standard curriculum yet essential to the mathematical enterprise. It guides the mathematically curious-undergraduates emerging from their comfort zones, high school students bored by what they are taught in math classes, general readers hungry for a challenge-through concepts and problems that encourage the active, hands-on learning that leads to real understanding. In ten chapters, readers meet prime numbers, graph theory, Pick's Theorem, continued fractions, curves of constant diameter, computer logic, projective geometry and perspective, fractals, knots and links, and catastrophe theory, including the broader mathematical and historical setting. Along the way, they build their cognitive toolkit, encountering such ideas as theorem, proof, and algorithm organically and in context. Each chapter includes two problem sets, with answers provided in a final chapter. The authors, both prominent educators and mathematicians, invite readers to think deeply about the problems they investigate and to enjoy the process of searching for solutions.