In the study of mathematics non-routine problems, puzzles, paradoxes, and sophisms often delight and fascinate. Captivating examples can excite, enlighten, and inspire learners and spur their passion for discovery. Furthermore, thought-provoking exercises and contemplation of paradoxes can naturally engage students and offer them a unique opportunity to understand more fully the history and development of mathematics. “Justification of otherwise inexplicable notions on the grounds that they yield useful results has occurred frequently in the evolution of mathematics [15].”

The teaching and learning process often loses its effectiveness for lack of appropriate intellectual challenges and for insufficient active involvement or emotional investment from students in the experience. What we tend to remember most are knowledge and learning experiences tied to intense thinking, noteworthy discovery, or inspired creativity. This book presents problems and examples that may lead students to contemplate conceptual issues in calculus and to comprehend the subtleties of this subject more deeply.

In that light, this book aims to enhance the teaching and learning of a first-year calculus course. The following major topics from a typical singlevariable calculus course are explored in the book: functions, limits, derivatives, and integrals.