This undergraduate textbook facilitates an active transition to advanced mathematics. The resolution of problems is the primary focus of this publication; each problem has been selectively selected to illustrate, clarify, or expand upon a certain idea. The reader is led through comprehensive debates and imaginative perspectives as they investigate the links between several fundamental aspects of mathematics through more than 300 different activities.
This book begins with a lighthearted investigation of the fundamental concepts of mathematics, such as definitions, axioms, and proofs. It is then followed by three more sections, each divided into two parts. After that, a look will be taken at the fundamental notions of logic, sets, and functions, and then the attention will shift to the various methods of proof. After going over the fundamentals of a foundational class, the author then discusses various advanced topics that provide options for extension or additional research. The appendices throughout the text discuss historical viewpoints, current trends, and outstanding questions, demonstrating that mathematics is an active and dynamic human endeavor.