K. P. Bogart wrote Combinatorics through Guided Discovery, available freely online. In the preface, he writes (emphasis mine):
The point of learning from this book is that you are learning how to discover ideas and methods for yourself, not that you are learning to apply methods that someone else has told you about. The problems in this book are designed to lead you to discover for yourself and prove for yourself the main ideas of combinatorial mathematics. There is considerable evidence that this leads to deeper learning and more understanding.
Can you recommend other books that are similar? Note that "guided discovery" can take a few different forms.
Best Answer
Linear Algebra Problem Book by Halmos. From the description:
Distilling Ideas: An Introduction to Mathematical Thinking by Katz and Starbird.
This book gives an inquiry based learning approach to some topics in graph theory, group theory, and calculus.
Number Theory Through Inquiry by Marshall, Odell, and Starbird. From the description: