Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)

This comprehensive textbook is designed for students who want to learn mathematics in an engaging and interactive way.

With over 200 illustrations and a conversational writing style, this book makes complex concepts accessible and easy to understand.

The author's use of "scratch work" and proof sketches provides students with a big-picture view of how to come up with proofs on their own, rather than simply presenting terse formulas.

The text covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions, and relations, as well as an introduction to higher mathematics through examples and theorems.

Additionally, each chapter includes "pro-tips" on studying math, historical notes, and comments on mathematical culture.

The book also features an introduction to unsolved problems in mathematics after each chapter's exercises.

With its relaxed and conversational tone, this textbook is perfect for students who want to learn math in a fun and engaging way.