Textbook in PDF format How do you know whether something is true or not? Surely, you’ve been told that the angles of a triangle add to 180◦ , for example, but how do you know for sure? What if you met an alien who had never studied basic geometry? How could you convince him/her/it that this fact is true? In a way, this is what mathematics is all about: devising new statements, deciding somehow whether they are true or false, and explaining these findings to other people (or aliens, as the case may be). Unfortunately, it seems like many people think mathematicians spend their days multiplying large numbers together; in actuality, though, mathematics is a far more creative and writing-based discipline than its widely-perceived role as ever-more-complicated arithmetic. One aim of this book is to convince you of this fact, but that’s merely a bonus. This book’s main goals are to show you what mathematical thinking, problem-solving, and proof-writing are really all about, to show you how to do those things, and to show you how much fun they really are!