Definitions are useful for experts in a field. It is much faster to just refer to a concept by its name rather than explaining it every time.<p>Unfortunately, definitions are a terrible thing for students. Even more unfortunately, most books are written in the following style:<p>1. Here's a paragraph-long definition that makes no sense to you at this point.<p>2. Here's a proof of this thing you don't yet understand.<p>3. Oh, you want to practice? Here's an example problem and a solution. When you see a problem like this one, plug numbers into this formula in the bold box.<p>4. A bunch more problems to try plugging numbers into yourself.<p>5. The discussion on what this thing is actually useful for is outside the scope of this book. Read about that somewhere else.<p>The best teachers actually explain how the thing they are teaching works. They start with a limited concept the student can understand, and then refine it to make it more formal. Good textbooks do this too. The bad ones start with the definition in a box.<p>The problem is that by the time a professor writes a textbook, this stuff is second nature to them. The prof is an expert. So he/she starts with the definition, since that is how the professor commonly communicates this concept. The book then ends up looking like the author is trying to make him/herself look smart at the expense of the reader. Writing an accessible book is a rare talent.<p>Wow this turned into a long rant :)