a book and its audience.

In the spirit of procrastination, earlier I stopped reading a section from Mattila for a moment, and turned the book over. This line caught my eye:

Essentailly self-contained, this book is suitable for graduate students and researchers in mathematics.

Wow. Then I remembered something else, pulled out Evans-Gariepy, and flipped to their preface. It was as I remembered it.

This book is definitely not for beginners. We explicitly assume our readers are at least fairly conversant with both Lebesgue measure and abstract measure theory. The expository style reflects this expectation. We do not offer lengthy heuristics or motivation, but as compensation have tried to present all the technicalities of the proofs: "God is in the details."

It feels like a pleasant difference from the usual disclaimer of many books I've encountered, which would read something like

This book is suitable for beginning graduate students and advanced undergraduates.

I suppose nothing is wrong with such an assessment, except that it damages my ego and my self-esteem. It's the same philosophy with the terms "clear" or "obvious" or "easy," relative to proofs and arguments you see.

If I didn't know any better, I could swear that either (1) many authors underestimate the content of their books, or (2) I'm not as intelligent as I would like to be. Being that my "beginning" years of graduate school are fast ending, the bar of expectation has been raised and it is now a good question whether I can vault over that bar.

---

On a more objective and less self-deprecating note, I wonder how authors determine the "level" of the books they write.

Many books do arise out of lectures from a class taught to graduate students, which explains why the reading level is set for graduate students. The exposition is meant to be organized, and the key results are understood to a level which omits most of the mess from thought experiments and previous endeavors.

In short, many good books are polished. It's easy to read such books and forget that the viewpoint is retrospective, and a generation ago, the path of argument could have been rather confusing and unclear. Unless the choice is deliberate, most books and lecturers may never show you the "wrong paths" that were taken to argue this or that, and depending on relevance and clarity, it's purely a judgment call.

It's like how some authors rewrite history to suit a particular image or ideology: to oversimplify, nations win wars because our side has "just cause" and our enemies are "evil."

In some mathematics books, it feels more like one timeline of reality or possibility is presented: the prevailing and practical one, up to some consensus. It's not so much rewriting history, because there could be alternate realities; we just choose not to study them.

But enough of philosophy. I'm curious to hear what you guys think: how do and how should authors label the "level" of books they write? Should they account for the factors below, or are there missing factors?

• How specialised the topics are, or how obscure a field.
  
• The treatment of the topics, and amount of technical details.
  
• Better sales, varying by the size of the audience

Or could it be there is no good scale?