lower division books like calculus, are chosen by a committee, and a commitment is even made to use it for so many years. I am currently teaching from and complaining about a book, the nth iterate of thomas, by others including hass and maybe finney, that is just terrible. Excelent books are available but considered too hard for todays students, who are often deficient in algebra trig and geometry, plus all forms of formal reasoning.
Upper level books, meaning 4th year, grad level, math major books, or grad degree, even linear algebra and proof theory books, are usually chosen by the professor, who is allowed to choose his/her own books.
I have used my own notes at times, providing them free to the students, as I do some of them to the entire world on my website. Other professors choose to use their own books, but these in my opinion are among the very best books available, both pedagogically and mathematically.
In lower level courses we have been in the position of choosing books by our own faculty, which in my view were not the best books available mathematically on the subject of calculus. But these books are among the very best available for the average audience now taking calculus and were written by our professors with that fact in mind.
These professors do profit from these sales, and deserve to do so. We are free to drop these books at any time, and recently did so in favor of the thomas hass finney book, which unfortunately is greatly inferior to the book by our own former professors.
In graduate level courses the books available are mostly excellent, written by profesionals for people wishing to become professionals. Still they are often too hard for students to read, and hence a new generation of easier books even at the graduate level has become common, e.g. dummit and foote in grad algebra. this is a good book but not an excellent book.
the book by lang used to be standard for grad algebra and that by hungerford was considered second tier. now lang is considered much too hard, the book by hungerford is even considered hard, and that of dummit foote is the default choice many places.
you notice there is a steady tendency downwards, even at the grad level. so this year i found myself criticizing the DF book that I had chosen for the grad algebra course, at the request of some of the students who said they liked it.
At the grad level, for a person like myelf who has a phD but is not a specialist in algebra, to write an algebra book, is considered odd. Even in algebraic geometry which is my speciality, we prefer to sue books not just by algebraic geometers, but by world famous figures at or near the fields medal status, such as those by Mumford, Hartshorne, Shafarevich,...
My notes in most cases consist of the result of reading and teachiong from books by better authors and filling in gaps which I or my students have found troubling, or adding material or expanding where it seems helpful. Some books, even by top authors have errors which it is fun to find and correct.
So my notes contain as much help as I am able to give, and may be easier to read than standard books, but the danger for the student in choosing a book by someone not of top stature is that the insight only a master can give is lost. An author cannot give what he does not have, and only the best see deepest.
since my own research is in riemann surfaces and their jacobians and moduli, theta divisors and their singularities, and torelli theorems, it is only in these areas that i feel qualified to comment knowledgeably. and yet ironically, it was only recently that i learned to appreciate the work of my friend George Kempf on the topic of riemann singularities theorems, done over 30 years ago!
indeed some of my writings on the topic must have puzzled some people, for their naivete, these past three decades. on the other hand i have been part of some research in areas of this question where kempfs ideas did not apply, so there is a good side to trying your best, even in ignorance. I.e. it is possible for someone more knowledgeable to write a more complete book, and yet for someone else less so to do some new research in that very subject. i.e. knowing and doing are different, so there is hope for all of us.
