Permission to use Online Notes I am a new professor in Mathematics and I am running an independent study on Diophantine equations with a student of mine.  Online I have found a wealth of very helpful expository notes written by other professors, and I would like to use them for guided reading.  I am wondering whether it is customary to ask permission of the author before using his or her online notes for my own reading course. 
Also, if anyone has suggestions for good sources Diophantine Equations please feel free to enlighten me.
 A: Echoing Gerhard Paseman's comment more-or-less: it certainly never hurts to ask permission, or at least to explicitly express interest in use of on-line resources. Some on-line resources have indications of restrictions or lack thereof (e.g., Creative Commons License). In all cases, I think one should acknowledge on-line resources just as one would acknowledge traditional paper-media resources. Credit where credit is due. 
Another point, more practical, is that the on-line versions may get updated, corrected, and revised, while downloaded (or printed) versions will certainly not. Thus, there is the "just in time" ("JIT") mechanism in play for on-line resources, namely, not to download (or print) until the last possible moment.
... and echoing anon, as well.
Edit: The concern about depending upon on-line work that later proves flawed should also be directed at "refereed journal" publications, because many journals nowadays explicitly tell referees that they are not responsible for determining correctness! It is supposedly the author's responsibility! Thus, if there's no scandalous outcome, perhaps no one has seriously attempted to corroborate. 
And, yes, one can argue that things are put on-line to be used. But, still, I think credit should be given, just as with physical books and papers. E.g., just because I've purchased a book doesn't mean I don't owe an intellectual debt to the author, and to the people cited in the book. I think it is completely comparable to say that one should not, by failing to say anything to the contrary, give the impression that ideas one gleaned from someone else's writing are one's own. Being on-line or not does not suspend the rules of responsible, ethical scholarly conduct.
Other discussions in this and other forums have attempted to distinguish "logical dependence" from "acknowledgement of prior art". I have known some otherwise-reputable mathematicians who have explicitly said that since they deliberately avoid looking at other peoples' officially published work, they never have to mention it, perhaps despite having heard informal discussions of it. Or, if there's no logical dependence on someone else's stuff, it doesn't have to be mentioned, supposedly. I realize others will disagree, but I think "prior art" deserves as much mention as anything else. All the other things can be dodged, if one tries hard enough! I think we should respect prior art, as well as noting technical-logical dependence, and I do not think that on-line or not makes much difference in this.
A: The world has changed rapidly with the advent of the web and desktop publishing, so it's going to be difficult to say what is customary. You will probably find that there are generational differences as well as differences between fields and institutions. For example, what is customary at MIT is for professors to put their course materials in OpenCourseware.
It's always been common for a set of lecture notes to be written down, then polished over the years, and eventually transformed into a textbook. That means that the distinction between a textbook and a set of lecture notes has always been fuzzy. However, I think the amount of fuzziness has increased recently, because publication in print no longer has to mark the threshold. Many people go through the whole process of evolution on the web, with no involvement from an editor or the traditional publishing industry.
But to the extent that the distinction between free online lecture notes and a free online textbook is detectable, detecting it may help you to guess what is the most polite and constructive approach.
If it's really a complete, standalone book, then the author has put a lot of effort into making it into a polished product, and will definitely be grateful to hear that the effort is paying off, and that you and your students are using it. With traditional books, the author always knows how many sales s/he's made; with a free online book, s/he doesn't know unless the users take the trouble to make contact.
If it's really a set of lecture notes, then it may be less polished and self-contained. The author may feel that its unfinished state doesn't reflect as well on him/her as he/she would like professionally, and may have only put the notes online with the intention of making them available to his/her own students.
As the author of some free online physics textbooks, I find it a nuisance that there are so many outdated versions of the books sitting on the web. The most recent version is the best and reflects the best on me. For this reason, I'd suggest not mirroring people's notes on your own server, even if they have a Creative Commons license that permits that. If you're concerned that they'll evaporate off of the author's server, just keep a private copy as insurance against that eventuality.
I have a hard time believing that anyone who has posted lecture notes online will be upset that a student studying them prints them out so s/he can read them, highlight them, etc. However, I think many people would be more sensitive about a situation where the notes are being reproduced and sold in a campus bookstore or at a copy shop. Sometimes they'll state their expectations explicitly on the web page. If they choose an explicit license such as a Creative Commons license, then just make sure you don't violate the license.
Solutions to problems can be a sticky point. E.g., if you're thinking of distributing solutions to your students, I would discuss this with the author of the problems. Distributing solutions on paper may be more acceptable than distributing them electronically.
A: The Stanford Copyright & Fair Use Overview is pretty clear about what constitutes fair use in the classroom and what doesn't:

Rules for Reproducing Text Materials for Use in Class
The guidelines permit a teacher to make one copy of any of the following: a chapter from a book; an article from a periodical or newspaper; a short story, short essay, or short poem; a chart, graph, diagram, drawing, cartoon, or picture from a book, periodical, or newspaper.
Teachers may photocopy articles to hand out in class, but the guidelines impose restrictions. Classroom copying cannot be used to replace texts or workbooks used in the classroom. Pupils cannot be charged more than the actual cost of photocopying. The number of copies cannot exceed more than one copy per pupil. And a notice of copyright must be affixed to each copy.
Examples of what can be copied and distributed in class include:
  
  
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*a complete poem if less than 250 words or an excerpt of not more than 250 words from a longer poem
  
*a complete article, story, or essay if less than 2,500 words or an excerpt from any prose work of not more than 1,000 words or 10% of the work, whichever is less; or
  one chart, graph, diagram, drawing, cartoon, or picture per book or per periodical issue.
  
  
  Not more than one short poem, article, story, essay, or two excerpts may be copied from the same author, nor more than three from the same collective work or periodical volume (for example, a magazine or newspaper) during one class term. As a general rule, a teacher has more freedom to copy from newspapers or other periodicals if the copying is related to current events.
The idea to make the copies must come from the teacher, not from school administrators or other higher authority. Only nine instances of such copying for one course during one school term are permitted. In addition, the idea to make copies and their actual classroom use must be so close together in time that it would be unreasonable to expect a timely reply to a permission request. For example, the instructor finds a newsweekly article on capital punishment two days before presenting a lecture on the subject.
Teachers may not photocopy workbooks, texts, standardized tests, or other materials that were created for educational use. The guidelines were not intended to allow teachers to usurp the profits of educational publishers. In other words, educational publishers do not consider it a fair use if the copying provides replacements or substitutes for the purchase of books, reprints, periodicals, tests, workbooks, anthologies, compilations, or collective works.

Note that this does not apply if the work is licensed appropriately. For example, the Stanford Copyright & Fair Use Overview quoted above is licensed CC BY-NC and this answer is licensed CC BY-SA. For course notes, it makes sense to use such a license since that is probably the intended use of the work. Contact the author(s) and recommend that they license their work in a manner they find appropriate.

The Stanford Copyright & Fair Use Overview also has a clear notice regarding online material:

If You Want to Use Material on the Internet
Each day, people post vast quantities of creative material on the Internet -- material that is available for downloading by anyone who has the right computer equipment. Because the information is stored somewhere on an Internet server, it is fixed in a tangible medium and potentially qualifies for copyright protection. Whether it does, in fact, qualify depends on other factors that you would have no way of knowing about, such as when the work was first published (which affects the need for a copyright notice), whether the copyright in the work has been renewed (for works published before 1978), whether the work is a work made for hire (which affects the length of the copyright) and whether the copyright owner intends to dedicate the work to the public domain. If you want to download the material for use in your own work, you should be cautious. It's best to track down the author of the material and ask for permission. Generally, you can claim a fair use right for using a very small portion of text for commentary, scholarship or smilar purposes.

The thing to take away from this is that there is no substitute for proper licensing. If you intend for something to be used in some way or another: make that clear!
A: Rule of thumb: it's OK to print out one copy of online notes for your own private use without requesting permission (that's why they are posted). So if you and your students will each be printing your own copies, there should be no need to request permission. If you are going to print a stack of copies to hand out, or place them in the library, you should probably request permission. 
Some notes say what can be done with them.
Added: to answer your specific question, no, it is not customary. I have several online notes which googling shows are often used in courses. I never get requests for permission, except sometimes when the instructor is planning to print copies and hand them out (or sell them at cost) to the class, or when the notes are to be placed in a library.
A: Yes, asking permission is the right thing to do.  If you don't get it, the right thing to do is to mention the resource to your students, along with the proviso that you do not have permission to copy it, and suggest they do their best not to make or distribute paper or electronic copies beyond viewing it in a browser until after they get permission.
Gerhard "Ask Me About System Design" Paseman,  2012.01.05
