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Do students need books to learn in courses? For example, I found that books often contain some mistakes and therefore it is better for me to study those things on the Internet where I can concentrate on one thing, learn the best knows methods of that subject and then move to the next. Okay, that course wasn't really advanced.

But if you have to decide whether one should write a traditional book or editable lecture notes like in http://stacks.math.columbia.edu/, which one would a lecturer choose?

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    Your question is a bit ambiguous, could you clarify. I'm not sure if you want to compare contributing to stacks.math.columbia.edu/ to writing a text book or if you want to know if you as a student which you should read for a more advanced subject. – richiebful Aug 22 '14 at 20:12
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    Materials on the Internet contain mistakes too. – J W Aug 22 '14 at 20:13
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    I hope you are confident in your ability to separate the wheat from the chaff of those things you find "on the Internet." – Bob Brown Aug 22 '14 at 20:21
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    Well, I study mathematics and thusfar I have managed to prove everything from the axioms. In minor subjects there are things that I don't know but I have used google and forums to find details. – student Aug 22 '14 at 20:29
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    There is a bit of confusion here; do you mean "paper (dead tree) books vs ebooks and online notes", or "all of the above vs browsing randomly on Wikipedia, Planetmath, Google and the like looking for the proof you need"? – Federico Poloni Aug 23 '14 at 11:08
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No, Students don't need a book. They DO need good resources.

Maybe its an eBook or a PDF compiled from your teaching notes or outline/slides (Hopefully cited well) and things like short stories needed for a language class can often be found online in their entirity, for free legally, when copyright has expired.

For a language class, using a Sherlock Holmes story could prevent students from needing to buy a book as they're out of copyright. You can also look for material that is licensed as Creative Commons which allows for free use, such as material from MIT open courseware, Khan Academy, and P2P Univerity. You can learn more about Creative Commons for Education here.

Long story short, make good content, and use it legally, either by using stuff people have given to the public, or under doctrines such as Fair Use.

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To answer your title question--Student do NOT need books, they just need quality resources.

The best option for this will vary depending on the subject, class size and teaching style (the latter more than the former), and the students' learning ability. For example, in a undergrad intro course filled with students of average ability, a standard textbook may be the best option, perhaps supplemented with a few additional resources (links to videos, papers, etc). However, when you are teaching an advanced course, with students who both know how to learn on their own and have some experience with the subject matter, a textbook may still be a good option (depending on your institution's policy, you may be required to assign on for the course), but students will learn more and better if you provide them with primary sources, seminal papers in the field, and thought-provoking position papers, in addition to the textbook.

As for which a lecturer should do,

write a traditional book or editable lecture notes

that will depend on all the above factors, as well as individual talent and motivation. Not all faculty members will necesarily want to write a textbook, though almost all will write lecture ntoes.

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Depends on the class. I've been in classes where the handouts were a book -- a pre-publication version of a textbook that the professor was developing. In those cases, the handouts contained as much detail, and expressed it as clearly, as the final book would -- and luckily these were good instructors AND good writers, so the books were decent ones -- and the chapters were provided sufficiently far in advance of our needing them to permit reading ahead, so I didn't feel a need to consult other textbooks as well.

If any of those requirements is not met -- if the notes cover only the material addressed in the lecture and homework, or if they aren't clear and complete and correct, or if they aren't provided in a more-than-timely manner -- then you probably do need a textbook to back them up.

If in any doubt, you need to specify an alternative textbook or textbooks that students may optionally want to consult (which is good practice even when you do specify a primary text).

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