Sadly, things are not that simple. I see two main points here, and will address them separately. Also, I'm assuming you're in the US, because the law is decidedly different in other places.
*Disclaimer* I am not a lawyer (yet), and you should not rely on my thoughts. If you really want to keep the notes, consult an attorney.
1. IP RIGHTS. Teachers/Professors claiming IP rights in their lecture materials has come up a few times in my recent recollection. The theory is that they own the copyright in the material that they teach and your notes are derivative works. In the US, derivative works belong to the copyright holder, regardless of who did the works. Thus, if you write a song and I do a remix of it, you generally own the remix despite my hard work.
What makes this interesting are a few twists and turns in copyright law:
(a) IDEA-EXPRESSION DICHOTOMY. Copyright only extends to expression, and does not include the idea being expressed. Thus any copyright in your teacher's work does not extend to the underlying concepts. As to whether or not your notes are infringing on your teacher's expression of the ideas is a difficult question, and would be answered by a court.
(b) FIXATION REQUIREMENT. Copyright only applies to things that are fixed. Thus, a concert or dance performance is not copyrightable *unless* they record or otherwise 'fix' the performance. Thus, if your teacher did not fix their work in the form of powerpoint, lecture notes, or something else, it may not be protectable. Again, a question for the court. (Note that your teacher may have copyrightable lecture notes, from which the lecture would be a derivative work, and thus copyrightable.)
(c) WORK MADE FOR HIRE. If your teacher made any copyrightable work in the course of his/her job, it is possible that any copyright belongs to the educational institution. if that is the case, any rights associated with it are the institution's and thus your teacher has no standing to demand anything with respect to the work.
(d) LICENSE. It is possible that as a student you have a license (implied or explicit) to any work by your teacher that allows you to take notes, etc. This is highly case specific, so I cannot comfortably comment further
(e) FAIR USE. Given the educational setting and other circumstances, there is a high likelihood that your notes fall under the fair use exception in copyright. Thus even if your teacher has a full and valid copyright in the lectures, etc., you may be able to take notes nonetheless. (See http://www.copyright.gov/fls/fl102.html for more information.)
2. TAKING YOUR NOTES. Taking the notes from you backpack. Regardless of who owns the IP rights in the notes (see #1), your teacher should not be able to go into your backpack to take them, as that is your private property. If the notes ultimately belong to the teacher, you may be ordered to turn them over by a court. Before that, however, I see no obligation to do so.
My university is phasing in OSX this summer. I've been there watching the endeavour, and its interesting to me. With OS9 they used macadmin, which authenticated to its own password server that sourced from the domain server. Now, everything is LDAP based, which is much easier to configure. The problem is that LDAP is all clear text. So, as I understand it, they had to use kerberos to encode and decode the passwords as they travel around the network. It was a pain in the ass to get working, but in the end it all sources from the same server, and unlike macadin, they dont have to unintstall the password setup to install more software.
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You wrote them? They belong to you.
Sadly, things are not that simple. I see two main points here, and will address them separately. Also, I'm assuming you're in the US, because the law is decidedly different in other places.
*Disclaimer* I am not a lawyer (yet), and you should not rely on my thoughts. If you really want to keep the notes, consult an attorney.
1. IP RIGHTS. Teachers/Professors claiming IP rights in their lecture materials has come up a few times in my recent recollection. The theory is that they own the copyright in the material that they teach and your notes are derivative works. In the US, derivative works belong to the copyright holder, regardless of who did the works. Thus, if you write a song and I do a remix of it, you generally own the remix despite my hard work.
What makes this interesting are a few twists and turns in copyright law:
(a) IDEA-EXPRESSION DICHOTOMY. Copyright only extends to expression, and does not include the idea being expressed. Thus any copyright in your teacher's work does not extend to the underlying concepts. As to whether or not your notes are infringing on your teacher's expression of the ideas is a difficult question, and would be answered by a court.
(b) FIXATION REQUIREMENT. Copyright only applies to things that are fixed. Thus, a concert or dance performance is not copyrightable *unless* they record or otherwise 'fix' the performance. Thus, if your teacher did not fix their work in the form of powerpoint, lecture notes, or something else, it may not be protectable. Again, a question for the court. (Note that your teacher may have copyrightable lecture notes, from which the lecture would be a derivative work, and thus copyrightable.)
(c) WORK MADE FOR HIRE. If your teacher made any copyrightable work in the course of his/her job, it is possible that any copyright belongs to the educational institution. if that is the case, any rights associated with it are the institution's and thus your teacher has no standing to demand anything with respect to the work.
(d) LICENSE. It is possible that as a student you have a license (implied or explicit) to any work by your teacher that allows you to take notes, etc. This is highly case specific, so I cannot comfortably comment further
(e) FAIR USE. Given the educational setting and other circumstances, there is a high likelihood that your notes fall under the fair use exception in copyright. Thus even if your teacher has a full and valid copyright in the lectures, etc., you may be able to take notes nonetheless. (See http://www.copyright.gov/fls/fl102.html for more information.)
2. TAKING YOUR NOTES. Taking the notes from you backpack. Regardless of who owns the IP rights in the notes (see #1), your teacher should not be able to go into your backpack to take them, as that is your private property. If the notes ultimately belong to the teacher, you may be ordered to turn them over by a court. Before that, however, I see no obligation to do so.
My university is phasing in OSX this summer. I've been there watching the endeavour, and its interesting to me. With OS9 they used macadmin, which authenticated to its own password server that sourced from the domain server. Now, everything is LDAP based, which is much easier to configure. The problem is that LDAP is all clear text. So, as I understand it, they had to use kerberos to encode and decode the passwords as they travel around the network. It was a pain in the ass to get working, but in the end it all sources from the same server, and unlike macadin, they dont have to unintstall the password setup to install more software.