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(10/11 - 10:15am) About the exam: The exam is Friday and covers up to section 5.2. It will have two prelim-style questions, one worth 40 points and one worth 60 points.
The exam will be delivered to our classroom a little early, so you can have a little more time. It will be an envelope with the questions and separate blank paper for the answer. You can pick up a copy and start on it as soon as they are delivered.
When you are done, put your answers in the same envelope. (Remember to take the questions with you!) Then, either someone will pick up the envelope at around 11:05 or I will ask one of the students to do so and put them in my mailbox. (A little time extension would be OK if the person picking it up is fine with it, but not more than 5 extra minutes.)
There will be no one proctoring the in-class part of the exam. But I will trust you will follow the rules, which are the usual ones: do your own, no talking (of any kind!), no notes, books, or computers, etc. Treat it like you would if I were there. If I find out about any cheating or breaking of the rules, I will do my best to have the person kicked out of our graduate program.
You will also be able to take the questions home and redo or fix problems that you think you could not do well on the exam. (You do not have to turn in a question you think you got 100% right or cannot improve!) You can get at most 50% of the remaining points on the question you redid. (E.g., if you got 20 out 30 in class, if you can get it 100% correct at home, your grade will be increased to 25. E.g., if you got 16 out 30 in class, if you can fix only 50% of what you've missed in class, your grade will be increased to 19.5.)
Note that you will only get credit from what you've done at home for things you haven't already done in class! (E.g., if you got 20 points in class and turn in the same problem from home, you will not get any extra points.) In particular, if you got stuck at some point in class, you can just continue from there at home.
You will turn in the problems on Monday (10/17) at the beginning of the class.
You are to treat these problems as a take-home exam: no talking to anyone about anything on the exam (not even if you think it is easy or hard), no books except Dummit and Foote, no notes except your own, no computers, no Internet search, etc. Again, if I find out you've broke any of these rules, I will do my best to have you kicked out of our graduate program.
Please let me know if you have any questions.
(08/16 - 5:00pm) Please, check this section often. I will put announcements and important info here.
(08/16 - 5:00pm) Please, hit the ``Refresh'' or ``Reload'' button on your web browser every time you visit this page, so that you can see the most recent updates.
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Instructor: Luís Finotti
Office: Ayres Hall 243
Phone: 974-1321 (please do not ask me to call back -- leave your e-mail)
e-mail: lfinotti@utk.edu
Office Hours: Tu,Th 10am-11am or by appointment (subject to change!!)
Textbook: D. Dummit and R. Foote, Abstract Algebra, 3rd edition, 2003, Wiley. (ERRATA!)
Prerequisite: Undergraduate Abstract Algebra.
Class: MWF 10:10-11:00 at Ayres Hall 112. (Section 1.)
Exams: Midterm 10/14 (Wed) in class (+ take home part). Final: 12/07 (Wed) from 8am to 10am, in our regular classroom. (I'd like to change the date if everyone agrees.)
Grade: Roughly: 28% for HW + 27% for the Midterm + 45% for the Final. Note the weight of the HWs! (Since this is a graduate course, there will be more leeway on these weights.)
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Here is the Midterm and the Midterm with solutions.
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Here is the Final and the Final with solutions.
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This is the first course of the graduate sequence in Modern Algebra. We will likely cover topics in Group Theory and Ring Theory in this course, leaving Modules and Field/Galois Theory for the second semester.
The amount to be covered is very large, and thus the pace of the class might be a bit fast. In order to not go too fast, I will assume some background in Groups and Rings. These will be only basic topics that anyone should have seen in an undergraduate algebra course. I might quickly remind you of some of these basic facts, but I might skip some altogether. In this category are included: definitions and basic examples of groups and rings, subgroups and subrings, definitions of normal subgroup and ideal, homomorphisms and isomorphisms, and others. On the other hand, if I skip a fact or definition with which you are not familiar, the students should feel free to stop me and ask about it.
Also, in the same spirit of keeping the pace reasonable, I would like to propose we have extended class time: If all are able, I think it would be to the students advantage to have a one-hour lecture instead of a fifty minute lecture. If all are having classes and/or teaching at Ayres Hall (or nearby), a ten minute interval should be enough to get you to your classes. (We could also try something in between.)
We will likely cover the first two parts of the textbook (leaving the latter two for the second semester). These include the first nine chapters. Some sections might be left out depending on time, some we will go over very quickly, since they should be review, but we will certainly cover all topics required for the prelim. We will also likely cover some topics from the fifth part, such as localization, noetherian/artinian rings and discrete valuation rings.
Homeworks will be posted regularly at the section Homework of this page. No paper copy of the HW assignments will be distributed in class. It is your responsibility to check this page often!. Besides HW assignments, other important information will be posted here. (Check the section Important Notes often!)
Problems likely to be assigned are posted below, but are subject to change. So, you can always start early, even if the assignment is not posted. (Chances of changes are small.)
The HWs will be collected on Wednesdays. Each HW will have problems from the previous week (Monday, Wednesday and Friday lectures). The problems to be turned in, as well as due dates, will be clearly posted here. Note that not all of the problems turned in will be graded, but you won't know which until you get them back. I will also recommend extra problems that you do not have to turn in. On the other hand, I very strongly recommend that you do those problems too!
No late HWs will be accepted, except in extraordinary circumstances which are properly documented.
It is your responsibility to keep all your graded HWs and Midterms! It is very important to have them in case there is any problem with your grade.
I will do my best to post solutions. If I do, they will be posted in this page. If I do not and you have a question, you can come talk to me.
In my opinion, doing the HW is one of the most important parts of the learning process, so the weight for them is equal to the weight of a single midterm, and I will assume that you will work very hard on them.
Also, you should try to come to my office hours if you are having difficulties with the course. I will do my best to help you. Please try to come during my scheduled office hours, but feel free to make an appointment if that would be impossible.
You will have to check your e-mail at least once a week, preferably daily. I will use your UT e-mail (from Blackboard) to make announcements. I will assume that any message that I sent via e-mail will be read in a week or less, and it will be considered an official communication.
I have an On-line Feedback Form where you can anonymously send me your comments and suggestions. I will consider your comments and try to do whatever I can to resolve possible problems before it is too late. So, please, feel free to use it whenever you have any constructive comment or suggestion. (In fact, I would greatly appreciate it.) If you don't want you comments to be anonymous, just send me an e-mail or come by my office and we can discuss the problem.
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Here are some other books you might find helpful:
Here are some which are more on the level of undergraduate algebra:
The first two books are considered ``easier'' books. The Artin's book is of a bit higher level (and has a slightly different focus).
The last one is a ``standard'' text for a first course in abstract algebra, but have a higher level of difficulty than the previous two. It's been used for the honors section of the undergraduate algebra course here at UT, and it might be even on the level of a graduate course.
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Academic Integrity
Study, preparation and presentation should involve at all times the student's own work, unless it has been clearly specified that work is to be a team effort. Academic hon- esty requires that the student present his or her own work in all academic projects, including tests, papers, homework, and class presentation. When incorporating the work of other scholars and writers into a project, the student must accurately cite the source of that work. (See Academic Standards of Conduct, pg. 12.)
All students should follow the Honor Statement: from Hilltopics 2011/2012, pg. 12:
Honor Statement
``An essential feature of The University of Tennessee is a commitment to maintaining an atmosphere of intellectual integrity and academic honesty. As a student of the University, I pledge that I will neither knowingly give nor receive any inappropriate assistance in academic work, thus affirming my own personal commitment to honor and integrity.''
You should also be familiar with the Classroom Behavior Expectations.
Students with disabilities that need special accommodations should contact the Office of Disability Services and bring me the appropriate letter/forms.
For Sexual Harassment and Discrimination information, please visit the Office of Equity and Diversity.
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Wednesday, August 17 - Classes begin.
Friday, August 26 - Last day to add, change grade options, or drop a full semester course without a "W".
Monday, September 05 - Labor Day Holiday. (No class.)
Thursday-Friday, September 29-30 - Fall Break. (No class.)
Friday, October 14 - Midterm.
Tuesday, November 08 - Last day to drop a full term course with a "W".
Thursday-Friday, November 24-25 - Thanksgiving. (No class.)
Tuesday, November 29 - Last Class Day.
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Please read: I will try to post here a few solutions. The new solutions will be added to this same file.
Disclaimer: I will have to put these solutions together rather quickly, so they are subject to typos and conceptual mistakes. (I expect you to be a lot more careful when doing your HW than I when preparing these.) You can contact me if you think that there is something wrong and I will fix the file if you are correct.
Solutions to Selected HW Problems (Click on ``Refresh'' or ``Reload'' if you don't see the changes!)
CHANGE LOG:
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This list is subject to change without prior notice. The official assignments will be posted below.
Section 1.7: 8, 11, 14, 15, 18, 19, 21, 23.
Section 2.1: 4, 5 (you cannot use Lagrange's Theorem), 14.
Section 2.2: 1, 2, 4, 7, 10, 12(b), (d), (e).
Section 2.3: 1, 8, 9, 11, 12, 16, 23 (use 22 without proof).
Section 2.4: 2, 3, 7, 10, 14(c-d), 15, 19.
Section 3.1: 1, 3, 9, 14, 21, 28 (use 27 without proof), 29, 41.
Section 3.2: 4, 10, 11, 14, 18, 19, 21.
Section 3.3: 1, 3, 7, 10.
Section 3.4: 2, 4, 5, 7, 10.
Section 3.5: 3, 4, 9, 12.
Section 4.1: 1, 7(a-d), 9.
Section 4.2: 11, 12, 13.
Section 4.3: 1, 2, 26, 27, 29, 30.
Section 4.4: 8(b-c), 13, 14, 18, 20 (you can skip the QD_16 group).
Section 4.5: 2, 12, 15, 16, 17, 22, 25, 27, 32, 33, 36, 44.
Section 4.6: 1, 2, 3, 4.
Section 5.1: Just browse to see the problems.
Section 5.2: 2, 3, 5, 6, 9.
Section 5.4: 4, 5, 11.
Section 5.5: 1, 2, 6, 8, 18, 20, 21, 24.
Section 6.1: 3, 4, 7, 9, 10, 12, 21, 25.
Section 6.3: 1, 3, 11.
Section 7.1: 3, 8, 13, 14, 15, 23, 25(c). Also, take a look at others. Many should be quite easy.
Section 7.2: 3, 4, 5, 10.
Section 7.3: 3, 5, 8, 13, 17, 22, 24, 26, 29, 34(c-d).
Section 7.4: 2, 10, 11, 13, 15, 16, 19, 25, 36, 38, 39, 40, 41.
Section 7.5: 4, 5, 6.
Section 15.4: 21, 22, 23.
Section 7.6: 1, 3, 5(b-c), 7.
Section 8.1: 1, 2, 3, 4, 8(a), 10, 11.
Section 8.2: 3, 6, 8.
Section 8.3: 5(a-c), 9, 11.
Section 9.1: 8, 17. Take at look at some of the easy/compuational ones.
Section 9.2: 4, 12(a-c). Take at look at some of the easy/compuational ones.
Section 9.3: 1, 2, 4(a-d).
Section 9.4: 3, 4, 12. Also look at the easy/computational ones, such as 1, 2, 9, 10, 11, 18.
Section 9.5: 7. Take at look at the others.
Section 9.6: 1.
Section 15.1: 1, 2, 4.
Section 16.1: 2, 3, 4.
Section 16.2: 1, 3, 4.
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HW1 - Due on Wednesday 08/24:
Read sections 1.1 to 1.6. (This should be a review.) You don't have to turn in any problems from those sections, but I recommend you try a few to make sure you still remember that material.
Section 1.7: Turn in: 19, 21. Do not turn in: 8, 11, 14, 15, 18, 23.
HW2 - Due on Wednesday 08/31:
Section 2.1: Turn in: 5 (you cannot use Lagrange's Theorem). Do not turn in: 4, 14.
Section 2.2: Turn in: 10. Do not turn in: 1, 2, 4, 7, 12(b), (d), (e).
Section 2.3: Turn in: 16. Do not turn in: 1, 8, 9, 11, 12, 23 (use 22 without proof).
Section 2.4: Turn in: 15. Do not turn in: 2, 3, 7, 10, 14(c-d), 19.
HW3 - Due on Wednesday 09/07:
Section 3.1: Turn in: 14. Do not turn in: 1, 3, 9, 21, 28 (use 27 without proof), 29, 41.
Section 3.2: Turn in: 4, 19. Do not turn in: 10, 11, 14, 18, 21.
HW4 - Due on Wednesday 09/14:
Section 3.3: Turn in: 1, 3, 10.
HW5 - Due on Wednesday 09/21:
Section 3.4: Turn in: 4, 10. Do not turn in: 2, 5, 7, 9.
Section 3.5: Turn in: 12. Do not turn in: 3, 4, 9.
Section 4.1: Turn in:7(d), 9. Do not turn in: 1, 7(a)-(c).
Section 4.2: Turn in: 11. Do not turn in: 12, 13.HW6 - Due on Wednesday 09/28:
Section 4.3: Turn in: 26, 30. Do not turn in: 1, 2, 27, 29.
HW7 - Due on Wednesday 10/05:
Section 4.4: Turn in: 8(b-c), 13, 18(a), (d). Do not turn in: 14, 18(b), (c), 20 (you can skip the QD_16 group)
HW8 - Due on Wednesday 10/12:
Section 4.5: Turn in: 17, 25, 44. Do not turn in: 15, 16, 22, 27.
Section 4.6: Turn in: 2, 3. Do not turn in: 1, 4.
Section 5.1: Just browse to see the problems.
HW9 - Due on Wednesday 10/19:
Section 5.2: Turn in: 5, 6. Do not turn in: 2, 3, 9.
Section 5.4: Turn in: 5. Do not turn in: 4, 11.
HW10 - Due on Wednesday 10/26:
Section 5.5: Turn in: 6, 8, 20, 24. Do not turn in: 1, 2, 18, 21.
HW11 - Due on Wednesday 11/02:
Section 6.1: Turn in: 9, 21. Do not turn in: 3, 4, 7, 10, 12, 25.
Section 6.3: Do not turn in: 1, 3, 11.
Section 7.1: Turn in: 23. Do not turn in: 3, 8, 13, 14, 15, 25(c). Also, take a look at others. Many should be quite easy.
Section 7.2: Turn in: 5. Do not turn in: 3, 4, 10.
HW12 - Due on Wednesday 11/09:
Section 7.3: Turn in: 13, 17, 29, 34(d). Do not turn in: 3, 5, 8, 22, 24, 26, 34(c).
Section 7.4: Turn in: 13, 25. Do not turn in: 2, 10, 11, 15, 16, 19.
HW13 - Due on Wednesday 11/16:
Section 7.5: Turn in: 5, 6. Do not turn in: 4.
Section 15.4: Turn in: 22. Do not turn in: 21, 23.
HW14 - Not to be turned in (practice for the final):
Section 7.6: 1, 3, 5(b-c), 7.
Section 8.1: 1, 2, 3, 4, 8(a), 10, 11.
Section 8.2: 3, 6, 8.
Section 8.3: 5(a-c), 9, 11.
Section 9.1: 8, 17. Take at look at some of the easy/compuational ones.
Section 9.2: 4, 12(a-c). Take at look at some of the easy/compuational ones.
Section 9.3: 1, 2, 4(a-d).
Section 9.3: 1, 2, 4(a-d).
Section 9.4: 3, 4, 12. Also look at the easy/computational ones, such as 1, 2, 9, 10, 11, 18.
Section 9.5: 7. Take at look at the others.
Section 9.6: 1.
Section 15.1: 1, 2, 4.
That's all!
PLEASE, HIT ``REFRESH'' (OR ``RELOAD'') IN YOUR BROWSER WHEN VISITING THIS PAGE!!!!!!! I usually get messages asking for the update in the HW when it has already been updated. Since I change this page often, some times the browser don't see the changes. But, if you hit refresh and there is still problems missing, feel free to write me.
If it is already Friday afternoon and there still is a ``More to come'' after the HW assignment due on the coming Wednesday, write me an e-mail at lfinotti@utk.edu, and I'll update it and let you know.
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