Instructor Contact and General Information

Instructor: Luís Finotti
Office: Ayres Hall 251
Phone: 974-1321 (don't leave messages! -- e-mail me if I don't answer!)
Office Hours: MW from 11:10 to 12:10, or by appointment.
Textbook: D. Dummit and R. Foote, Abstract Algebra, 3rd edition, 2003, Wiley. (ERRATA!)
Prerequisite: One year of undergraduate abstract algebra.
Class Meeting Time: MWF 10:10-11 at Ayres 112.
Exams: Midterm: 10/15 (Monday) during class.
Final: 12/10 (Monday) from 10:15am to 12:15pm.
Grade: 20% for HW, 30% for the Midterm, 50% for the Final.
See here for letter grade ranges.

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Course Information

Course Content

This is the first course of the graduate sequence in Abstract Algebra. We will likely cover topics in Group Theory and Ring Theory in this course, leaving Modules and Fields/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.

To be more precise, the following sections from our textbook, will be either assumed (and skipped) or only partially covered or reviewed:

On the other hand, if I skip a fact or definition with which you are not familiar, you should feel free to stop me and ask about it.


Chapters and Topics

We should cover Chapters 1 to 9 of the textbook (skipping the sections mentioned above), except for Chapter 6, of which we will only cover 6.1 (and maybe 6.3). We will also skip Gröbner basis in section 9.6.

We should also cover parts of sections 15.1-4 and 16.1-2.

Other topics (and digressions) might also be squeezed in as time allows.


Homework Policy

Homework 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!. I will try to also add the due dates to Canvas's Calendar, but this page has the official assignment (and due dates).

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, especially if you plan to take the Algebra Prelim.

Problems likely to be assigned are posted below, and so, although they are subject to change, it is not likely it will happen often. So, you can always start working on the HW early, even if the assignment is not posted.

Note that I might sometimes get too ambitious in posting problems, i.e., I might think we will cover a section during the week, put exercises from it in the next assignment, and then end up not being able to finish it. In this case I might have to take a few problems off the assignment. The bottom line is the following: the assignment is not final until I remove the "More to come" from it. (If you've done problems which were removed, just saved them for the following week.)

Finally, if there is still a "More to come" in an assignment on a Friday, please write me right away so that I can update it. If I delay in replying, you can proceed with the Problems Likely To Be Assigned.

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 Canvas. 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 I will assume that you will (and urge you to) 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.


Piazza (Discussion Board)

We will use Piazza for discussions. The advantage of Piazza is that it allows us (or simply me) to use math symbols efficiently and with good looking results (unlike Canvas).

To enter math, you can use LaTeX code. (See the section on LaTeX below.) The only difference is that you must surround the math code with double dollar signs ($$) instead of single ones ($). Even if you don't take advantage of this, I can use it, making it easier for you to read the answers.

You can access Piazza through the link on top of this page or directly here: (There is also a link at the Links section.)

To keep things organized, I've set up a few different folders/labels for our discussions:

Note you can use more than one label per post.

I urge you to use Piazza often for discussions! (This is specially true for Feedback!) If you are ever thinking of sending me an e-mail, think first if it could be posted there. That way my answer might help others that have the same questions as you and will be always available to all. (Of course, if it is something personal (such as your grades), you should e-mail me instead.)

Note that you can post anonymously. (Just be careful to check the proper box!) But please don't post anonymously if you don't feel compelled to, as it would help me to know you, individually, much better.

Students can (and should!) reply to and comment on posts on Piazza. Discussion is encouraged here!

Also, please don't forget to choose the appropriate folder(s) (you can choose more than one, like a label) for your question. And make sure to choose between Question, Note or Poll.

When replying/commenting/contributing to a discussion, please do so in the appropriate place. If it is an answer to the question, use the Answer area. (Note: The answer area for students can be edited by other students. The idea is to be a collaborative answer. Only one answer will be presented for students and one from the instructor. So, if you want to contribute to answer already posted, just edited it.) You can also post a Follow Up discussion instead of (or besides) an answer. There can be multiple follow ups, but don't start a new one if it is the same discussion.

Important: Make sure you set your "Notifications Settings" on Piazza to receive notifications for all posts: Click on the gear on the top right of the Piazza site, the choose "Account/Email Setting", then "Edit Email Notifications" and then check "Automatically follow every question and note". Preferably, also set "Real Time" for both new and updates to questions and notes. I will consider a post in Piazza official communication in this course, I will assume all have read every single post there!

You can also use Piazza for Private Messages. I'd prefer you use e-mail to talk to me, unless it is a math question (in which either you or I would need to enter math symbols) that cannot be posted for all (such as an exam question). You can also send private messages to fellow students, but keep in mind that I can see those too! (So, not really that private...)

You should receive an invitation to join our class in Piazza via your "" e-mail address before classes start. If you don't, you can sign up here: If you've register with a different e-mail (e.g., you do not need to register again, but you can consolidate your different e-mails (like and in Piazza, so that it knows it is the same person. (Only if you want to! It is not required as long as you have access to our course there!) Just click on the gear icon on the top right of Piazza, beside your name, and select "Account/Email Settings". Then, in "Other Emails" add the new ones.

Important: Please do not use Piazza for math questions if you can come see me in person (especially during office hours). You will benefit much more if you come see me! A five minute conversation will be much more productive that a half-hour exchange in Piazza.


Communications and E-Mail Policy

You are required to set up notifications for Piazza (as explained above) and for Canvas to be sent to you immediately. For Canvas, check this page and/or this video on how to set your notifications. Set notifications for Announcements to "right away"! (Basically: click on the Account button on the top left, then click "Notifications". Click on the check mark ("notify me right away") for Announcements.)

Moreover, I may send e-mails with important information directly to you. I will use the e-mail given to me by the registrar and set up automatically in Canvas. (If that is not your preferred address, please make sure to forward your university e-mail to it!)

All three (notifications from Piazza, notifications from Canvas and e-mails) are official communications for this course and it's your responsibility to check them often!



Please, post all comments and suggestions regarding the course using Piazza. Usually these should be posted as Notes and put in the Feedback folder/label (and add other labels if relevant). These can be posted anonymously (or not), just make sure to check the appropriate option. Others students and myself will be able to respond and comment. If you prefer to keep the conversation private (between us), you can send me an e-mail (not anonymous), or a private message in Piazza (possibly anonymous).


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Legal Issues


All students should be familiar with Hilltopics' Students Code of Conduct and maintain their Academic Integrity: from Hilltopics Academics:

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 honesty requires that the student present their 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. For additional information see the applicable catalog or the UT Libraries site. See also Honor Statement (below).

All students should follow the Honor Statement (also from Hilltopics Academics):

Honor Statement

"An essential feature of the University of Tennessee, Knoxville, 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.

We are in a honor system in this course!



Students with disabilities that need special accommodations should contact the Student Disability Services and bring me the appropriate letter/forms.


Sexual Harassment and Discrimination

For Sexual Harassment and Discrimination information, please visit the Office of Equity and Diversity.


Campus Syllabus

Please, see also the Campus Syllabus.


Additional Bibliography

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 in some parts.


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This is not necessary to our class! I leave it here in case someone wants to learn how type math, for instance to type their HW. But again, you can ignore this section if you want to.

LaTeX is the most used software to produce mathematics texts. It is quite powerful and the final result is, when properly used, outstanding! Virtually all professional math text you will ever see is done with LaTeX, or one of its variants.

LaTeX is available for all platforms and freely available.

The problem is that it has a steep learning curve at first, but after the first difficulties are overcome, it is not bad at all.

One of the first difficulties one encounters is that it is not WYSIWYG ("what you see is what you get"). It resembles a programming language: you first type some code and then this code is processed to produce a nice document (a non-editable PDF file, for example). Thus, one has to learn how to "code" in LaTeX, but this brings many benefits.

I recommend that anyone with any serious interest in producing math texts to learn it! On the other hand, I don't expect all of you to do so. But note that there are processors that can make it "easier" to create LaTeX documents, by making it "point-and-click" and (somewhat) WYSIWYG.

Here are some that you can use online (no need to install anything and files are available online, but you do need to register):

We will use the first one, CoCalc in our course, so you have to register for it, and thus might as well use it. It is probably the best of the services anyway, and it can do a lot more than just LaTeX. You should have received, by the first day of classes, an invitation to collaborate on a project that I've created for this course (Math 504 -- Summer 2018).

If you want to install LaTeX in your computer (so that you don't need an Internet connection), check here.

I might need to use some LaTeX symbols when writing in our online meetings, but it should be relatively easy to follow. I will also provide samples and templates that should make it much easier for you to start.

A few resources:


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Problems Likely To Be Assigned

The ones below (Sections 1.7 to 3.3) are for review only and will not be assigned to be turned in!

Section 1.7: 8, 11, 14, 15, 18, 19, 21, 23.

Section 2.1: 4, 5 (you cannot use Lagrange's Theorem), 14. (These are for review only and will not be assigned to be turned in!)

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.


This list is subject to change without prior notice. The official assignments will be posted below.

Section 3.4: 2, 4, 5, 7, 9, 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, 17, 19, 23, 24, 25, 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 09/12:

Section 3.4: Turn in: 4, 7, 9. Do not turn in: 2, 5, 10.

Section 3.5: Turn in: 12. Do not turn in: 3, 4, 9.

Section 4.1: Turn in: 9. Do not turn in: 1, 7(a-d).


HW2 - Due on Wednesday 09/19:

Section 4.2: 11.

Section 4.3: 17, 27.


HW3 - Due on Wednesday 09/26:

Section 4.4: 12.

Section 4.5: 22, 33, 44.


HW4 - Due on Wednesday 10/03:

Section 4.6: 3, 4.

Section 5.2: 5.

Section 5.4: 5.


HW5 - Due on Wednesday 10/10:

Section 5.5: 6, 8, 18.


HW6 - Due on Wednesday 11/07:

Section 7.4: 25, 39.

Section 7.5: 5.


HW7 - Due on Wednesday 11/14:

Section 15.4: 22.

Section 7.6: 1, 7.


HW8 - Due on Wednesday 11/28:

Section 9.1: 10.

Section 9.2: 12.

Section 9.3: 4.

Section 9.4: 4.


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, and I'll update it and let you know.


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