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Instructor Contact and General Information

  
Instructor: Luís Finotti
Office: Ayres Hall 251
e-mail: lfinotti@utk.edu
Office Hours: By appointment only, in-person or with Zoom.
Textbook: D. Dummit and R. Foote, Abstract Algebra, 3rd edition, 2003, Wiley. (ERRATA!)
Prerequisites: One year of undergraduate abstract algebra.
Class Meeting Time: MWF 9:10-10:00 at Ayres Hall 111.
Exams: Midterm: 10/16 (Wed) in class, Final: 12/10 (Tue) from 10:30 to 12:30.
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.

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Course Policies

Homework Policy

Homework will be posted regularly in Canvas under Assignments and you will submit a PDF directly thorugh it. The dates will also be available there. On the other hand, you should start working on problems from the sections we've been working on as soon as possible! But roughly, problems from sections we finish during a week will be due in the following Wednesday. The problems that will be assign are below, in Problems Likely to be Assigned.

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.

No late HWs will be accepted, except in extraordinary circumstances which are properly documented.

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.

Ed (Discussion Board)

We will use Ed for online discussions. The advantage of Ed (over other discussion boards) is that it allows us (or simply me) to use math symbols efficiently and with good looking results (unlike Canvas) and to post (and run!) formatted code. It also allows anonymous posts (also unlike Canvas).

Ed also uses Markdown (mostly) and allows the use of LaTeX.

You can access Ed through here: https://edstem.org/us/courses/62178/discussion/. (There is also a link at the “Navigation” section on the top of this page.)

To keep things organized, I’ve set up a few different categories for our discussions:

I urge you to use Ed 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 Ed. Discussion is encouraged here!

Also, please don’t forget to choose the appropriate category for your question. And make sure to choose between Question and Post.

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. If you have a comment, question, or suggestion, you can use the Comment area.

You can also use Ed for Private Posts, by checking the corresponding box. Posts marked as private will be only viewed by the student who posted and me. Only use this what you have to ask cannot be shared with all, e.g., if you are sharing something from your HW. Otherwise, don’t make it private, as other students might have the same questions as you.

You should receive an invitation to join our class in Ed via your “@vols.utk.edu” e-mail address before classes start. If you don’t, you can sign up here: https://edstem.org/us/join/q3HAGu. If you’ve register with a different e-mail (e.g., @tennessee.edu) you do not need to register again, but you can consolidate your different e-mails (like @vols.utk.edu and @tennessee.edu) in Ed, so that it knows it is the same person. (Only if you want to! It is recommended but not required as long as you have access to our course there!) Just click on the Account icon on the top right of Ed, select Emails, and then Add email address.

Communications and E-Mail Policy

You are required to set up notifications for Ed and for Canvas to be sent to you immediately.

On Ed, click on the Account icon on the top left, then Settings. In the new page click on Notifications. Under New Thread Digest, set the drop down box to Instant. I will consider a post in Ed official communication in this course, I will assume all have read every single post there!

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 the profile button on left, under UT’s “T”, 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 Ed, notifications from Canvas, and e-mails) are official communications for this course and it’s your responsibility to check them often!

Feedback

Please, post all comments and suggestions regarding the course using Ed. Usually these should be posted as Post and put in the Feedback category. These can be posted anonymously (or not), just make sure to check the appropriate option. Other 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 Ed (possibly anonymous).

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Conduct

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

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 the Student Code of Conduct and 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!

 

Disabilities

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

 

Reporting Student Concerns

To report conduct violations, academic misconduct, accessibility barriers, among others, visit Rporting Student Concerns (Dean of Students).

Campus Syllabus

Please, see also the Campus Syllabus (Fall 2024).

 

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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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LaTeX

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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Links

   

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Handouts

   

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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 in Canvas.

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/computational ones.

Section 9.2: 4, 12(a-c). Take at look at some of the easy/computational 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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