## Navigation

- Canvas: important announcements, solutions, grades, calendar, etc.
- Piazza: our "Q&A - Math Related" for this course.
- Instructor Contact and General Info:
- Course Description and Information:
- Legal Issues:
- Additional Bibliography
- LaTeX
- Links
- Handouts

## 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!) |

e-mail: |
lfinotti@utk.edu |

Office Hours: |
MW 9am to 10am or by appointment. (Subject to change.) |

Textbook: |
D.A. Marcus "Number Fields", 2nd Edition, 2018. Springer.. |

Prerequisite: |
Math 551/552, Math 651 recommended. |

Class Meeting Time: |
MWF 10:10-11:00 at Ayres 121. |

Exams: |
None! |

Grade: |
HW average, dropping lowest score. |

See here for letter grade ranges. |

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## Course Information

### Course Content

This course is a one-semester introduction to Algebraic Number Theory, a very important branch of mathematics.

### Chapters and Topics

We should cover Chapters 1 to 5 from the textbook. If time allows, we will go as far a possible into Chapters 6 to 8.

### Homework Policy

Homeworks will be posted regularly in Canvas. You will also turn in your HW as PDF file (preferably typed, but scanned is OK) in Canvas.

Every week you will choose yourself two or three problems that you will turn in. You can do problems from our textbook (preferably) or any other book in the listed Additional Bibliography below. If you want to do exercises from another text, please check with me first.

To get an A, a minimum number of correct problems must be turned in by the due date.

If a problem you turn in is too far from correct, you might need to redo it in order to that problem to count towards the necessary number to get an A.

**You also need to turn in your problems by the due
date!** I will allow one delayed HW per student only, unless
there is a compelling reason to allow a second one.

Every time some problems are due, a new assignment will be created on Canvas. (You should receive a notification every time a new assignment is created.) The due date will be usually one week after the assignment was created. (You are always able to see the due dates in the calendar in Canvas.)

Once the HW is graded, you will be able to see your grade and my comments (if any) in Canvas.

**I also urge all to read the material and keep up with the
course!** Even those less interested in the subject
should be prepared enough to follow the lectures! This is
essential to get the bare minimum out of the course!

### 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: https://piazza.com/utk/fall2019/math651/home. (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:

*HW:*Ask*math*question about HW.*Chapter:*Select the chapter of the book to which the question refers.*Class:*Ask questions about something done in class.*Class Structure:*Ask questions about the class, such as "how is the graded computed", "when is the final", etc. in this folder. (Please read the Syllabus first, though!)*Feedback:*Give (possibly anonymous) feedback about the course using this folder.*Other:*In the unlikely event that your question/discussion doesn't fit in any of the above, please use this folder.

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 "@tennessee.edu" e-mail address before classes start. If you don't, you can sign up here: https://piazza.com/utk/fall2019/math651. If you've register with a different e-mail (e.g., @vols.utk.edu) you do not need to register again, but you can consolidate your different e-mails (like @vols.utk.edu and @tennessee.edu) 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!**

### Feedback

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

### Conduct

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 studentâ€™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 alsoHonor 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.

### 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.

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## Additional Bibliography

Here are some other books you might find helpful:

- A. Frohlich and M.J. Taylor, "Algebraic Number Theory", 1st Edition, Cambridge University Press, 1993. An excellent book, but more appropriate for a two-semester course.
- J. Neukirch, "Algebraic Number Theory", 1999. Springer. -- Another excellent book, often used for this sort of courses.
- S. Lang, "Algebraic Number Theory", 2nd Ed., 1994. Springer. -- Perhaps a bit dry, but a good resource.
- Z.I. Borevich and
I.R. Shafarevich. "Number
Theory", 1966. Academic Press.
*Out of print!*-- A classic and excellent book! You can find some scanned copies if you Google it. - J.W.S. Cassels and A. Frohlich
(editors), "Algebraic
Number Theory", 1967. Academic Press.
*Out of print!*-- Another classic! Quite hard to read (it is not quite a textbook), but you learn from the masters: Cassles, Hasse, Serre, Tate, Birch, Swinnerton-Dyer, Atiyah, etc. You can find some scanned copies if you Google it. - W. Stein, "Algebraic
Number Theory - A Computational Approach",
2012.
*Freely available!*-- Also a good book, from which I plan to take some of the computational ideas. - L.J. Goldstein "Analytic
Number Theory", 1971. Prentice Hall.
*Out of print!*-- Despite the title, it would be also a good choice for this course. - J.S. Milne "Algebraic
Number Theory", 2014.
*Freely Available!*-- I am not very familiar with this one, but looks good and his books are indeed usually very good.

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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):

- https://cocalc.com/ (This one is much more than just LaTeX. We will use this one for our meetings.)
- https://www.sharelatex.com/
- https://www.overleaf.com

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:

- Here is a video I've made for Math 506 where I talk about LaTeX and producing documents with it: Introduction to LaTeX and Sage Math Cloud (noting, again, that Sage Math Cloud was the previous name for CoCalc). (Not in great detail, but might be enough to get you started.)
- TUG's Getting Started: some resources, from installation to first uses.
- A LaTeX Primer by D. R. Wilkins: a nice introduction. Here is a PDF version.
- Art of Problem Solving LaTeX resources. A very nice and simple introduction! (Navigate with the links under "LaTeX" bar on top.)
- LaTeX Symbol Lookup: Draw a symbol and the app will try to identify it and give you its LaTeX code.
- LaTeX Wikibook: A lot of information.
- LaTeX Cheat Sheet.
- Cheat Sheet for Math.
- List of LaTeX symbols.
- Comprehensive List of Math Symbols.
- Constructions: a very nice resource for more sophisticated math expressions.

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## Links

- Math 652 (Spring 2016). Another Algebraic Number Theory I taught, but very different (using Frohlich and Taylor's book).
- Some statements in Field/Galois Theory (from Math 552).
- Piazza
- Cocalc: it can be use for computations (using Sage) and LaTeX. I will try to show you some examples of computations in class if we have time.
- UT Knoxville Home
- UTK's Math Department.
- UT Knoxville Home
- UTK's Math Department.
- Services for Current Students and MyUTK (registration, view your grades, etc.).
- Office of the Registrar
- Academic Calendars, including dates for add and drops, other deadlines, final exam dates, etc.
- Hilltopics.
- Students Disability Services
- Office of Equity and Diversity (includes sexual harassment and discrimination).
- My homepage

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## Handouts

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