Math 555: Number Theory I - Fall 2008

Math 555: Number Theory I - Fall 2008



Important Notes


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Instructor Contact and General Information


Instructor: Luís Finotti

Office: Ayres Hall 212-D

Phone: 974-1321 (please do not ask me to call back -- leave your e-mail)


Office Hours: MW 11:00am-12:00pm or by appointment (subject to change!!)


Textbook: K. Ireland and M. Rosen, ``A Classical Introduction to Modern Number Theory'', 2nd Edition, 1990, Springer.

Prerequisite: One year of undergraduate abstract algebra (recommended).

Class: TTh 11:10-12:25 at Ayres Hall 309B. (Section 1.)

Exams: Midterm: 10/14 (Tue); Final: 12/09 (Tue) from 10:15am to 12:15pm.

Grade: 30% for HW + 30% for the Midterm + 40% for the Final. Note the weight of the HWs!


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Course Information

Course Description

This will be an introductory course in number theory. Very little background will be assumed, but you should be familiar with groups, rings, and fields at the undergraduate level. On the other hand, the course will tailored to the students. Depending on the background of the audience, we will be able to cover more or even different topics. In particular, the knowledge of Galois Theory would be beneficial, but it will not be assumed. Also, some knowledge of basic real and complex analysis will be assumed, again on an undergraduate level, but I will give more details on those if needed.

We will start with very basic topics, such as factorization and congruences. I hope, depending on the audience, to move along those rather quickly, so that we can get to the more interesting parts soon, such as quadratic reciprocity, Gauss and Jacobi sums, equations over finite fields, and zeta function (for varieties over finite fields).

Course Structure

As stated above, I will try to tailor the course to the students. This makes it harder to have a very precise plan, but here is what I hope to cover:

This might be too ambitious. I might skip a few sections in between, or just give an overview in some cases. I find it difficult to really choose much here, as the topics are all very interesting to me, and I am eager to cover them all. But I will try to keep my enthusiasm from overloading you, and you should help me with that.


Homeworks will be assigned after every class and will be posted 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!)

The HWs will be collected on Thursdays. Each HW will have problems from the previous week (Tuesday and Thursday lectures). The problems to be turned in, as well as due dates, will be clearly posted here. I will suggest a few problems and ask you to turn in two or three problems a week.

It's unlikely I will post solutions, but if you want to see some solution, you can come see me.

In my opinion, doing the HW is one of the most important parts of the learning process, so the weight for them is the same as the weight of the 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.

Finally, 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. You can check all your scores at Blackboard. (Blackboard will be used only for scores. This is the official site for the course.)


You will have to check your e-mail at least once a week, preferably daily. I will use your e-mail (given to me by the registrar's office) to make announcements. If that is not your preferred address, write me an e-mail letting me know ASAP. 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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Additional Bibliography

There are many good books in number theory. Not all cover all the topics covered by our text. The best source of alternative bibliography is Ireland and Rosen's book itself. At the end of each section it gives references to other texts. In any case, here are a few standard books:


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Legal Issues


All students should be familiar and maintain their Academic Integrity: from
Hilltopics 2008/2009, pg. 40:

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 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.

All students should follow the Honor Statement: from Hilltopics 2008/2009, pg. 11:

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.

Sexual Harassment and Discrimination

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

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Important dates:


Wednesday, August 20 - Classes begin.

Friday, August 29 - Last day to add, change grade options, or drop a full semester course without a "W".

Monday, September 01 - Labor Day Holiday. (No class.)

Thursday-Friday, October 09-10 - Fall Break. (No class.)

Tuesday, October 14 - Midterm.

Tuesday, October 21 - Last day to drop a full term course with a "W".

Tuesday, November 11 - Last day to drop with a WP/WF.

Thursday-Friday, November 27-28 - Thanksgiving. (No class.)

Tuesday, December 02 - Last Class Day.

Tuesday, December 09 - Final.


More dates.


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HW1 - Due on Thursday 09/04:

Chapter 1: Do NOT turn in: take a look at all problems. Turn in: 12, 30.

Chapter 2: Do NOT turn in: 1 to 9. Turn in: 10.


HW2 - Due on Thursday 09/11:

Chapter 2: Do NOT turn in: 11 to 27. Turn in: 21, 27.


HW3 - Due on Thursday 09/18:

Chapter 3: 11, 15 (note that the last term is 1/(p-1)), 17. (As usual, also take a look at all others.)


HW4 - Due on Thursday 09/25:

Chapter 4: 5, 11, 22. (As usual, also take a look at all others.)


HW5 - Due on Thursday 10/02:

Chapter 5: 10, 11 ("quadratic character" here means Legendre symbol). (Take a look at all others from 1 to 12.)


HW6 - Due on Thursday 10/16:

Chapter 5: 26, 27, 28. (Take a look at all others from 13 to the end.)


HW7 - Due on Thursday 10/30 (no HW due on 10/23):

Chapter 6: 3, 8, 15. (Take a look at all others.)


HW8 - Due on Thursday 11/06:

Chapter 7: 4, 5, 9. (Also do 3, but do not turn it in, and take a look at all others.)


HW9 - Due on Tuesday 11/25 (no HW due on 11/13 or 11/20!):

Chapter 8: 8, 15, 26.


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 Monday, write me an e-mail at, and I'll update it and let you know.


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