Math 555: Number Theory I - Fall 2010

Math 555: Number Theory I - Fall 2010



Important Notes


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Instructor Contact and General Information


Instructor: Luís Finotti

Office: Aconda Court 211-H

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


Office Hours: T,Th 10am-11am 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 HBB 132. (Section 1.)

Grade: Your grade will be your HW average.


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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 be 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 for the second semester, 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 much 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).

In fact, we have a few options. We could deal with more computational aspects, cryptography, analytic number theory... It depends on the interest of the class. The default will be to sample a little of everything.

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 the default:

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 ``due'' on Thursdays. Each HW will have problems from the previous week (Tuesday and Thursday lectures). I will not be very strict on dates, but I do not want you to turn in all your homework on the last day! I will also suggest a few problems, but you have the freedom to choose the ones you intend to do. As long as you turn in two to three (three if you choose really easy ones, please) a week, you should be fine. (Assuming you are getting most of the problems right.)

Of course, you get out what you put in, so students interested in algebra and number theory should at least try to do the harder problems, even if you do not turn them in. You are always welcome to come discuss problems with me.

In any event, no matter what you turn in, you should take a look at all exercises, as you will find interesting results and applications there. Sometimes we might need some results that were exercises from previous sections.

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

Besides HW, I would urge you to review the material often! I really don't want students to get lost in class, by forgetting theorems and definitions. Most of all, I want you to be able to follow the lectures! Of course, one way to make yourself keep up is to work on problems often, so try to not let your HWs be late often.

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.

I will keep all your HW 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, please make sure to forward your university e-mail to it!) 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 2010/2011, pg. 41:

Academic Integrity

The university expects that all academic work will provide an honest reflection of the knowledge and abilities of both students and faculty. Cheating, plagiarism, fabrication of data, providing unauthorized help, and other acts of academic dishonesty are abhorrent to the purposes for which the university exists. In support of its commitment to academic integrity, the university has adopted an Honor Statement.

All students should follow the Honor Statement: from Hilltopics 2010/2011, 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 18 - Classes begin.

Friday, August 27 - Last day to add, change grade options, or drop a full semester course without a "W".

Monday, September 06 - Labor Day Holiday. (No class.)

Thursday-Friday, October 07-08 - Fall Break. (No class.)

Tuesday, October 19 - Last day to drop a full term course with a "W".

Tuesday, November 10 - Last day to drop with a WP/WF.

Thursday-Friday, November 25-26 - Thanksgiving. (No class.)

Tuesday, November 30 - Last Class Day.  

More dates.


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HW1 - ``Due'' on Thursday 09/02:

Chapter 1: Choose 2 or 3. (If you want suggestions: 12, 30, 38.)


HW2 - ``Due'' on Thursday 09/09:

Chapter 2: Choose 2 or 3. (If you want suggestions: choose 2 or 3 from 13, 21, 26, 27.)


HW3 - ``Due'' on Thursday 09/16:

Choose 2 or 3 more problems from Chapters 1 and 2.


HW4 - ``Due'' on Thursday 09/23:

Chapter 3: Choose 2 or 3. (If you want suggestions: choose 2 or 3 from 11, 15 (note that the last term is 1/(p-1)), 17, 23, 25, 26.)


HW5 - Due on Thursday 09/30:

Chapter 4: Choose 2 or 3. (If you want suggestions: 5, 11, 22.)


HW6 - Due on Thursday 10/21:

Chapter 5: Choose 2 or 3. (There are too many good problems in this section. If you really want suggestions: 26, 27, 28.)


HW7 - Due on Thursday 10/28:

Chapter 5: Choose another 2 or 3.


HW8 - Due on Thursday 11/11 (note the date):

Chapter 6: Choose 2 or 3 from 1 to 8. (If you want suggestions: 3, 7, 8.)


HW9 - Due on Thursday 11/18:

Chapter 6: Choose another 2 or 3 from 9 to 28.


HW10 - Due on Tuesday 11/23:

Chapter 7: Choose another 2 or 3. (If you want suggestions: 7, 14, 15, 17.)


And 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 Thursday afternoon and there still is a ``More to come'' after the HW assignment due on the coming week, write me an e-mail at, and I'll update it and let you know.


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