Math 659: Introduction to p-Adics - Spring 2013

Math 659: Introduction to p-Adics - Spring 2013



Important Notes


Back to the TOP.

Instructor Contact and General Information


Instructor: Luís Finotti

Office: Ayres Hall 243

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


Office Hours: M, W 10am-11am or by appointment (subject to change!!)


Textbook: F. Q. Gouvêa, p-Adic Numbers: An Introduction, 2nd edition, Springer, 1997.

Prerequisite: Math 551/552 or equivalent.

Class: MWF 1:25-2:15 at Ayres Hall 114. (Section 3.)

Exams: No exams.

Grade: HW only. Getting most of the problems right would give an A.


Back to the TOP.

Course Information:

This is the first course of the graduate sequence in p-Adic Numbers. p-Adic numbers are an important part of number theory and an important example of DVRs in Algebra.

Course Structure

We will try to cover as much as we can from the text book. We might add a full proof of Hasse-Minkowski Theorem and perhaps something on Witt vectors.


Homeworks will be posted regularly at the section Homework of this page. You will choose three problems (or two, if the problems are longer/harder/have multiple parts) from the list given to turn in every week (or whenever the due date specifies it). Note that 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!)

Although I won't be able to grade more than three problems a week, I strongly recommend those interested in the area to do more problems (preferably all). Of course, you get out of this course 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.

The HWs will be collected on Wednesdays. I will accept an eventually late HW, but it should not become the norm. (You maybe late only once or twice during the semester!) Failure to turn in HWs will effectively affect your grade.

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.)


I will assume you check your e-mail at least once a day. 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 less than twenty four hours, 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.


Back to the TOP.

Additional Bibliography

Here are some other books you might find helpful:


Back to the TOP.

Legal Issues


All students should be familiar and maintain their Academic Integrity: from
Hilltopics 2012/2013, pg. 46:

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 2012/2013, pg. 16:

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.

Campus Syllabus

Please, see also the Campus Syllabus.


Back to the TOP.



Back to the TOP.



Back to the TOP.



HW1 - Due on Wednesday 01/23:

Read Section 1.1. I will go over a few things from Sections 1.2 and 1.3 in class, but not from 1.1.

Problems: choose two problems from section 1.1.


HW2 - Due on Wednesday 01/30:

Problems: choose three (or two if long or multiple parts) problems from sections 1.2, 1.3 and 2.1.


HW3 - Due on Wednesday 02/06:

Problems: choose three (or two if long or multiple parts) problems from sections 2.2, 2.3 and 2.4.


HW4 - Due on Wednesday 02/13:

Problems: choose three (or two if long or multiple parts) problems from sections 3.1, 3.2 and 3.3. (Note that 3.2 was not really covered in class. You can skip problems from there or not, as you wish.)


HW5 - Due on Wednesday 02/27 (no HW due on 02/20, but you can start on problems from 3.4):

Problems: choose three (or two if long or multiple parts) problems from sections 3.4, 3.5 and 4.1.


HW6 - Due on Wednesday 03/06:

Problems: choose three (or two if long or multiple parts) problems from sections 4.2 and 4.3.


HW7 - Due on Wednesday 03/13:

Problems: choose three (or two if long or multiple parts) problems from sections 4.4 and 4.5 (up to Problem 169).


HW8 - Due on Wednesday 03/20:

Problems: choose three (or two if long or multiple parts) problems from sections 4.5 (from Problem 170 on) and 4.6.


HW9 - Due on Wednesday 04/24 (no HW due on 04/03):

Problems: choose three (or two if long or multiple parts) problems from sections 5.1 to 5.3, up to Problem 212.


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


Back to the TOP.