Elementary Number Theory
Fall 2008
MW 1:30-2:50, LART 210; 3 credit hours
Other resources
Syllabus
Please feel free to come by my office any time during scheduled
office hours.
You are welcome to
come at other times, but in that case you might want to make
an appointment, just to make sure that I will be there then. You can
make an appointment simply by talking to me before or after class, by
calling me at
my office
or at home, or by sending
e-mail.
You may also ask any questions directly via phone or e-mail. If I'm
not in when you call, please leave a message on the voice-mail or
answering machine with your name, number, and a good time for me to
call you back. I will try to respond to your phone or e-mail message
as soon as possible.
Prerequisites:
Calculus II (Math 1312). This is entirely a mathematical maturity requirement,
as we will use no calculus in this course.
COURSE OBJECTIVES:
Upon successful completion of this course, you will be able to construct simple proofs using the basic definitions of number theory. You will be able to
apply fundamental theorems of number theory in appropriate situations. Specific topics
include: divisibility; Diophantine equations; prime numbers; modular arithmetic; Chinese
Remainder Theorem; and Fermat's Little Theorem. If time permits, we will see how these
concepts can be used in public key cryptography.
Note that your previous math courses may not have included any proofs, or asked you to
prove anything. This course will mostly be about proofs, which may be a radical change
for you.
Textbook:
Number Theory Through Inquiry, by Marshall, Odell, and Starbird, Chs.
1-5.
This book differs from other texts for proof-based courses, in that the proofs of
the theorems are not included. The point of this is for you, the student, to fill in these
details, in order to be more actively involved with the material. To make this task more
manageable, intermediate results to help guide you are included. Read the introduction
carefully for more details.
Course structure:
The course is built around student presentations of proofs of results, and solutions to problems, from the textbook, while I serve as moderator. (I will also occasionally
give short presentations to put topics into a wider context.) I will announce the approximate schedule I expect us to follow one or two class periods in advance, and maintain
that information on the course website.
I will pick students (sometimes asking for volunteers on harder proofs) to present their
work in class. Presentations will be evaluated on: the quality and correctness of the
content; the clarity of the presentation; the difficulty of the problem; and the frequency
of your contributions. Making substantial progress, or asking a good question, about a
harder problem without solving it may be worth as much as solving an easier problem.
When you are in the audience, you are still expected to be actively engaged in the presentation. This means checking to see if every step of the presentation is clear and convincing
to you, and speaking up when it is not. When there are gaps in the reasoning, the class
will work together to fill the gaps.
You will work outside of class to prove results, solve problems, and write your work to
turn in as homework, ideally before the material is presented to the whole class. Even
after a particular problem or proof is presented to the class, you may turn it in up to one
week later, but only for reduced credit. Please keep copies of your written work for your
use while I am grading it.
GRADES:
Participation and Homework (40%)
Your presentations, audience participation, and written
homework submissions will contribute approximately equally to this portion of your
grade. This is based on your overall contribution to keeping the course moving (which
includes forward progress, making sure presentations are complete and correct, helping
other students' understanding) and on your ongoing understanding of the material. I
will use the following rubric:
- A Clear, correct presentations to most problems; helpful audience participation including appropriate feedback and good questions; most problems written up in
advance.
- B Correct presentations to routine problems; active audience participation including
questions and discussions; routine problems written up in advance, harder problems
written up eventually, but clearly.
- C Correct presentations to easier problems, and reasonable attempts at routine problems; responding in the audience when called on, posing questions when you are
confused, and participating in discussions; most problems written up eventually,
mostly correct.
- D Less than satisfactory work, but an apparent honest effort to understand material.
At least some presentations with reasonable attempts; participating in the audience
with questions or comments; most problems written up eventually.
Exams (15% each)
There will be two in-class, closed-book exams on the following days:
- Wed., 24 Sep.
- Wed., 22 Oct.
Each exam will cover material from the beginning of the semester, though the second
exam will focus more on material since the first exam. Makeup tests can be given only
in extraordinary and unavoidable circumstances, and with advance notice.
Final (30%)
The final exam will be comprehensive over all material we discuss in class. The
final will be on
Wed., 10 Dec., 4:00-6:45 p.m.
POLICIES:
Collaboration:
You may not consult books, the Internet, other people outside of class, or
other sources to solve the problems or write your solutions. I do strongly encourage
you to work with your classmates on the problems in advance. I also encourage you
to talk to me frequently, more than in other courses. Feel free to ask questions about
the material, show me your work before presenting it in class, and even just talk about
your frustrations.
Academic dishonesty:
It is UTEP's policy, and mine, for all suspected cases or acts of alleged scholastic dishonesty to be referred to the Dean of Students for investigation and
appropriate disposition. See Section 1.3.1 of the Handbook for Operating Procedures.
Attendance:
Due to the course structure, attendance is mandatory. There is no particular
penalty for missing a particular class, but you cannot get a good participation grade if
you miss too many classes. I will usually "excuse" an absence if you tell me about it
in advance, or, in cases of emergencies, as soon as possible afterwards.
Drop date:
The deadline for student-initiated drops with a W is Friday, October 31. After
this date, you can only drop with the Dean's approval, which is granted only under
extenuating circumstances.
I hope everyone will complete the course successfully, but if you are having doubts
about your progress, I will be happy to discuss your standing in the course to help you
decide whether or not to drop. You are only allowed three enrollments in this course,
and students enrolled after Fall 2007 are only allowed six withdrawals in their entire
academic career, so please exercise the drop option judiciously.
Courtesy:
We all have to show courtesy to each other, and the class as a whole, during class
time. Please arrive to class on time (or let me know when you have to be late, and
why); do not engage in side conversations when one person (me, or another student)
is talking to the whole class; turn off your cell phone (or at least set it to not ring out
loud), and do not engage in phone, email, or text conversations during class.
Disabilities:
If you have, or suspect you have, a disability and need an accommodation, you
should contact the Disabled Student Services Office (DSSO) at 747-5148, dss@utep.edu,
or Union East room 106. You are responsible for presenting to me any DSS accommodation letters and instructions.
Exceptional circumstances:
If you anticipate the possibility of missing large portions of class
time, due to exceptional circumstances such as military service and/or training, or
childbirth, please let me know as soon as possible.