**Text:** ** ***Elementary
Number Theory* by W. Edwin Clark. After August 21, 2002, the text
can be obtained from **Pro-Copy**, 5219 E. Fowler Ave. (adjacent
to Publix) , for the cost of reproduction and binding ---about $13.50**.**
[If you have a postscript reader and printer you can download and print
the text from here. Note that it
is prepared for two-sided printing.] We will also cover four Maple
worksheets which may be downloaded free from here.
But
you must have Maple 7 or Maple 8 on your computer to open the worksheets.

**Course Objectives: **
The plans are to cover the entire text and work all the problems in the
text. The main topics are: Basic properties of the integers. *Divisibility
and factorization:* this includes prime numbers, greatest common divisors,
the Euclidean Algorithm, Bezout's Lemma, Blankinship's Method,
and the Fundamental Theorem of Arithmetic. *Congruences:* this includes
modular arithmetic, Fermat's Little Theorem, probabilistic
primality tests , Euler's Theorem. *Arithmetic functions:* this includes
the Euler phi funtion, the number of positive divisors function, the sum
of positive divisor functions, perfect numbers and Mersenne primes. The
RSA public key cryptographic scheme. Students will also learn how
to use the programming language Maple
to perform number theoretic calculations.

**HOMEWORK policy:** Homework
will be assigned frequently. Students will be responsible for knowing how
to work correctly all assigned problems. Homework will be collected each
Tuesday unless otherwise announced in class. All assigned problems will
be collected, but only a few randomly selected problems will be graded.
Students should ask in class about problems they are unsure of -- after
the homework has been graded. If a given problem is not solved completely
*significant
effort shown on the homework paper will count for full credit.*Such
effort includes writing down of all definitions involved in the statement
of the problem, writing down all previous material related to the statement
of the problem, and working out a number of typical examples related
to the problem. __Late homework will not be aqccepted, however,__ __I
will drop the two lowest homework grades.__

**DATES of EXAMS and QUIZZES:**

** Tuesday
Quizzes:** On each Tuesday, unless there is a holiday, a quiz will
be given *at the beginning of class.* This quiz will cover definitions
and statements of named theorems presented in class any time prior to the
quiz. The quizzes will also cover examples from class and simple computations
that will be easy for those doing their homework. __There will be no makeups
for student who are late or fail to take a quiz. However, I will drop the
lowest 2 quiz grades .__

** Exam
1:
**Tuesday, September 24

** Exam
2:
**Thursday, October 24

** Exam
3:
**Tuesday, December 3

** Final
Exam:
**Thursday, December 12, 3:30PM -- 5:30 PM

**COURSE GRADES: **I
will calculate the average of the grades on the Tuesday Quizzes, Homework,
Exams 1, 2 and 3. Your course grade will be based on the maximum of this
average and your Final Exam grade. __Instead of having makeup exams,
the Final Exam will serve as a makeup of any of the missed other exams.__
I will use the following scale to assign plus/minus letter grades

98-100 = A+, 93-97 = A, 90-92
= A-,

88-89 = B+, 83-87= B, 80-82
= B-,

78-79 = C+, 73-77 = C, 70-72=C-,

68-69 = D+, 63-67 = D, 60-62
= D-,

0-59 = F.

**Class Mailing List:**

__I__t is important for
students to have email accounts from USF and/or a private internet service
provider and as soon as possible join the class mailing list, **numtheory**.
If you are now on the course website, the easiest way to join right now
is to click on the link join **numtheory** below and fill in your email
address and name in the places indicated. Then without making any other
changes in the form click on the SAVE button at the bottom of the form.
You will then be a member. You may join several times from different
accounts if you wish.

I will use this mailing list
to communicate with the class so it is very important that you subscribe
as soon as possible AND read your email frequently. The first message from
the list will explain how to use the list. If you don't get a Welcoming
Message immediately, let me know after you have checked that you typed
in your email address correctly. Possible Quiz questions will usually distributed
via this mailing list.

**To obtain an email account go to:**

http://www.acomp.usf.edu/helpcenter/services/email_accounts.html

For techincal support for connecting from home, using email, etc, go to:

**IMPORTANT DATES:**

- August 26 - Monday - first day of classes for the Fall Semester
- September 2 - Monday Labor Day
- October 18 - Friday - Honors Convocation (tentative)
- November 11 - Monday - Veteran's Day
- November 28 & 29 - Thursday and Friday - Thanksgiving Holiday
- December 6 - Friday - last day of classes for the Fall Semester
- December 7-13 - Saturday to Friday - Final Exam Week

**SPECIAL NOTICES:**

- Students who anticipate being absent from class due to a religious observance must provide notice of the date(s) to the instructor, in writing, by the second class meeting.
- See me if you desire permission to sell notes or tapes of class lectures.
- Any student who feels s/he may need an accommodation based on the impact of a disability should contact me privately to discuss your specific needs. Please contact Student Disability Services in SVC 1133 (813) 974-4309 to coordinate reasonable accommodations for students with documented disabilities.
- The URL for the USF policy in the undergraduate catalog regarding academic dishonesty is: http://www.ugs.usf.edu/catalogs/0203/adadap.htm

**Maple
Worksheets:** You must have **Maple 7** or **Maple
8** on your computer to be able to read these worksheets. Students may
download the following Maple worksheets. Sometimes a single or double
click will allow you to download the files. Some times you may have
to hold down the right mouse button (on a
**Mac** just hold down
the single mouse button) then select **Download file to disk** or **Save
file to Disk**. Then you should be able to open the file with Maple.
You might open Maple first and then while in Maple choose
**Open** from
the **File** menu item.

**Quiz Grades**

Please check that your grades were recorded correctly and that you agree with the average.

Homework Grades and Exam Grades will be posted here later.

The average was obtained by dropping the lowest two quiz scores, adding
the rest, then dividing by the maximum possible score, namely 3*(8) and
finally multiplying by 100 to convert to a percent. I rounded up to the
nearest integer to obtain the Average Quiz Grade. Students not handing
in a codename are listed as "no codename"

1 2 3 4 5 6 7 8 9 10 Average

Codename

-------------------------------------------------------------------

Skye 2.80 2.90
3.00 2.00 2.90 2.00 2.80 3.00 2.90 2.00 93

-------------------------------------------------------------------

Naiad 2.50 3.00 3.00
3.00 3.00 3.00 3.00 3.00 3.00 3.00 100

-------------------------------------------------------------------

Barry Bonds .90 2.60 1.70 2.50 3.00 1.70 1.00 1.00 2.00
2.00 69

-------------------------------------------------------------------

PAKIZ 2.90 2.50 2.90
2.50 3.00 2.80 2.80 3.00 3.00 3.00 98

-------------------------------------------------------------------

mky 1.50
3.00 2.00 2.90 3.00 2.90 2.50 0.00 2.00 3.00 89

-------------------------------------------------------------------

Cody 2.50 2.90
1.00 2.00 2.00 2.50 0.00 3.00 2.00 1.00 75

-------------------------------------------------------------------

Molly 2.00 2.90 3.00
3.00 2.00 1.50 0.00 2.50 3.00 .80 83

-------------------------------------------------------------------

NCC 3.00
2.40 2.80 3.00 2.90 2.00 2.90 2.50 2.00 2.00 90

-------------------------------------------------------------------

Misha 1.00 2.50 3.00
3.00 3.00 3.00 3.00 3.00 2.00 2.50 96

-------------------------------------------------------------------

Smiley 2.00 3.00 3.00 1.80
3.00 0.00 2.00 3.00 3.00 0.00 87

-------------------------------------------------------------------

apathy 1.50 2.90 3.00 1.80
1.90 3.00 0.00 0.00 3.00 2.00 80

-------------------------------------------------------------------

breezeshooter 2.50 0.00 1.00 1.50 2.90 3.00 2.80 1.00 2.50 1.50
74

-------------------------------------------------------------------

Flame 3.00 3.00 3.00
3.00 3.00 3.00 3.00 3.00 3.00 3.00 100

-------------------------------------------------------------------

sasha 2.30 3.00 3.00
0.00 2.30 2.30 2.80 3.00 2.90 3.00 93

-------------------------------------------------------------------

Hez
.50 2.40 3.00 0.00 1.60 2.00 2.00 1.50 2.80 0.00 66

-------------------------------------------------------------------

Red ninja 1.00 2.70 0.00 2.00 2.50 1.80 1.90
0.00 3.00 2.00 71

-------------------------------------------------------------------

Traveller 3.00 3.00 3.00 3.00 2.90 3.00 3.00
3.00 3.00 3.00 100

-------------------------------------------------------------------

slobot 2.50 3.00 3.00 1.50
3.00 3.00 1.00 2.00 3.00 3.00 94

-------------------------------------------------------------------

LARV 2.00 2.90
0.00 3.00 3.00 0.00 2.80 0.00 2.90 2.50 80

-------------------------------------------------------------------

**Interesting Number Theory Webpages:**

- http://www.utm.edu/research/primes/ Chris Caldwell's webpage on prime numbers records, research, etc.
- http://www.machine-creativity.com/programs/nwn/project.html Simon Colton's Numbers with Names Project.
- http://www.best.com/~cgd/home/flt/flt01.htm Charles Daney's webpage on Fermat's Last Theorem
- http://www.math.uga.edu/~ntheory/N14.html Historical and biographical number theory links.
- http://www.research.att.com/~njas/sequences/ Sloane's Encyclopedia of Integer Sequences.
- http://www.ams.org/new-in-math/primes.html American Mathematical Society page on primes.
- http://www.math.niu.edu/~rusin/known-math/welcome.html Dave Rusin's Mathematical Atlas.