Elementary Number Theory - MAS 4214-901

Spring Semester 2003--MW 7:30-8:45 PHY 120    Instructor: W. Edwin Clark
   Office: PHY 326 A
   Office Hours: MW 2:00-3:00. (Also, immediately after class or by appointment.)
   Email: eclark@math.usf.edu ( If you need to contact me, email is the best way. I read my email frequently from home as well as from the office. Voice mail is not as likely to reach me. )
   Homepage: http://www.math.usf.edu/~eclark/ (This syllabus will be on my homepage in case you lose it. You may also go there if you are curious about my research and academic genealogy.)

Text: Elementary Number Theory by W. Edwin Clark. 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:

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. The basic theorem will be given in the text and implementation will be described in the Maple worksheets.
Computational aspects: Students will also learn how to use the programming language Maple to perform number theoretic calculations.

HOMEWORK: Homework will be assigned frequently. Students will be responsible for knowing how to work correctly all assigned problems. Homework will be collected every Monday unless otherwise announced in class. All assigned problems will be collected, but only a few randomly selected problems will be graded. Hints may be given for difficult problems before the assignment is due if requested. 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 accepted. However,I will drop the two lowest homework grades.

DATES of EXAMS and QUIZZES:

Monday Quizzes: On each Monday, 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: Monday, February 10

Exam 2: Monday, March 24

Exam 3: Monday, April 21

Final Exam: See the Spring 2003 Final Exam Matrix

COURSE GRADES: I will calculate the average of the grades on the Monday 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 for any of the missed 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.

Join the Class Mailing List (numtheory).

It 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.

To join send an email from your own email account with no subject and no message to the email address:

join-numtheory@lists.cas.usf.edu

This will subscribe the address you have sent the message from. If you wish you can join from another account. 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.

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. Previews of Monday 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:

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

IMPORTANT DATES:

January 6 - Monday Spring, first day of classes
January 20 - Monday Martin Luther King, Jr.
March 10 -15 USF Spring Break
April 25 - Friday Spring, last day of classes
April 26 - May 2 Spring Final Exams

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.

OpenQuestions worksheet#1 worksheet#2 worksheet#3 worksheet#4

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.