# Elementary Number Theory - MAS 4214-001

Fall Semester 2002--TR 03:30-04:45  EMB 100
Instructor: W. Edwin Clark
Office: PHY 326 A
Office Hours: TR 2:00 to 3:25. (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.  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:

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.  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.

join  numtheory

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:

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

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.

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.

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

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
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Skye          2.80 2.90 3.00 2.00 2.90 2.00 2.80 3.00 2.90 2.00   93
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Naiad         2.50 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00  100
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Barry Bonds   .90 2.60 1.70 2.50 3.00 1.70 1.00 1.00 2.00 2.00   69
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PAKIZ         2.90 2.50 2.90 2.50 3.00 2.80 2.80 3.00 3.00 3.00   98
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mky           1.50 3.00 2.00 2.90 3.00 2.90 2.50 0.00 2.00 3.00   89
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Cody          2.50 2.90 1.00 2.00 2.00 2.50 0.00 3.00 2.00 1.00   75
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Molly         2.00 2.90 3.00 3.00 2.00 1.50 0.00 2.50 3.00 .80   83
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NCC           3.00 2.40 2.80 3.00 2.90 2.00 2.90 2.50 2.00 2.00   90
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Misha         1.00 2.50 3.00 3.00 3.00 3.00 3.00 3.00 2.00 2.50   96
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Smiley        2.00 3.00 3.00 1.80 3.00 0.00 2.00 3.00 3.00 0.00   87
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apathy        1.50 2.90 3.00 1.80 1.90 3.00 0.00 0.00 3.00 2.00   80
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breezeshooter 2.50 0.00 1.00 1.50 2.90 3.00 2.80 1.00 2.50 1.50   74
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Flame         3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00 3.00  100
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sasha         2.30 3.00 3.00 0.00 2.30 2.30 2.80 3.00 2.90 3.00   93
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Hez             .50 2.40 3.00 0.00 1.60 2.00 2.00 1.50 2.80 0.00   66
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Red ninja     1.00 2.70 0.00 2.00 2.50 1.80 1.90 0.00 3.00 2.00   71
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Traveller     3.00 3.00 3.00 3.00 2.90 3.00 3.00 3.00 3.00 3.00  100
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slobot        2.50 3.00 3.00 1.50 3.00 3.00 1.00 2.00 3.00 3.00   94
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LARV          2.00 2.90 0.00 3.00 3.00 0.00 2.80 0.00 2.90 2.50   80
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