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.
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:
SPECIAL NOTICES:
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
-------------------------------------------------------------------
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