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Fayetteville State University
COLLEGE OF BASIC AND APPLIED SCIENCES
Department of Mathematics and Computer Science
MATH 472-02 Theory of Numbers
Fall 2007
1. Locator Information:
Instructor: __ Dr. Xin Tang____
Course # and Name: Math 472 Theory of Numbers
Office Location: Smith Hall 216
Semester Credit Hours: 3 hours
Office hours: MWF 9:30am-10:50am &MF2:00pm-4:00pm
Day and Time Class Meets: MWF 1:00pm-1:50pm
Office Phone: 910-672-2206
Total Contact Hours for Class: 3 hours
Email address:[email protected]
a.
b.
c.
FSU Policy on Electronic Mail: Fayetteville State University provides to each student, free of
charge, an electronic mail account ([email protected]) that is easily accessible via the Internet.
The university has established FSU email as the primary mode of correspondence between university
officials and enrolled students. Inquiries and requests from students pertaining to academic records,
grades, bills, financial aid, and other matters of a confidential nature must be submitted via FSU email.
Inquiries or requests from personal email accounts are not assured a response. The university
maintains open-use computer laboratories throughout the campus that can be used to access electronic
mail.
Rules and regulations governing the use of FSU email may be found at
http://www.uncfsu.edu/PDFs/EmailPolicyFinal.pdf
2. Course Description: Mathematics 472, Theory of Numbers, is a study of the elementary
properties of integers, divisibility, Euclid Algorithm, prime numbers, and congruences.
PREREQUISITE: Junior Standing.
3. Disabled Student Services: In accordance with Section 504 of the 1973 Rehabilitation Act
and the Americans with Disabilities Act (ACA) of 1990, if you have a disability or think you
have a disability to please contact the Center for Personal Development in the Spaulding
Building, Room 155 (1st Floor); 910-672-1203.
4. Textbook: Eynden, Charles Vanden., Elementary Number Theory, 2nd ed, Waveland Press,
Inc.
5. Student Learning Outcomes – Upon the completion of this course, the students shall
demonstrate an understanding of various basic topics in Elementary Number Theory. The
students shall learn how to use algebra to describe patterns and relations, and to model and
solve problems. In addition, the students shall try to understand the role of axiomatic systems
and proofs in different branches of mathematics, such as algebra and geometry.
DPI COMPETENCIES
The DPI competencies covered are listed below:
6.1 Understand elementary number theory including modular arithmetic, the Fundamental Theorem of
Arithmetic, basic results about primes, composites, multiples and divisors.
NCATE STANDARDS
The NCATE Standards covered in this course are listed below:
1.1.7 Use algebra to describe patterns, relations and functions, and to model and solve problems
1.1.9 Understand the role of axiomatic systems and proofs in different branches of mathematics , such
as algebra and geometry
1.1.11 Describe and represent mathematical relationships
6.
Course Requirements and Evaluation Criteria- Evaluation in the course shall be by
continuous assessment. Mode of assessment would include homework assignments, chapter
exams, class attendance and participation, and final examination. The grading scale for
determining the course grade and weights given to various activities are given below.
a. A = 92-100%
B = 83-91%
C=73-82%
D=64-72%
F=Below 64%
b. Students are only allowed to miss less than 5 classes for acceptable reasons.
c. Homework: 25 points (Two lowest homework grades will be dropped); Tests (4): 45
points (Lowest test grade will be dropped); Final Exam: 30 points; 5 bonus points for
proper attendance and participation.
d. No make-up exams or late assignments accepted.
GENERAL REQUIREMENTS:

The student is expected to pre-study each lesson in advance, complete all assignments, and
spend adequate time on class work to insure success in the course. At least two hours of
study is expected for each class hour.
 It is the responsibility of the student to avail himself/herself at all class meetings, and obtain
additional help as needed. Consult the University Catalogue on Class Attendance Policy.
 Students are expected to enter the classroom on time and remain until the class ends. Late
arrivals and early departures without appropriate excuses will not be tolerated.
 Each student is encouraged to participate in class discussion for a clearer understanding and
meet with the instructor when additional assistance is needed.
All class discussions should be done in a soberly, orderly, and respectful manner.
7.
Academic Support Resources – Additional information will be posted at:
http://faculty.uncfsu.edu/xtang/math_472-01.html or through Blackboard.
Course Outline and Assignment
*The following Course Outline and Assignments are subject to change if appropriate.*
8.
Class
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Topic Covered
1.1 The GCD and LCM
1.2 The Division Algorithm
1.3 The Euclidean Algorithm
1.4 Linear Combinations
1.5 Congruences
1.6 Mathematical Induction
Review for Exam 1
Exam 1
Analysis of Exam 1
2.1 Prime Factorization
2.2 The Fundamental Theorem of
Arithmetic
2.3 The Importance of Unique
Factorization
2.4 Prime Power Factorizations
2.5 The Set of Primes is Infinite
2.6 A Formula T(n)
3.1 The Sum of the Divisors
3.2 Multiplicative Functions
Review for Exam 2
Exam 2
Analysis of Exam 2
3.3 Perfect Numbers
3.4 Mersenne and Fermat Numbers
3.5 The Euler Phi Function
3.6 The Mobius Inversion Formula
4.1 Solving Linear Congruences
4.2 The Chinese Reminder Theorem
Assignment
6,8,16, 26, 34
2, 14, 16, 18, 32
2, 14,18,21,29
2, 8, 14, 22, 36
2, 18, 32, 38, 45
12, 18, 24, 35, 54,
4, 10, 14, 18, 35
2, 6, 10, 16, 22
2, 6, 8, 11, 20, 24
4, 8, 16, 28, 34,42
2, 8, 14, 16, 18
10, 14, 20, 23, 24, 32, 45
8, 14, 24, 36, 40, 46
8, 10, 13, 22, 23
6, 12, 19, 22, 30
1, 6, 10, 16, 19
4, 12, 18, 22, 41
2, 12, 14, 18
6, 14, 18, 26, 39, 42, 45
6, 18, 23, 31, 40
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
Review for Exam 3
Exam 3
Analysis of Exam 3
4.3 The Theorems of Fermat and Euler 2, 10, 14, 28, 32, 43, 47
4.4 Primality Testing
4, 8, 12, 20
4.5 Public-Key Cryptography
2, 10, 22, 28, 32
5.1 Polynomial Congruences
2, 12, 22, 26, 30
5.2 Congruences with Prime Power 2, 14, 19, 26
Moduli
5.3 Quadratic Residues
2, 16, 20, 26, 34, 38
5.4 Quadratic Reciprocity
2, 12, 20, 30, 40
5.5 Flipping a Cone over the 4, 8, 14, 20, 24
Telephone
Review for Exam 4
Exam 4
Analysis of Exam 4
Review for Final Exam
Review for Final Exam
Final Exam
9. Teaching Strategies: The majority of the material of the course will be given in lecture format.
There is a short review before and after each lecture. Student discussions, cooperative learning groups
will be strongly encouraged
10. Bibliography:
1. Burton, David M. Elementary Number Theory. 4thed., McGraw-Hill 1998.
2. Burton,David M. The History of Mathematics.,3rd ed., McGraw-Hill
3. Koblitz, Neal., A Course in Number Theory., 2nded., Sringer-Verlag, New York.
4. Rose,H.E., A Course in Number Theory., 2nd ed., Oxford Univ Press., New York.
REVISION OF GRADES – STUDENT RESPONSIBILITIES
The following revisions become effective on August 16, 2007.
WN GRADE DISCONTINUED:
 WN - Withdrawal due to non-attendance - discontinued, effective August 16, 2007.
STUDENTS: Do not expect faculty to withdraw you for non-attendance. Drop or withdraw*
from classes according to the deadlines published in the catalog. *See warning below about class
withdrawals.
NEW TYPE OF GRADE: INTERIM GRADES – (New name for “midterm grade,” with additional
purposes). Interim grades will be assigned from the first week of the semester until the deadline for class
withdrawals. Interim grades are used for informational and warning purposes only; they are not part of
your permanent transcript and have no effect on your GPA. Instructors may assign interim grade of F
to warn students of poor academic performance or they may assign “X” or “EA” grades. (See below for
explanations) After midterm, faculty will assign all students an interim grade of A – F to inform students
of their academic status as of midterm.
 INTERIM GRADE X = NO SHOW – Assigned to students who are on a class roster, but never
attend class. For warning purposes only; NOT a final grade.
STUDENTS: Check interim grades early in the semester. If you have an X grade, either begin
attending the class or withdraw* from it. *See warning below about class withdrawals. If you do
not take action in response to an X grade, you will receive a final grade of FN. (See “FN” below)
 INTERIM GRADE EA = EXCESSIVE ABSENCES - Assigned to students whose class absences
exceed 10% of the total contact hours. For warning purposes only, NOT a final grade.
STUDENTS: Check your interim grades often. If you have an “EA” grade for a class, you are in
jeopardy of failure if you do not take immediate actions. Either resume attending the class or
withdraw from it. *See warning below about class withdrawals.
NEW FINAL GRADE:
 FN = FAILURE DUE TO NON-ATTENDANCE – Assigned to students who are on class roster,
but never attend the class. An FN grades is equivalent to an F grade in the calculation of the
GPA.
STUDENTS: You must attend (or withdraw* from) all the classes for which you are enrolled.
*See warning below about class withdrawals.
WARNING ABOUT CLASS WITHDRAWALS:
 When you withdraw from a class, you are wasting your money and time. You receive no refund
for withdrawing from individual classes and you slow your progress toward degree completion.
 If you withdraw from or fail more than one-third of your classes, you will no longer be eligible for
financial aid.
 STRIVE TO EARN CREDIT FOR ALL THE CLASSES IN WHICH YOU ENROLL;
WITHDRAW FROM CLASSES ONLY WHEN IT IS ABSOLUTELY NECESSARY!