OU COURSE SYLLABUS
OU MATH 706 – NUMBER THEORY
Prepared by:
Recommending Approval:
Approved:
MELANIO G. ROMANO JR.
ROLANDO D. DOLLETE, Ph.D.
FLOR AMOR B. MONTA, Ph.D.
CLSU-OU Department Chair
CLSU-OU Director
Faculty
GRADUATE COURSE SYLLABUS
1. Catalogue No.
2. Course Title
3. Course Description
OU MATH 706
Number Theory
The theory of numbers is concerned with the properties of integers, more particularly with positive
integers. It imparts some historical background in which the subject evolves. Thus, the integral of this
course requires the students active participation, for nobody can learn number theory, without solving
problems. The computational problems develop basic techniques and test understanding of concepts,
while those of theoretical in nature give practice in constructing proofs.
4. No. of
3 Units / 3 hours per week (51 hours per semester)
Units/Teaching Hours
5. Course Philosophy
Explore outcomes of Number Theory using analytical thinking and logical skills that mathematicians
employ when engaging in a mathematical undertaking.
5.1 Course Vision
To be globally competitive, well-trained and competent professional teachers who are capable of
understanding and applying the knowledge gained from the course – Number Theory.
5.2 Course Mission
To provide professional teachers with advanced knowledge in the teaching and learning of Number
Theory.
5.3 Course Goals
1. Develop and train professional teachers to better understand and apply the concept of Number Theory.
2. Effective and efficient teaching-learning styles and techniques.
5.4 Course Objectives 1. Develop the ability to solve problems using the learned principles and theorems of the course.
2. Apply the learned concepts to other math-related subjects.
3. Produce professionally prepared teachers of mathematics.
6. Course Requirements
Evaluation Items
 Term Examinations
50%
 Quizzes
35%
 Problem Set
15%
MELANIO G. ROMANO JR.
Faculty member, Department of Education, Open University
7. Instructional content /
Number of hours
CHAPTER 1:
Some Preliminary
Considerations
Time allotment: 5 hrs.
1.1 Early Number
Theory
1.2 Mathematical
Induction
1.3 Binomial Theorem
Specific Objectives
1. Recall the origin of the early
number theories.
2. Use mathematical induction to
derive formulas.
3. Establish the binomial theorem by
mathematical induction.
References/Materials
1.
2.
3.
CHAPTER 2:
Divisibility Theory in
the Integers
Time allotment: 10 hrs.
2.1 Division
Algorithm
2.2 Divides Relation
2.3 Greatest Common
Divisor
2.4 Euclidean
Algorithm
2.5 Least Common
Multiple
2.6 Diophantine
Equation
1. Carry out Division algorithm in
establishing divisibility
statements.
2. Use the concept of Division
algorithm in finding the greatest
common divisor.
3. Represent the greatest common
divisor as a linear combination of
x and y.
4. Find the least common multiple
and greatest common divisor of a
given number.
5. Determine the solutions of Linear
Diophantine equations in n
unknowns.
1.
2.
3.
Burton, David M. 1994.
Elementary Number
Theory. W.B. Brown
Communications, Inc.
Niven, Ivan M. and
Zuckerman, Herbert S.
1980. An Introduction to
the Theory of Numbers.
John Wiley and Sons, Inc.
Rosen, Kenneth C. 1992.
Elementary Number
Theory and Its
Applications. 3rd edition.
Addison-Wesley
Burton, David M. 1994.
Elementary Number
Theory. W.B. Brown
Communications, Inc.
Niven, Ivan M. and
Zuckerman, Herbert S.
1980. An Introduction to
the Theory of Numbers.
John Wiley and Sons, Inc.
Rosen, Kenneth C. 1992.
Elementary Number
Theory and Its
Applications. 3rd edition.
Addison-Wesley
Teaching Strategies
1. Reading of the module.
2. Interaction through the
internet with students
3. Face to face interaction
with the students.
4. Giving Problem Set.
1. Reading of the module.
2. Interaction through the
internet with students
3. Face to face interaction
with the students.
4. Giving Problem Set.
Evaluation
1. Chapter Quiz
2. Problem Set
1. Chapter Quiz
2. Problem Set
Remarks
CHAPTER 3:
Primes and Their
Distributions
Time allotment: 8 hrs.
3.1 The Fundamental
Theorem of
Arithmetic
3.2 Sieve of
Eratosthenes
3.3 Goldbach
Conjecture
1. Find the prime factorization of
integers using the Fundamental
theorem of arithmetic.
2. Use the Sieve of Eratosthenes in
obtaining sequence of primes.
CHAPTER 4:
Theory of
Congruences
Time allotment: 8 hrs.
4.1 Karl Friedrich
Gauss
4.2 Basic Properties of
Congruence
4.3 Linear Congruence
4.4 Quadratic
Congruence
1. Apply the basic properties of
congruence in proving
mathematical assertions.
2. Find special criteria under which a
given integer is divisible by
another integer.
3. Solve linear and quadratic
congruence problems.
CHAPTER 5:
Fermat’s Theorem
Time allotment: 6 hrs.
5.1 Pierre de Fermat
5.2 Fermat’s
Factorization
Method
5.3 Little Fermat’s
Theorem
5.4 Wilson’s Little
Theorem
1. Use the Fermat’s factorization
method to factor large integers.
2. Apply the Little’s Fermat’s theorem
deduce Fermat’s theorem.
3. Determine whether a given number
is prime using Wilson’s theorem.
1. Burton, David M. 1994.
Elementary Number
Theory. W.B. Brown
Communications, Inc.
2. Niven, Ivan M. and
Zuckerman, Herbert S.
1980. An Introduction to
the Theory of Numbers.
John Wiley and Sons, Inc.
3. Rosen, Kenneth C. 1992.
Elementary Number
Theory and Its
Applications. 3rd edition.
Addison-Wesley
1. Burton, David M. 1994.
Elementary Number
Theory. W.B. Brown
Communications, Inc.
2. Niven, Ivan M. and
Zuckerman, Herbert S.
1980. An Introduction to
the Theory of Numbers.
John Wiley and Sons, Inc.
3. Rosen, Kenneth C. 1992.
Elementary Number
Theory and Its
Applications. 3rd edition.
Addison-Wesley
1. Burton, David M. 1994.
Elementary Number
Theory. W.B. Brown
Communications, Inc.
2. Niven, Ivan M. and
Zuckerman, Herbert S.
1980. An Introduction to
the Theory of Numbers.
John Wiley and Sons, Inc.
1. Reading of the module.
2. Interaction through the
internet with students
3. Face to face interaction
with the students.
4. Giving Problem Set.
1. Chapter Quiz
2. Problem Set
1. Reading of the module.
2. Interaction through the
internet with students
3. Face to face interaction
with the students.
4. Giving Problem Set.
1. Chapter Quiz
2. Problem Set
1. Reading of the module.
2. Interaction through the
internet with students
3. Face to face interaction
with the students.
4. Giving Problem Set.
1. Chapter Quiz
2. Problem Set
CHAPTER 6.
Continued Fractions
Time allotment: 5 hrs.
6.1 Finite Continued
Fractions
6.2 Infinite Continued
Fractions
1. Express rational numbers as finite
continued fractions.
2. Determine the rational number
represented by the simple continued
fraction.
3. Compute the convergents of a
simple continued fraction.
4. Determine the infinite continued of
irrational numbers.
5. Find a rational number that will
approximate irrational number with
accuracy to four decimal places.
CHAPTER 7.
Some Number
Theoretic Functions
Time allotment: 6 hrs.
7.1 Quadratic
Reciprocity
7.2 Pythagorean
Triples
7.3 Fibonacci Numbers
1. Use quadratic reciprocity in solving
quadratic congruence.
2. Obtain all primitive Pythagorean
triples base on the given condition.
3. Use the concept of Fibonacci
numbers to establish some
mathematical congruence.
1. Burton, David M. 1994.
Elementary Number
Theory. W.B. Brown
Communications, Inc.
2. Niven, Ivan M. and
Zuckerman, Herbert S.
1980. An Introduction to
the Theory of Numbers.
John Wiley and Sons, Inc.
3. Rosen, Kenneth C. 1992.
Elementary Number
Theory and Its
Applications. 3rd edition.
Addison-Wesley
1. Burton, David M. 1994.
Elementary Number
Theory. W.B. Brown
Communications, Inc.
2. Niven, Ivan M. and
Zuckerman, Herbert S.
1980. An Introduction to
the Theory of Numbers.
John Wiley and Sons, Inc.
3. Rosen, Kenneth C. 1992.
Elementary Number
Theory and Its
Applications. 3rd edition.
Addison-Wesley
1. Reading of the module.
2. Interaction through the
internet with students
3. Face to face interaction
with the students.
4. Giving Problem Set.
1. Reading of the module.
2. Interaction through the
internet with students
3. Face to face interaction
with the students.
4. Giving Problem Set.