______BS-Math_-Math-80-Number-Theory.docx

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Republic of the Philippines
Cagayan State University
www.csu.edu.ph
COLLEGE of ARTS AND SCIENCES
Revision No. 02 February 2019
SYLLABUS IN MATH 80 – NUMBER THEORY
Intended Graduate
Attributes
The Cagayan State University aims to produce graduates who will exhibit:
Competence :critical thinker, creative problem-solver, competitive performer regionally, nationally and globally
Social Responsibility :sensitive to ethical demands and compassionate particularly to the marginalized, steward of the environment for future
generations while championing development and socially just and an advocate of economic and social equity
Unifying Presence :uniting theory and practice, uniting strata of society, uniting tradition and innovation, uniting the nation, the ASEAN region and the
world and uniting the University and the community.
College Intended
Learning Outcomes
Graduates of the college will be able to:
Display advanced knowledge in the fields of arts and sciences; (Knowledge)
Apply research-based concepts, theories and principles to current problems and issues; (Skills)
Provide responsiveness and empowering community extension services for the development of the people in the countryside.
Demonstrate a strong sense of commitment and moral values (Attitude)
Department Intended
Learning Outcomes
(DILO)
Graduates of the Department of Natural Sciences and Mathematics are expected to:
1. Demonstrate broad and coherent knowledge and understanding in the core areas of physical and natural sciences.
2. Apply critical and problem-solving skills using the scientific method.
3. Interpret relevant and scientific data and make judgements that include reflection on relevant scientific and ethical issues.
4. Carry out basic mathematical and statistical computations and use appropriate technologies in (a) the analysis of data; and (b) pattern recognition,
generalization, abstraction, critical analysis and problem solving.
5. Communicate information, ideas problems and solutions, both orally and in writing, to other scientists, decision makers and the public
6. Relate science and mathematics to other disciplines.
7. Design and perform safe and responsible techniques and procedures in laboratory or field practices.
8. Critically evaluate input from others.
9. Appreciate the limitations and implications of science in everyday life.
10. Commit to the integrity of data.
F-ODI-2056

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Program Intended
Learning Outcomes
(PILO)
Graduates of BS in Mathematics program should be able to:
1. Gain mastery in the core areas of mathematics: algebra, analysis and geometry.
2. Demonstrate skills in pattern recognition, generalization, abstraction, critical analysis, synthesis, problem-solving and rigorous argument.
3. Develop an enhanced perception of the vitality and importance of mathematics in the modern world including inter-relationships within math and its
connections to other disciplines.
4. Appreciate the concept and role of proof and reasoning and demonstrate knowledge in reading and writing mathematical proofs.
5. Make and evaluate mathematical conjectures and arguments and validate their own mathematical thinking.
6. Communicate mathematical ideas orally and in writing using clear and precise language
Course Learning Outcome and Relationship to Program Outcome
Course Outcomes Program Outcomes
PILO1 PILO2 PILO3 PILO4 PILO5
Find the factors of a number
Identify prime and non-prime numbers
Apply the principle of mathematical induction
Find the prime factorization of a number
Define Greatest Common Divisor
Finding the Greatest Common Divisor of two
integers using the Euclidean Algorithm
Applying the Division Algorithm to compute the
quotient and remainder in the division of two
integers.

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Expressing the GCD as a linear combination of two
given relatively prime integers.
Solving a linear congruences
Using the Chinese Remainder Theorem to solve a
system of two or more simultaneous linear
congruences.
Perform operations among members of a given
complete residue system
Determine whether or not a given complete residue
system
Applying Fermat’s little theorem to establish
congruences with a prime modulus
Applying Wilson’s theorem to establish congruences
with a prime modulus.
Explain the fundamentals of cryptography
Design and evaluate security protocols appropriate
for a given situation
Find the order of an integers
Prove that an integer is a primitive root

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Course Code Math 80 Course Title Number Theory
Credit Units 3 Semester Second School Year 2021-2022 Number of Lecture Hours 54
Pre-Requisite/s Math 71 – Fundamental Concepts of Math Co-Requisite/s None Number of Laboratory Hours None
Course Description
The course in number theory includes divisibility properties and rules, prime numbers, greatest common divisors and prime factorization
and congruence, cryptography, primitive roots and indices.
Grading System
Submission of Assigned Activity 20%
Student Engagement/Forum Discussion 30%
Quizzes and Unit Exam 30%
Major (Midterm/Final Exam) 20%
TOTAL: 100%

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OUTCOME- BASED LEARNING PLAN IN NUMBER THEORY
Intended Learning Outcome
(ILO) Learning Content
Time
Allotment
Teaching and Learning
Activities Teaching and Learning
References/Resources
Learning
Assessment
Find the factors of a number
Identify prime and non-prime
numbers
Apply the principle of
mathematical induction
Chapter I. Divisibility and Primes
1. Review of the flowchart of
Algebra of numbers
2. Divisibility Rules
3. Prime Numbers
4. Mathematical Induction
3 hrs Inductive/Deductive Method
Analytical Method
Problem Solving Approach
Board Work
Burton, David.
Elementary Number
Theory (6th
Edition)
Seat work
Quizzes
Practical exams
Find the prime factorization of a
number
Define Greatest Common Divisor
Finding the Greatest Common
Divisor of two integers using the
Euclidean Algorithm
Applying the Division Algorithm
to compute the quotient and
remainder in the division of two
integers.
Chapter 2. Greatest Common Divisor
and Prime Factorization
1. Greatest Common Divisors
2. The Euclidean Algorithm
3. The Fundamental Theorem of
Arithmetic
4. Fermat Numbers and
Factorization Methods
5. Linear Diophantine Equations
Analytical Method
Board Work
Burton, David.
Elementary Number
Theory (6th
Edition)
Seat work
Quizzes
Practical exams

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Expressing the GCD as a linear
combination of two given
relatively prime integers.
MIDTERM EXAMINATION
Solving a linear congruences
Using the Chinese Remainder
Theorem to solve a system of two
or more simultaneous linear
congruences.
Chapter 3. Congruences
1. Introduction to congruences
2. Linear congruences
The Chinese Remainder
Theorem
Analytical Method
Board Work
Burton, David.
Elementary Number
Theory (6th
Edition)
Seat work
Quizzes
Practical exams
Perform operations among
members of a given complete
residue system
Determine whether or not a given
complete residue system
Applying Fermat’s little theorem
to establish congruences with a
Chapter 4. Some Special Congruences
1. Wilson’s theorem and Fermat’s
Little Theorem
2. Euler’s Theorem
Analytical Method
Burton, David.
Elementary Number
Theory (6th
Edition)
Seat work
Quizzes
Practical exams

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prime modulus
Applying Wilson’s theorem to
establish congruences with a
prime modulus.
Board Work
Explain the fundamentals of
cryptography
Design and evaluate security
protocols appropriate for a given
situation
Chapter 5. Cryptology
1. Charater ciphers
2. Exponential Ciphers
3. Public Key Cryptology
Analytical Method
Board Work
Burton, David.
Elementary Number
Theory (6th
Edition)
Seat work
Quizzes
Practical exams
Find the order of an integers
Prove that an integer is a primitive
root
Chapter 6. Primitive Roots and Indices
1. The order of an integer and
primitive roots
2. Primitive roots and primes
3. Existence of primitive roots
4. Index Arithmetic
Analytical Method
Board Work
Burton, David.
Elementary Number
Theory (6th
Edition)
Seat work
Quizzes
Practical exams
FINAL EXAMINATION

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COURSE POLICIES
Class Etiquette Online activities are the usual subjects of many forms of bullying. The class does not tolerate any form of bullying such as smart-
shaming.
Academic Integrity Even with the sudden shift of delivery to online modality, academic integrity must always be observed. All forms of cheating are strictly
prohibited. Anyone who violates will be dealt with disciplinary action by the instructor.
Dropping and Incomplete Remarks A student is considered officially dropped upon submission of the instructor’s copy of the duly accomplished dropping slip before the
scheduled deadline of the dropping. Meanwhile, a student incurs an incomplete remarks on his/her transcript if he/she purposely
missed a requirement.
Missed Examinations Any missed written examinations, quizzes, homework and activities will incur a grade of zero.
Online Platform Google Meet/Zoom shall be adopted as the course platform for the entire semester. Otherwise, the lecturer shall update the students to
the mode of passing of papers if changes shall be made.
Values Integration and Gender Sensitivity: Manifest sensitivity to gender issues

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Additional Readings and Other Materials:
Required for student
Burton, David. Elementary Number Theory (6th
Edition).
Other readings and references
1. Niven, I., Zuckerman, H., Montgomery, H., An Introduction to the Theory of Numbers
2. Crawford, Matthew. Introduction to Number Theory

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Prepared by:
BS MATHEMATICS Faculty Members Date of Revision/Enrichment: July 2022
Reviewed by: Noted by:
LUDIVINA P. CAUILAN, PhD JANE R. SAMBRANA, PhD
Department Chair College Dean
Recommending Approval:
LIRIO GUDINA C. MANGAWIL, Ph.D.
Director of Instruction
Approved by:
MARIDEN VENTURA-CAUILAN, DPA, CESO
Vice President for Academic Affairs

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