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Syllabus ( MATH 449 )


   Basic information
Course title: Number Theory
Course code: MATH 449
Lecturer: Assoc. Prof. Dr. Gülşen ULUCAK
ECTS credits: 5
GTU credits: 3 (3+0+0)
Year, Semester: 2018, Fall
Level of course: First Cycle (Undergraduate)
Type of course: Area Elective
Language of instruction: English
Mode of delivery: Face to face
Pre- and co-requisites: None
Professional practice: No
Purpose of the course: The overall goal of this course is to analyze the fundamental concepts of number theory and to engage the student in actively investigating numbers, number operations and relationships among them. In addition, to emphasize the importance of number theory in cryptology and similar fields.
   Learning outcomes Up

Upon successful completion of this course, students will be able to:

  1. Develop an understanding for the basics of number theory an use them.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.

    Method of assessment

    1. Written exam
  2. Formulate proofs in basic level.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

    Method of assessment

    1. Written exam
  3. Grasp the applications of number theory in other areas such as Coding Theory and Cryptography.

    Contribution to Program Outcomes

    1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
    2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
    3. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
    4. Exhibiting professional and ethical responsibility.

    Method of assessment

    1. Written exam
    2. Homework assignment
   Contents Up
Week 1: Integers, Divisibility, Prime Numbers
Week 2: Greatest Common Divisors, Euclidean algorithm
Week 3: Fundamental Theorem of Arithmetic, Factorization of Numbers
Week 4: Fermat Numbers, Linear Diophantine equations
Week 5: Congruences: Linear congruences, The Chinese Remainder Theorem, Wilson’s Theorem, Fermat’s Little Theorem
Week 6:
Some Number Theoretic Functions
Week 7: Cryptology
Week 8: Cryptology
Week 9: Midterm exam
Week 10: Primitive Roots
Week 11: Primitive Roots
Week 12: Quadratic Residues
Week 13:
Quadratic Residues
Week 14: Continued Fractions
Week 15*: Final exam
Week 16*: Retake Exam
Textbooks and materials:
Recommended readings: 1. Elementary Number Theory and Its Applications, K.H. Rosen, (4th edition) Addison-Wesley 2000.
2. An Introduction to the Theory of Numbers, I. Niven, H. S. Zuckerman, H. L. Montgomery


  * Between 15th and 16th weeks is there a free week for students to prepare for final exam.
Assessment Up
Method of assessment Week number Weight (%)
Mid-terms: 9 40
Other in-term studies: 0
Project: 0
Homework: 0
Quiz: 0
Final exam: 16 60
  Total weight:
(%)
   Workload Up
Activity Duration (Hours per week) Total number of weeks Total hours in term
Courses (Face-to-face teaching): 3 14
Own studies outside class: 4 14
Practice, Recitation: 0 0
Homework: 0 0
Term project: 0 0
Term project presentation: 0 0
Quiz: 0 0
Own study for mid-term exam: 8 1
Mid-term: 2 1
Personal studies for final exam: 10 1
Final exam: 2 1
    Total workload:
    Total ECTS credits:
*
  * ECTS credit is calculated by dividing total workload by 25.
(1 ECTS = 25 work hours)
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