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 corequisites: 
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


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

Develop an understanding for the basics of number theory an use them.
Contribution to Program Outcomes

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.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.
Method of assessment

Written exam

Formulate proofs in basic level.
Contribution to Program Outcomes

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.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.
Method of assessment

Written exam

Grasp the applications of number theory in other areas such as Coding Theory and Cryptography.
Contribution to Program Outcomes

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.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Exhibiting professional and ethical responsibility.
Method of assessment

Written exam

Homework assignment


Contents


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) AddisonWesley 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



Method of assessment 
Week number 
Weight (%) 

Midterms: 
9 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 

0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface 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 midterm exam: 
8 
1 

Midterm: 
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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