MATH 406 | Course Introduction and Application Information - Department of Mathematics

Course Name

Number Theory

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
MATH 406	Spring	3	0	3	6

Prerequisites	None
Course Language	English
Course Type	Required
Course Level	First Cycle
Mode of Delivery	-
Teaching Methods and Techniques of the Course	Discussion Problem Solving Q&A
National Occupation Classification	-
Course Coordinator	Doç. Dr. Sevin GÜMGÜM
Course Lecturer(s)	Prof. Dr. Tahsin ÖNER
Assistant(s)	Araş. Gör. Merve KAHRAMAN ARİMAN Araş. Gör. Sıla Selenay KOÇ

Course Objectives	The aim of this course is to gain concrete problem-solving skills using the basic concepts and structures of number theory.
Learning Outcomes	The students who succeeded in this course; will be able to solve some problems by means of the mathematical induction and well ordering relation. will be able to apply the divisibility structure of integer numbers, Euclid and the division algorithms, and Chinese remainder theorem. will be able to find the solutions of the linear Diophantine equations. will be able to explain the basic structures and properties of the congruences. will be able to define Euler-Fermat, Wilson and Lagrange theorems will be able to construct the solution formats of the systems of the congruences
Course Description	Sum and product notations; Well ordering relation; Induction principle; Divisibility; Division and Euclidean algorithms; Prime numbers; Modules in integers; Congruences; G.C.D; L.C.M.; Linear Diophantine equations; Euler-Fermat, Wilson, Lagrange and Chinese remainder theorems; Euler's function; Congruence systems
Related Sustainable Development Goals

Course Category	Core Courses	X
	Major Area Courses
	Supportive Courses
	Media and Management Skills Courses
	Transferable Skill Courses

Week	Subjects	Related Preparation
1	Mathematical induction, Well ordering relation, Divisibility	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (prerequisites and section 2.2)
2	Greatest common divisor, Least common multiple	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 2.4 and 2.5)
3	Least common multiple, Linear Diophantine eqautions	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 2.5 and 2.7)
4	Prime numbers	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 2.5 and 2.7)
5	Prime numbers	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (section 3)
6	Congruences, Linear congruences	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 4.2 and 4.4)
7	Linear congruences, System of linear congruences	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 4.4 and 4.6)
8	Fermat’s little theorem, Wilson’s theorem	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 5.2 and 5.4)
9	Midterm Exam
10	Arithmetic Functions	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 6.2, 6.4 and 6.6)
11	Arithmetic Functions	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 6.2, 6.4 and 6.6)
12	Euler’s phi-function, Euler’s theorem	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 7.2 and 7.4)
13	Euler’s phi-function, Euler’s theorem	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (sections 7.2 and 7.4)
14	Properties of phi-function	“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433. (section 7.6)
15	Semester Review
16	Final Exam

Course Notes/Textbooks

“Number Theory and its Applications”, S. Kundu and S. Mazumder, CRS Press, Taylor & Francis Group, Addison Wesley, 2022, ISBN: 9781032231433.

Suggested Readings/Materials

A Classical Introduction to Modern Number Theory, K. Ireland, M. Rosen, Grad. Text in Math., 2nd edition, Springer-Verlag, 1990. ISBN: 9780387973296

Semester Activities	Number	Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques	2	10
Portfolio
Homework / Assignments
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm	1	40
Final Exam	1	50
Total

Weighting of Semester Activities on the Final Grade	3	50
Weighting of End-of-Semester Activities on the Final Grade	1	50
Total

Semester Activities	Number	Duration (Hours)	Workload
Theoretical Course Hours (Including exam week: 16 x total hours)	16	3	48
Laboratory / Application Hours (Including exam week: '.16.' x total hours)	16		0
Study Hours Out of Class	14	3	42
Field Work			0
Quizzes / Studio Critiques	2	10	20
Portfolio			0
Homework / Assignments			0
Presentation / Jury			0
Project			0
Seminar / Workshop			0
Oral Exam			0
Midterms	1	30	30
Final Exam	1	40	40
		Total	180

#	Program Competencies/Outcomes	* Contribution Level
#	Program Competencies/Outcomes	1	2	3	4	5
1	To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics.	-	-	-	X	-
2	To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics.	-	-	-	-	-
3	To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials.	-	-	-	-	-
4	To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning.	-	-	X	-	-
5	To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals.	-	-	-	-	-
6	To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project.	-	-	-	-	-
7	To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge.	-	-	-	-	-
8	To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field.	-	-	-	-	-
9	To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security.	-	-	-	-	-
10	To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking.	-	-	-	X	-
11	To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language.	-	-	-	-	-
12	To be able to speak a second foreign language at a medium level of fluency efficiently.	-	-	-	-	-
13	To be able to relate the knowledge accumulated throughout the human history to their field of expertise.	-	-	-	-	-