Mathematics (English) Preview
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code:

MATH305

Course Name:

Elementary Number Theory

Semester:

Fall

Course Credits:

ECTS

Language of instruction:

English

Course Condition:

Does the Course Require Work Experience?:

Type of course:

Compulsory Courses

Course Level:

Bachelor

TR-NQF-HE:6. Master`s Degree

QF-EHEA:First Cycle

EQF-LLL:6. Master`s Degree

Mode of Delivery:

Face to face

Course Coordinator:

Araş. Gör. GAMZE AKAR UYSAL

Course Lecturer(s):

Assist. Prof. Dr. Doğa Can Sertbaş

Course Assistants:

Course Objective and Content

Course Objectives:	The aim of the course is to teach the fundamental concepts of number theory and provide the necessary foundation for solving advanced-level problems in this field.
Course Content:	The content of the course consists of the binomial theorem, the Euclidean algorithm, the fundamental theorem of arithmetic, Chinese Remainder Theorem, Fermat’s Little Theorem, Wilson’s Theorem, Möbius Inversion Formula, Euler’s Theorem, primitive roots, Legendre Symbol, perfect numbers, Pythagorean triples, Lagrange’s Theorem and Fibonacci numbers.

Learning Outcomes

The students who have succeeded in this course;
1) Calculate the greatest common divisor using the Euclidean algorithm.
2) Apply the Chinese Remainder Theorem to solve a system of linear congruences.
3) Understand that the prime factorization of any natural number greater than 1 is unique, up to ordering.
4) Calculate the squares in the residue class of a prime using the quadratic residue law.
5) Comprehend the generation of Pythagorean triples of some certain form.

Course Flow Plan

Week	Subject	Related Preparation
1)	The Well Ordering Principle and the binomial theorem
2)	The greatest common divisor and the Euclidean algorithm
3)	The fundamental theorem of arithmetic and the sieve of Eratosthenes
4)	The theory of congruences and the Chinese Remainder Theorem
5)	Fermat’s Little Theorem and Wilson’s Theorem
6)	Multiplicative functions and the Möbius Inversion Formula
7)	Euler’s ϕ function and Euler’s Theorem
8)	Midterm Exam
9)	Primitive roots and the theory of indices
10)	The Legendre Symbol and the quadratic reciprocity law
11)	Perfect numbers and Mersenne primes
12)	Pythagorean triples and “Fermat’s Last Theorem”
13)	Representation of integers as sums of squares
14)	Fibonacci numbers and continued fractions

Sources

Course Notes / Textbooks:	Burton, D.M., Elementary Number Theory, 1980, ISBN 9780205069651, Allyn and Bacon Inc.
References:	lecture notes

Course - Program Learning Outcome Relationship

Course Learning Outcomes	1	2	3	4	5
Program Outcomes
1) Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.
2) Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3) Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.
4) Have the ability to think analytically and use the time effectively in the process of deduction.
5) Have the ability to search the literature, understand and interpret scientific articles.
6) Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7) Have the ability to work efficiently in interdisciplinary teams.
8) Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9) Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10) Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.
11) Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Course - Learning Outcome Relationship

No Effect	1 Lowest	2 Average	3 Highest

	Program Outcomes	Level of Contribution
1)	Have the knowledge of the scope, history, applications, problems, methods of mathematics and knowledge that will be beneficial to humanity as both scientific and intellectual discipline.	2
2)	Have the ability to establish a relationship between mathematics and other disciplines and develop mathematical models for interdisciplinary problems.
3)	Have the ability to define, formulate and analyze real life problems with statistical and mathematical techniques.	2
4)	Have the ability to think analytically and use the time effectively in the process of deduction.	3
5)	Have the ability to search the literature, understand and interpret scientific articles.
6)	Have the knowledge of basic software to be able to work in the related fields of computer science and have the ability to use information technologies at an advanced level of the European Computer Driving License.
7)	Have the ability to work efficiently in interdisciplinary teams.
8)	Have the ability to communicate effectively in oral and written form, write effective reports and comprehend the written reports, make effective presentations.
9)	Have the consciousness of professional and ethical responsibility and acting ethically; have the knowledge about academic standards.
10)	Have the ability to use a foreign language at least at B1 level in terms of European Language Portfolio criteria.	3
11)	Are aware of the necessity of lifelong learning; have the ability to access information, to follow developments in science and technology and to constantly renew themselves.

Assessment & Grading

Semester Requirements	Number of Activities	Level of Contribution
Midterms	1	% 40
Final	1	% 60
total		% 100
PERCENTAGE OF SEMESTER WORK		% 40
PERCENTAGE OF FINAL WORK		% 60
total		% 100

Workload and ECTS Credit Calculation

Activities	Number of Activities	Workload
Course Hours	14	42
Application	14	14
Study Hours Out of Class	14	45
Midterms	3	9
Final	1	3
Total Workload		113