Course Information

Course Name	Turkish	Sayılar Teorisi
	English	Number Theory
Course Code	MAT 448E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	8	3	3	-	-
Course Language		English
Course Coordinator		Recep Korkmaz
Course Objectives		1. To provide an introduction to the study of properties of integers. 2. To prepare students to graduate-level courses in number theory and algebra. 3. To demonstrate applications of number theory (such as public-key cryptography).
Course Description		Divisibility, Euclidean algorithm, prime numbers, congruances, Chinese remainder theorem, Fermat’s little theorem, Euler’s theorem primitive roots, congruances with prime-power moduli, Binomial theorem, algebraic integers, quadratic residues, quadratic reciprocity, Jakobi and Legendre symbols, Euler’s function, Möbius inversion formula, multiplicative functions, Continued fractions, rational approximation, Diophantine equations, Pell’s equation.
Course Outcomes		Students completing this course will be able to :. I. Understand the concept and properties of divisibility. Know the definitions and properties of greatest common divisor and least common multiple. Understan the Euclidean Algorithm, can solve the linear diophantine equations and understand the concept of a congruence. III. Determine if a number is prime, compute the prime power factorization of a number. IV. Be able to perform basic operations with congruences, compute the set of all solutions to linear congruence. Be able to apply Chinese remainder theorem. V. Describe the set of solutions of non-linear congruence equations and be able to solve systems of such equations. VI. Understand the concepts of quadratic residues and quadratic reciprocity. Understand and use arithmetic functions and their properties. VII. Understand the representation of rational and real numbers by continued fractions.
Pre-requisite(s)		non
Required Facilities
Other
Textbook		Elementary Number Theory, William Leveque, Dover Publications, Inc, NY, 1990.
Other References		Elementary Number Theory, Charles Vanden Eyden, McGraw-Hill Elementary Number Theory, Jones, G. and M. Jones, Springer.

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