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MAT 448E
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Course Information
Course Name
Turkish
Number Theory
English
Number Theory
Course Code
MAT 448E
Credit
Lecture
(hour/week)
Recitation
(hour/week)
Laboratory
(hour/week)
Semester

3
3


Course Language
English
Course Coordinator
Ergün Yaraneri
Course Objectives
1To provide an introduction to the study of properties of integers.
2To prepare students to graduatelevel courses in number theory and algebra.
3To demonstrate applications of number theory (such as publickey cryptography).
Course Description
Divisibility, Euclidean algorithm,prime numbers,congruences,Chinese remainder theorem,Fermat’s little
theorem,Euler’s theorem primitive roots,congruences with primepower moduli,Binomial theorem,algebraic
integers,quadratic residues,quadratic reciprocity,Jacobi and Legendre symbols,Euler’s function,Möbius inversion
formula,multiplicative functions,continued fractions,rational approximation,Diophantine equations,Pell’s equation.
Course Outcomes
I. Understand the concept and properties of divisibility. Know the definitions and properties of greatest common divisor and least common multiple.
II. Understand the Euclidean algorithm, can solve the linear diophantine equations and understand the concept of 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 nonlinear 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. Undertsand the representation of rational and real numbers by continued fractions.
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