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Course Information

Course Name
Turkish Number Theory
English Number Theory
Course Code
MAT 448E Credit Lecture
Semester -
3 3 - -
Course Language English
Course Coordinator Ergün Yaraneri
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,congruences,Chinese remainder theorem,Fermat’s little
theorem,Euler’s theorem primitive roots,congruences with prime-power 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 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. Undertsand the representation of rational and real numbers by continued fractions.
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