MATH 402

Course Code & Number

MATH 402

Course Title

Number Theory

Level

BS

Credit Hours/ ECTS Credits

(3+0+0) 3 TEDU Credits, 6 ECTS Credits

Year of Study:

Senior

Semester:

Spring

Type of Course:

Compulsory

Mode of Delivery:

Face-to-face

Language of Instruction:

English

Pre-requisite / Co-requisite::

Catalog Description

The division algorithm. The greatest common divisor. The Euclidean algorithm. Diophantine equations. Primes and their distribution. The fundamental theorem of arithmetic. Congruences. Bases of number systems. Divisibility tests. Linear congruences. The Chinese remainder theorem. Fermat’s little theorem. Wilson’s theorem. Number-theoretic functions. Euler’s phi-function. Euler’s theorem. Primitive roots. Indices.

Course Objectives

This course aims to teach students the basic concepts and skills in elementary number theory. More specifically, the goal is to teach the fundamental theories of integer arithmetic and modular arithmetic and use these theories to solve various applied and theoretical problems in number theory.

Course Learning Outcomes

Upon successful completion of this course, students will be able to

1. Describe fundamental concepts of integer arithmetic such as the division algorithm, the greatest common divisor, the Euclidean algorithm, primes, and the fundamental theorem of arithmetic,
2. Acquire basic notions of modular arithmetic such as congruences, bases of number systems, divisibility tests, and the Chinese remainder theorem,
3. Recall Fermat’s little theorem, Wilson’s theorem, and Euler’s Theorem,
4. Recognize the number-theoretic functions such as the sum and the number of divisors of an integer, the Möbius function, the greatest integer function, and Euler’s phi-function,
5. Explain the notions of primitive roots and indices.

Course Coordinator:

Dr. Fuat Erdem