Number Theory (MAY123)
 Ελληνική Έκδοση
 Undergraduate Courses Outlines
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 Department of Mathematics
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General
School  School of Science 

Academic Unit  Department of Mathematics 
Level of Studies  Undergraduate 
Course Code  MAY123 
Semester  1 
Course Title  Number Theory 
Independent Teaching Activities  Lectures (Weekly Teaching Hours: 4, Credits: 7.5) 
Course Type  General Background 
Prerequisite Courses   
Language of Instruction and Examinations  Greek, English 
Is the Course Offered to Erasmus Students  Yes (in English) 
Course Website (URL)  See eCourse, the Learning Management System maintained by the University of Ioannina. 
Learning Outcomes
Learning outcomes 
The main purpose of the course is the study of the structure and basic properties of natural numbers, and more generally of integers. This study is based on the fundamental concept of divisibility of integers, and the (unique) factorization of a natural number into prime factors.
We will formulate and prove several theorems concerning the structure of all integers through the concept of divisibility. During the course will analyse applications of Number Theory to other sciences, and particularly to Cryptography.


General Competences 
The course aims to enable the undergraduate student to acquire the ability to analyse and synthesize basic knowledge of the theory of numbers, to apply basic examples in other areas, and in particular to solve concrete problems concerning properties of numbers occurring in everyday life. The contact of the undergraduate student with the ideas and concepts of number theory, (a) promotes the creative, analytical and deductive thinking and the ability to work independently, (b) improves his critical thinking and his ability to apply abstract knowledge in various field. 
Syllabus
 Complex numbers.
 Divisibility.
 Congruences mod m.
 Chinese remainder theorem.
 Arithmetical functions and Moebius inversion formula.
 The theorems of Fermat, Euler and Wilson.
 Primitive roots mod p.
 The theory of indices and the Law of quadratic reciprocity.
 Applications to cryptography.
Teaching and Learning Methods  Evaluation
Delivery 
Classroom (facetoface)  

Use of Information and Communications Technology 
 
Teaching Methods 
 
Student Performance Evaluation 
Final written exam in Greek (in case of Erasmus students, in English) which includes analysis of theoretical topics and resolving application problems. 
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 