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- Undergraduate Courses Outlines
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|School||School of Science|
|Academic Unit||Department of Mathematics|
|Level of Studies||Undergraduate|
|Course Title||Number Theory|
|Independent Teaching Activities||Lectures (Weekly Teaching Hours: 4, Credits: 7.5)|
|Course Type||General Background|
|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.|
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.
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.
- Complex numbers.
- 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
|Use of Information and Communications Technology||
|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.