TEORIA DEI NUMERI

Academic year and teacher
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Versione italiana
Academic year
2019/2020
Teacher
FILIPPO ALFREDO ELLIA
Credits
6
Didactic period
Secondo Semestre
SSD
MAT/02

Training objectives

The main goal of the course is to introduce the student to the main tools of ‘’elementary number theory’’ (main theorem of arithmetic, congruences, two squares theorem, quadratic reciprocity law). We will also introduce the student to the use of a computer in number theory. Finally if time is left we will make a brief incursion in algebraic number theory (quadratic fields).
At the end of the course the student will be able to solve standard problems in elementary number theory and will be prepared for a more advanced study of (algebraic or analytic) number theory.

Prerequisites

Courses of Geometria 1 (Linear algebra) and Algebra 1.

Course programme

Historical introduction. The fundamental theorem of arithmetic.Congruences. Introduction to Maple. Perfect numbers. The two squares theorem. The quadratic reciprocity law. Quadratic fields.
For further informations see http://dm.unife.it/philippe.ellia/Didattica.html

Didactic methods

Lectures and exercises (homework). Exercises will be corrected under the supervision of the teacher (this requires a STRONG ACTIVE PARTICIPATION from the students).

Learning assessment procedures

Oral examination. The participation to the correction of the exercises during the course will be taken into consideration for the final mark.

Reference texts

Notes by the teacher.