General information

Module title Introduction to Number Theory
Language English
Module lecturer dr Stefan Barańczuk
Lecturer's email stefbar@amu.edu.pl
Lecturer position adiunkt
Faculty Faculty of Mathematics and Computer Science
Semester 2021/2022 (winter)
Duration 60
ECTS 6
USOS code 000

Timetable

Module aim (aims)

Students will be introduced to some of the basic results in Number Theory and their application to solving selected Diophantine equations and congruences and also to public key cryptography.

Pre-requisites in terms of knowledge, skills and social competences (where relevant)

Knowledge of some basic group theory is welcome, though not required.

Syllabus

Primes, Divisibility, the Fundamental Theorem of Arithmetic;Greatest Common Divisor, the extended Euclidean algorithm, modular multiplicative inverse;Congruences, Chinese Remainder Theorem, Euler's theorem, Wilson's theorem;Quadratic Residues and Reciprocity;Diophantine Equations;Sums of squares; Ring of Arithmetic Functions;Public key cryptography.

Reading list

Richard A. Mollin, "Fundamental Number Theory with Applications" (Second Edition) ;K. Ireland and M. Rosen, "A Classical Introduction to Modern Number Theory";MIT open course: https://ocw.mit.edu/courses/mathematics/18-781-theory-of-numbers-spring-2012/