The program is divided in a part of basic mathematics, in which the first notions of number theory are introduced, and a part where these notions are applied to cryptography and to the theory of error correcting codes.
Concrete abstract algebra
Niels Lauritzen
Cambridge University Press (2003)
Coding Theory: A First Course
San Ling, Chaoping Xing
Cambridge University Press (2004)
Learning Objectives
This course is meant to provide methods and tools to work in a discrete context, together with an introduction to some applications. It is also aimed at introducing students to modern scientific litterature.
Prerequisites
Basic linear algebra
Teaching Methods
Lecturing at the blackboard, with the students active participation. Questions and comments welcomed.
Exercise sheets are distributed regularly.
Type of Assessment
Oral examination.
Course program
In more detail:
a) from the ring of integers mod n to Euler function and Euler theorem
b) a brief inroduction ot public key cryptography and the RSA algorithm
c) from rings of polynomials to finite fields
d) brief introduction to complexity theory
e) theory of error correcting codes: linear codes, cyclic codes and their decoding. Bounds.